####***X####-^V3^-^P1^-^L1^-----<00> ###DEF1###-----<00> -----34Oroi ##1##-a41 S4ummetra meg4eqh l4egetai t6a t5wj a2ut5wj m4etrwj metro4umena, 2as4ummetra d4e, 35wn mhd6en 2end4exetai koin6on m4etron gen4esqai. ##2##-b41 E2uqe5iai dun4amei s4ummetro4i e2isin, 34otan t6a 2ap' a2ut5wn tetr4agwna t5wj a2ut5wj xwr4iwj metr5htai, 2as4ummetroi d4e, 34otan to5i@ 2ap' a2ut5wn tetrag4wnoi@ mhd6en 2end4exhtai xwr4ion koin6on m4etron gen4esqai. ##3##-g41 To4utwn 3upokeim4enwn de4iknutai, 34oti t5hj proteqe4ishj e2uqe4iaj 3up4arxousin e2uqe5iai pl4hqei 24apeiroi s4ummetro4i te ka6i 2as4ummetroi a3i m6en m4hkei m4onon, a3i d6e ka6i dun4amei. kale4isqw o25un 3h m6en proteqe5isa e2uqe5ia 3rht4h, ka6i a3i ta4uthj s4ummetroi e24ite m4hkei ka6i dun4amei e24ite dun4amei m4onon 3rhta4i, a3i d6e ta4uthj 2as4ummetroi 24alogoi kale4isqwsan. ##4##-d41 Ka6i t6o m6en 2ap6o t5h@ proteqe4ish@ e2uqe4ia@ tetr4agwnon ^+^ 3rht4on, ka6i t6a to4utwj s4ummetra 3rht4a, t6a d6e to4utwj 2as4ummetra 24aloga kale4isqw, ka6i a3i dun4amenai a2ut6a 24alogoi, e2i m6en tetr4agwna e24ih, a2uta6i a3i pleura4i, e2i d6e 34eter4a tina e2uq4ugramma, a3i 24isa a2uto5i@ tetr4agwna 2anagr4afousai. ###PROP###-----<00> -----a41 ##1##-D4uo megeq5wn 2an4iswn 2ekkeim4enwn, 2e6an 2ap6o to5u me4izono@ 2afaireq5hj me5izon 26h t6o 34hmisu ka6i to5u kataleipom4enou me5izon 26h t6o 34hmisu, ka6i to5uto 2ae6i g4ignhtai, leifq4hseta4i ti m4egeqo@, 36o 24estai 24elasson to5u 2ekkeim4enou 2el4assono@ me* g4eqou@. -24Estw d4uo meg4eqh 24anisa t6a AB, G, 35wn me5izon t6o AB: l4egw, 34oti, 2e6an 2ap6o to5u AB 2afaireq5hj me5izon 26h t6o 34hmisu ka6i to5u kataleipom4enou me5izon 26h t6o 34hmisu, ka6i to5uto 2ae6i g4ignhtai, leifq4hseta4i ti m4egeqo@, 36o 24estai 24elasson to5u G meg4eqou@. -T6o G g6ar pollaplasiaz4omenon 24estai pot6e to5u AB me5izon. pepollaplasi4asqw, ka6i 24estw t6o DE to5u m6en G pollapl4asion, to5u d6e AB me5izon, ka6i dihjr4hsqw t6o DE e2i@ t6a t5wj G 24isa t6a DZ, ZH, HE, ka6i 2afhjr4hsqw 2ap6o m6en to5u AB me5izon 26h t6o 34hmisu t6o BQ, 2ap6o d6e to5u AQ ^+^ me5izon 26h t6o 34hmisu t6o QK, ka6i to5uto 2ae6i gign4esqw, 34ew@ 26an a3i 2en t5wj AB diair4esei@ 2isoplhqe5i@ g4enwntai ta5i@ 2en t5wj DE diair4esesin. 24Estwsan o25un a3i AK, KQ, QB diair4esei@ 2isoplhqe5i@ o25usai ta5i@ DZ, AH, HE: ka6i 2epe6i me5iz4on 2esti t6o DE to5u AB, ka6i 2af4hjrhtai 2ap6o m6en to5u DE 24elasson to5u 3hm4iseo@ t6o EH, 2ap6o d6e to5u AB me5izon 26h t6o 34hmisu t6o BQ, loip6on 24ara t6o HD loipo5u to5u QA me5iz4on 2estin. ka6i 2epe6i me5iz4on 2esti t6o HD to5u QA, ka6i 2af4hjrhtai to5u m6en HD 34hmisu t6o HZ, to5u d6e QA me5izon 26h t6o 34hmisu t6o QK, loip6on 24ara t6o DZ loipo5u to5u AK me5iz4on 2estin. 24ison d6e t6o DZ t5wj G: ka6i t6o G 24ara to5u AK me5iz4on 2estin. 24elasson 24ara t6o AK to5u G. -Katale4ipetai 24ara 2ap6o to5u AB meg4eqou@ t6o AK m4egeqo@ 24elasson 26on to5u 2ekkeim4enou 2el4assono@ meg4eqou@ to5u G: 34oper 24edei de5icai.--3omo4iw@ d6e deixq4hsetai, k26an ^-^ 3hm4ish 25hj t6a 2afairo4umena. $-^P211^ <3<####BFV&####-----<00> ###10AP### <00> ##1ALT##-----24Allw@ t6o a41 qe4wrhma -2Ekke4isqw d4uo meg4eqh 24anisa t6a AB, G: ka6i 2epe6i 24elass4on 2esti t6o G, pollaplasiaz4omenon 24estai pot6e to5u AB meg4eqou@ me5izon. gegon4etw 3w@ t6o ZM ka6i dihjr4hsqw e2i@ <22> 24isa t5wj G, ka6i 24estw t6a MQ, QH, HZ, ka6i 2ap6o to5u AB 2afhjr4hsqw me5izon 26h t6o 34hmisu t6o BE, ka6i 2ap6o to5u EA me5izon 26h t6o 34hmisu t6o ED, ka6i to5uto 2ae6i gin4esqw, 34ew@ a3i 2en t5wj ZM diair4esei@ 24isai g4enwntai ta5i@ 2en t5wj AB diair4esesin. gegon4etwsan 3w@ a3i BE, ED, DA, ka6i t5wj DA 34ekaston t5wn KL, LN, NC 24estw 24ison, ka6i to5uto gin4esqw, 34ew@ a3i diair4esei@ to5u KC 24isai g4enwntai ta5i@ to5u ZM. -Ka6i 2epe6i t6o BE me5izon 26h t6o 34hmis4u 2esti to5u BA, ^+^ t6o BE me5iz4on 2esti to5u EA: poll5wj 24ara me5iz4on 2esti to5u DA. 2all6a t6o DA 24ison 2est6i t5wj CN: t6o BE 24ara me5iz4on 2esti to5u NC. p4alin, 2epe6i t6o ED me5izon 26h t6o 34hmis4u 2esti to5u EA, me5iz4on 2esti to5u DA. 2all6a t6o DA 2estin 24ison t5wj NL: t6o ED 24ara me5iz4on 2esti to5u NL. 34olon 24ara t6o DB me5iz4on 2esti to5u CL. 24ison d6e t6o DA t5wj LK. 34olon 24ara t6o BA me5iz4on 2esti to5u CK. 2all6a to5u BA me5iz4on 2esti t6o MZ: poll5wj 24ara t6o MZ me5iz4on 2esti to5u CK. ka6i 2epe6i t6a CN, NL, LK 24isa 2all4hloi@ 2est4in, 24esti d6e ka6i t6a MQ, QH, HZ 24isa 2all4hloi@, ka4i 2estin 24ison t6o pl5hqo@ t5wn 2en t5wj MZ t5wj pl4hqei t5wn 2en t5wj CK, 24estin 24ara 3w@ t6o KL pr6o@ t6o ZH, o34utw@ t6o KC pr6o@ t6o ZM. me5izon d6e t6o ZM to5u KC: me5izon 24ara ka6i t6o HZ to5u LK. ka4i 2esti t6o m6en ZH 24ison t5wj G, t6o d6e KL t5wj AD: t6o G 24ara me5iz4on 2esti to5u AD: 34oper 24edei de5icai.>3> $-^P3^-^L18^ ####***X#### ###PROP### ##2##-------b41 -2E6an d4uo megeq5wn <2<2ekkeim4enwn>2> 2an4iswn 2anqufairoum4enou 2ae6i to5u 2el4assono@ 2ap6o to5u me4izono@ t6o kataleip4omenon mhd4epote katametr5hj t6o pr6o 3eauto5u, 2as4ummetra 24estai t6a meg4eqh. -D4uo g6ar megeq5wn 24ontwn 2an4iswn t5wn AB, GD ka6i 2el4assono@ to5u AB 2anqufairoum4enou 2ae6i to5u 2el4assono@ 2ap6o to5u me4izono@ t6o perileip4omenon mhd4epote katametre4itw ^+^ t6o pr6o 3eauto5u: l4egw, 34oti 2as4ummetr4a 2esti t6a AB, GD meg4eqh. -E2i g4ar 2esti s4ummetra, metr4hsei ti a2ut6a m4egeqo@. metre4itw, e2i dunat4on, ka6i 24estw t6o E: ka6i t6o m6en AB t6o ZD katametro5un leip4etw 3eauto5u 24elasson t6o GZ, t6o d6e GZ t6o BH katametro5un leip4etw 3eauto5u 24elasson t6o AH, ka6i to5uto 2ae6i gin4esqw, 34ew@ o35u leifq5hj ti m4egeqo@, 34o 2estin 24elasson to5u E. gegon4etw, ka6i lele4ifqw t6o AH 24elasson to5u E. 2epe6i o25un t6o E t6o AB metre5i, 2all6a t6o AB t6o DZ metre5i, ka6i t6o E 24ara t6o ZD metr4hsei. metre5i d6e ka6i 34olon t6o GD: ka6i loip6on 24ara t6o GZ metr4hsei. 2all6a t6o GZ t6o BH metre5i: ka6i t6o E 24ara t6o BH metre5i. metre5i d6e ka6i 34olon t6o AB: ka6i loip6on 24ara t6o AH metr4hsei, t6o me5izon t6o 24elasson. 34oper 2est6in 2ad4unaton. o2uk 24ara t6a AB, GD meg4eqh metr4hsei ti m4egeqo@: 2as4ummetra 24ara 2est6i t6a AB, GD meg4eqh. -2E6an 24ara d4uo megeq5wn 2an4iswn, ka6i t6a 3ec5h@. ##3##-------g41 -D4uo megeq5wn summ4etrwn doq4entwn t6o m4egiston a2ut5wn koin6on m4etron e3ure5in. ^+^ -24Estw t6a doq4enta d4uo meg4eqh s4ummetra t6a AB, GD, 35wn 24elasson t6o AB: de5i d6h t5wn AB, GD t6o m4egiston koin6on m4etron e3ure5in. -T6o AB g6ar m4egeqo@ 24htoi metre5i t6o GD 26h o24u. e2i m6en o25un metre5i, metre5i d6e ka6i 3eaut4o, t6o AB 24ara t5wn AB, GD koin6on m4etron 2est4in: ka6i faner4on, 34oti ka6i m4egiston. me5izon g6ar to5u AB meg4eqou@ t6o AB o2u metr4hsei. -M6h metre4itw d6h t6o AB t6o GD. ka6i 2anqufairoum4enou 2ae6i to5u 2el4assono@ 2ap6o to5u me4izono@, t6o perileip4omenon metr4hsei pot6e t6o pr6o 3eauto5u di6a t6o m6h e25inai 2as4ummetra t6a AB, GD: ka6i t6o m6en AB t6o ED katametro5un leip4etw 3eauto5u 24elasson t6o EG, t6o d6e EG t6o ZB katametro5un leip4etw 3eauto5u 24elasson t6o AZ, t6o d6e AZ t6o GE metre4itw. -2Epe6i o25un t6o AZ t6o GE metre5i, 2all6a t6o GE t6o ZB metre5i, ka6i t6o AZ 24ara t6o ZB metr4hsei. metre5i d6e ka6i 3eaut4o: ka6i 34olon 24ara t6o AB metr4hsei t6o AZ. 2all6a t6o AB t6o DE metre5i: ka6i t6o AZ 24ara t6o ED metr4hsei. metre5i d6e ka6i t6o GE: ka6i 34olon 24ara t6o GD metre5i: t6o AZ 24ara t5wn AB, GD koin6on m4etron 2est4in. l4egw d4h, 34oti ka6i m4egiston. e2i g6ar m4h, 24estai ti m4egeqo@ me5izon to5u AZ, 36o ^+^ metr4hsei t6a AB, GD. 24estw t6o H. 2epe6i o25un t6o H t6o AB metre5i, 2all6a t6o AB t6o ED metre5i, ka6i t6o H 24ara t6o ED metr4hsei. metre5i d6e ka6i 34olon t6o GD: ka6i loip6on 24ara t6o GE metr4hsei t6o H. 2all6a t6o GE t6o ZB metre5i: ka6i t6o H 24ara t6o ZB metr4hsei. metre5i d6e ka6i 34olon t6o AB, ka6i loip6on t6o AZ metr4hsei, t6o me5izon t6o 24elasson: 34oper 2est6in 2ad4unaton. o2uk 24ara me5iz4on ti m4egeqo@ to5u AZ t6a AB, GD metr4hsei: t6o AZ 24ara t5wn AB, GD t6o m4egiston koin6on m4etron 2est4in. -D4uo 24ara megeq5wn summ4etrwn doq4entwn t5wn AB, GD t6o m4egiston koin6on m4etron h34urhtai. 34oper 24edei de5icai. ##3^1^Por^2##-----P4orisma -2Ek d6h to4utou faner4on, 34oti, 2e6an m4egeqo@ d4uo meg4eqh metr5hj, ka6i t6o m4egiston a2ut5wn koin6on m4etron metr4hsei. ##4##-------d41 -Tri5wn megeq5wn summ4etrwn doq4entwn t6o m4egiston a2ut5wn koin6on m4etron e3ure5in. -24Estw t6a doq4enta tr4ia meg4eqh s4ummetra t6a A, B, G: de5i d6h t5wn A, B, G t6o m4egiston koin6on m4etron e3ure5in. -E2il4hfqw g6ar d4uo t5wn A, B t6o m4egiston koin6on m4etron, ka6i 24estw t6o D: t6o d6h D t6o G 24htoi metre5i 26h o2u ^-^ <22>. metre4itw pr4oteron. 2epe6i o25un t6o D t6o G metre5i, metre5i d6e ^+^ ka6i t6a A, B, t6o D 24ara t6a A, B, G metre5i: t6o D 24ara t5wn A, B, G koin6on m4etron 2est4in. ka6i faner4on, 34oti ka6i m4egiston: me5izon g6ar to5u D meg4eqou@ t6a A, B o2u metre5i -M6h metre4itw d6h t6o D t6o G. l4egw pr5wton, 34oti s4ummetr4a 2esti t6a G, D. 2epe6i g6ar s4ummetr4a 2esti t6a A, B, G, metr4hsei ti a2ut6a m4egeqo@, 36o dhlad6h ka6i t6a A, B metr4hsei: 34wste ka6i t6o t5wn, A, B m4egiston koin6on m4etron t6o D metr4hsei. metre5i d6e ka6i t6o G: 34wste t6o e2irhm4enon m4egeqo@ metr4hsei t6a G, D: s4ummetra 24ara 2est6i t6a G, D. e2il4hfqw o25un a2ut5wn t6o m4egiston koin6on m4etron, ka6i 24estw t6o E. 2epe6i o25un t6o E t6o D metre5i, 2all6a t6o D t6a A, B metre5i, ka6i t6o E 24ara t6a A, B metr4hsei. metre5i d6e ka6i t6o G. t6o E 24ara t6a A, B, G metre5i: t6o E 24ara t5wn A, B, G koin4on 2esti m4etron. l4egw d4h, 34oti ka6i m4egiston. e2i g6ar dunat4on, 24estw ti to5u E ^-^ me5izon m4egeqo@ t6o Z, ka6i metre4itw t6a A, B, G. ka6i 2epe6i t6o Z t6a A, B, G metre5i, ka6i t6a A, B 24ara metr4hsei ka6i t6o t5wn A, B m4egiston koin6on m4etron metr4hsei. t6o d6e t5wn A, B m4egiston koin6on m4etron 2est6i t6o D: t6o Z 24ara t6o D metre5i. metre5i d6e ka6i t6o G: t6o Z 24ara t6a G, D metre5i: ka6i t6o t5wn ^+^ G, D 24ara m4egiston koin6on m4etron metr4hsei t6o Z. 24esti d6e t6o E: t6o Z 24ara t6o E metr4hsei, t6o me5izon t6o 24elasson: 34oper 2est6in 2ad4unaton. o2uk 24ara me5iz4on ti to5u E meg4eqou@ <22> t6a A, B, G metre5i: t6o E 24ara t5wn A, B, G t6o m4egiston koin6on m4etron 2est4in, 2e6an m6h metr5hj t6o D t6o G, 2e6an d6e metr5hj, a2ut6o t6o D. -Tri5wn 24ara megeq5wn summ4etrwn doq4entwn t6o m4egiston koin6on m4etron h34urhtai <2<34oper 24edei de5icai>2>. ##4^1^Por^2##-----P4orisma -2Ek d6h to4utou faner4on, 34oti, 2e6an m4egeqo@ tr4ia meg4eqh metr5hj, ka6i t6o m4egiston a2ut5wn koin6on m4etron metr4hsei. -3Omo4iw@ d6h ka6i 2ep6i plei4onwn t6o m4egiston koin6on m4etron lhfq4hsetai, ka6i t6o p4orisma proxwr5hsei. 34oper 24edei ^-^ de5icai. ##5##-------e41 -T6a s4ummetra meg4eqh pr6o@ 24allhla l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. -24Estw s4ummetra meg4eqh t6a A, B: l4egw, 34oti t6o A pr6o@ t6o B l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. -2Epe6i g6ar s4ummetr4a 2esti t6a A, B, metr4hsei ti a2ut6a m4egeqo@. metre4itw, ka6i 24estw t6o G. ka6i 3os4aki@ t6o G t6o A metre5i tosa5utai mon4ade@ 24estwsan 2en t5wj D, 3os4aki@ d6e t6o G t6o B metre5i, tosa5utai mon4ade@ 24estwsan 2en t5wj E. ^+^ -2Epe6i o25un t6o G t6o A metre5i kat6a t6a@ 2en t5wj D mon4ada@, metre5i d6e ka6i 3h mon6a@ t6on D kat6a t6a@ 2en a2ut5wj mon4ada@, 2is4aki@ 24ara 3h mon6a@ t6on D metre5i 2ariqm6on ka6i t6o G m4egeqo@ t6o A: 24estin 24ara 3w@ t6o G pr6o@ t6o A, o34utw@ 3h mon6a@ pr6o@ t6on D: 2an4apalin 24ara 3w@ t6o A pr6o@ t6o G, o34utw@ 3o D pr6o@ t6hn mon4ada. p4alin 2epe6i t6o G t6o B metre5i kat6a t6a@ 2en t5wj E mon4ada@, metre5i d6e ka6i 3h mon4a@ t6on E kat6a t6a@ 2en a2ut5wj mon4ada@, 2is4aki@ 24ara 3h mon6a@ t6on E metre5i ka6i t6o G t6o B: 24estin 24ara 3w@ t6o G pr6o@ t6o B, o34utw@ 3h mon6a@ pr6o@ t6on E. 2ede4ixqh d6e ka6i 3w@ t6o A pr6o@ t6o G, 3o D pr6o@ t6hn mon4ada: di' 24isou 24ara 2est6in 3w@ t6o A pr6o@ t6o B, o34utw@ 3o D 2ariqm6o@ pr6o@ t6on E. -T6a 24ara s4ummetra meg4eqh t6a A, B pr6o@ 24allhla l4ogon 24exei 36on 2ariqm6o@ 3o D pr6o@ 2ariqm6on t6on E: 34oper 24edei de5icai. ##6##-------st41 -2E6an d4uo meg4eqh pr6o@ 24allhla l4ogon 24exhj, 36on 2ariqm6o@ pr6o@ 2ariqm4on, s4ummetra 24estai t6a meg4eqh. -D4uo g6ar meg4eqh t6a A, B pr6o@ 24allhla l4ogon 2ex4etw, 36on 2ariqm6o@ 3o D pr6o@ 2ariqm6on t6on E: l4egw, 34oti s4ummetr4a 2esti t6a A, B meg4eqh. ^+^ -34Osai g4ar e2isin 2en t5wj D mon4ade@, e2i@ tosa5uta 24isa dihjr4hsqw t6o A, ka6i 3en6i a2ut5wn 24ison 24estw t6o G: 34osai d4e e2isin 2en t5wj E mon4ade@, 2ek toso4utwn megeq5wn 24iswn t5wj G sugke4isqw t6o Z. -2Epe6i o25un, 34osai e2is6in 2en t5wj D mon4ade@, tosa5ut4a e2isi ka6i 2en t5wj A meg4eqh 24isa t5wj G, 36o 24ara m4ero@ 2est6in 3h mon6a@ to5u D, t6o a2ut6o m4ero@ 2est6i ka6i t6o G to5u A: 24estin 24ara 3w@ t6o G pr6o@ t6o A, o34utw@ 3h mon6a@ pr6o@ t6on D. metre5i d6e 3h mon6a@ t6on D 2ariqm4on: metre5i 24ara ka6i t6o G t6o A. ka6i 2epe4i 2estin 3w@ t6o G pr6o@ t6o A, o34utw@ 3h mon6a@ pr6o@ t6on D <2<2ariqm4on>2>, 2an4apalin 24ara 3w@ t6o A pr6o@ t6o G, o34utw@ 3o D 2ariqm6o@ pr6o@ t6hn mon4ada. p4alin 2epe4i, 34osai e2is6in 2en t5wj E mon4ade@, tosa5ut4a e2isi ka6i 2en t5wj Z 24isa t5wj G, 24estin 24ara 3w@ t6o G pr6o@ t6o Z, o34utw@ 3h mon6a@ pr6o@ t6on E <2<2ariqm4on>2>. 2ede4ixqh d6e ka6i 3w@ t6o A pr6o@ t6o G, o34utw@ 3o D pr6o@ t6hn mon4ada: di' 24isou 24ara 2est6in 3w@ t6o A pr6o@ t6o Z, o34utw@ 3o D pr6o@ t6on E. 2all' 3w@ 3o D pr6o@ t6on E, o34utw@ 2est6i t6o A pr6o@ t6o B: ka6i 3w@ 24ara t6o A pr6o@ t6o B, o34utw@ ka6i pr6o@ t6o Z. t6o A 24ara pr6o@ 3ek4ateron t5wn B, Z t6on a2ut6on 24exei l4ogon: 24ison 24ara 2est6i t6o B t5wj Z. metre5i d6e t6o G t6o Z: ^+^ metre5i 24ara ka6i t6o B. 2all6a m6hn ka6i t6o A: t6o G 24ara t6a A, B metre5i. s4ummetron 24ara 2est6i t6o A t5wj B. -2E6an 24ara d4uo meg4eqh pr6o@ 24allhla, ka6i t6a 3ec5h@. ##6^1^Por^2##-----P4orisma -2Ek d6h to4utou faner4on, 34oti, 2e6an 25wsi d4uo 2ariqmo4i, 3w@ o3i D, E, ka6i e2uqe5ia, 3w@ 3h A, d4unat4on 2esti poi5hsai 3w@ 3o D 2ariqm6o@ pr6o@ t6on E 2ariqm4on, o34utw@ t6hn e2uqe5ian pr6o@ e2uqe5ian. 2e6an d6e ka6i t5wn A, Z m4esh 2an4alogon lhfq5hj, 3w@ 3h B, 24estai 3w@ 3h A pr6o@ t6hn Z, o34utw@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ B, tout4estin 3w@ 3h pr4wth pr6o@ t6hn tr4ithn, o34utw@ t6o 2ap6o t5h@ pr4wth@ pr6o@ t6o 2ap6o t5h@ deut4era@ t6o 34omoion ka6i 3omo4iw@ 2anagraf4omenon. 2all' 3w@ 3h A pr6o@ t6hn Z, o34utw@ 2est6in 3o D 2ariqm6o@ pr6o@ t6on E 2ariqm4on: g4egonen 24ara ka6i 3w@ 3o D 2ariqm6o@ pr6o@ t6on E 2ariqm4on, o34utw@ t6o 2ap6o t5h@ A e2uqe4ia@ pr6o@ t6o 2ap6o t5h@ B e2uqe4ia@: 34oper 24edei de5icai. $-^P212^-^L16^ <3<####BFV&####-----<00> ###10AP### ##6ALT## <00> -----24Allw@ t6o st41 -D4uo g6ar meg4eqh t6a A, B pr6o@ 24allhla l4ogon 2ex4etw, 36on 2ariqm6o@ 3o G pr6o@ 2ariqm6on t6on D: l4egw, 34oti s4ummetr4a 2esti t6a meg4eqh. ^+^ -34Osai g4ar e2isin 2en t5wj G mon4ade@, e2i@ tosa5uta 24isa dihjr4hsqw t6o A, ka6i 3en6i a2ut5wn 24ison 24estw t6o E: 24estin 24ara 3w@ 3h mon6a@ pr6o@ t6on G 2ariqm4on, t6o E pr6o@ t6o A. 24esti d6e ka6i 3w@ 3o G pr6o@ t6on D, t6o A pr6o@ t6o B: di' 24isou 24ara 2est6in 3w@ 3h mon6a@ pr6o@ t6on D, t6o E pr6o@ t6o B. metre5i d6e ka6i 3h mon6a@ t6on D: metre5i 24ara ka6i t6o E t6o B. metre5i d6e ka6i t6o E t6o A, 2epe6i ka6i 3h mon6a@ t6on G: t6o E 24ara 3ek4ateron t5wn A, B metre5i: t6a A, B 24ara s4ummetr4a 2estin, ka4i 2estin a2ut5wn koin6on m4etron t6o E: 34oper 24edei de5icai.>3> $-^P11^-^L17^ ####***X#### ###PROP### ##7##-------z41 -T6a 2as4ummetra meg4eqh pr6o@ 24allhla l4ogon o2uk 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. ^+^ -24Estw 2as4ummetra meg4eqh t6a A, B: l4egw, 34oti t6o A pr6o@ t6o B l4ogon o2uk 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. -E2i g6ar 24exei t6o A pr6o@ t6o B l4ogon, 36on 2ariqm6o@ pr6o@ 2ariqm4on, s4ummetron 24estai t6o A t5wj B. o2uk 24esti d4e: o2uk 24ara t6o A pr6o@ t6o B l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. -T6a 24ara 2as4ummetra meg4eqh pr6o@ 24allhla l4ogon o2uk 24exei, ka6i t6a 3ec5h@. ##8##-------h41 -2E6an d4uo meg4eqh pr6o@ 24allhla l4ogon m6h 24exhj, 36on 2ariqm6o@ pr6o@ 2ariqm4on, 2as4ummetra 24estai t6a meg4eqh. -D4uo g6ar meg4eqh t6a A, B pr6o@ 24allhla l4ogon m6h 2ex4etw, 36on 2ariqm6o@ pr6o@ 2ariqm4on: l4egw, 34oti 2as4ummetr4a 2esti t6a A, B meg4eqh. -E2i g6ar 24estai s4ummetra, t6o A pr6o@ t6o B l4ogon 34ecei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. o2uk 24exei d6e. 2as4ummetra 24ara 2est6i t6a A, B meg4eqh. -2E6an 24ara d4uo meg4eqh pr6o@ 24allhla, ka6i t6a 3ec5h@. ##9##-------q41 -T6a 2ap6o t5wn m4hkei summ4etrwn e2uqei5wn tetr4agwna pr6o@ 24allhla l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon ^+^ 2ariqm4on: ka6i t6a tetr4agwna t6a pr6o@ 24allhla l4ogon 24exonta, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, ka6i t6a@ pleur6a@ 34ecei m4hkei summ4etrou@: t6a d6e 2ap6o t5wn m4hkei 2asumm4etrwn e2uqei5wn tetr4agwna pr6o@ 24allhla l4ogon o2uk 24exei, 34onper tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i t6a tetr4agwna t6a pr6o@ 24allhla l4ogon m6h 24exonta, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6a@ pleur6a@ 34ecei m4hkei summ4etrou@. -24Estwsan g6ar a3i A, B m4hkei s4ummetroi: l4egw, 34oti ^-^ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B tetr4agwnon l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. -2Epe6i g6ar s4ummetr4o@ 2estin 3h A t5hj B m4hkei, 3h A 24ara pr6o@ t6hn B l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. 2ex4etw, 36on 3o G pr6o@ t6on D. 2epe6i o25un 2estin 3w@ 3h A pr6o@ t6hn B, o34utw@ 3o G pr6o@ t6on D, 2all6a to5u m6en t5h@ A pr6o@ t6hn B l4ogou diplas4iwn 2est6in 3o to5u 2ap6o t5h@ A tetrag4wnou pr6o@ t6o 2ap6o t5h@ B tetr4agwnon: t6a g6ar 34omoia sx4hmata 2en diplas4ioni l4ogwj 2est6i t5wn 3omol4ogwn pleur5wn: to5u d6e to5u G <2<2ariqmo5u>2> pr6o@ t6on D <2<2ariqm6on>2> l4ogou diplas4iwn 2est6in 3o to5u 2ap6o to5u G tetrag4wnou pr6o@ t6on 2ap6o to5u D tetr4agwnon: d4uo g6ar tetrag4wnwn 2ariqm5wn e35i@ m4eso@ ^+^ 2an4alog4on 2estin 2ariqm4o@, ka6i 3o tetr4agwno@ pr6o@ t6on tetr4agwnon <2<2ariqm6on>2> diplas4iona l4ogon 24exei, 24hper 3h pleur6a pr6o@ t6hn pleur4an: 24estin 24ara ka6i 3w@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B tetr4agwnon, o34utw@ 3o 2ap6o to5u G tetr4agwno@ <2<2ariqm6o@>2> pr6o@ t6on 2ap6o to5u D <2<2ariqmo5u>2> tetr4agwnon <2<2ariqm4on>2>. -2All6a d6h 24estw 3w@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B, o34utw@ 3o 2ap6o to5u G tetr4agwno@ pr6o@ t6on 2ap6o to5u D <22>: l4egw, 34oti s4ummetr4o@ 2estin 3h A ^-^ t5hj B m4hkei. -2Epe6i g4ar 2estin 3w@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B <22>, o34utw@ 3o 2ap6o to5u G tetr4agwno@ pr6o@ t6on 2ap6o to5u D <22>, 2all' 3o m6en to5u 2ap6o t5h@ A tetrag4wnou pr6o@ t6o 2ap6o t5h@ B <22> l4ogo@ diplas4iwn 2est6i to5u t5h@ A pr6o@ t6hn B l4ogou, 3o d6e to5u 2ap6o to5u G <2<2ariqmo5u>2> tetrag4wnou <2<2ariqmo5u>2> pr6o@ t6on 2ap6o to5u D <2<2ariqmo5u>2> tetr4agwnon <2<2ariqm6on>2> l4ogo@ diplas4iwn 2est6i to5u to5u G <2<2ariqmo5u>2> pr6o@ t6on D <2<2ariqm6on>2> l4ogou, 24estin 24ara ka6i 3w@ 3h A pr6o@ t6hn B, o34utw@ 3o G <2<2ariqm6o@>2> pr6o@ t6on D <2<2ariqm4on>2>. 3h A 24ara pr6o@ t6hn B, l4ogon 24exei, 36on 2ariqm6o@ 3o G pr6o@ 2ariqm6on t6on D: s4ummetro@ 24ara 2est6in 3h A t5hj B m4hkei. -2All6a d6h 2as4ummetro@ 24estw 3h A t5hj B m4hkei: ^-^ l4egw, 34oti t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B <22> l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. ^+^ -E2i g6ar 24exei t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B <22> l4ogon, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, s4ummetro@ 24estai 3h A t5hj B. o2uk 24esti d4e: o2uk 24ara t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B <22> l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. -P4alin d6h t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ B <22> l4ogon m6h 2ex4etw, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 34oti 2as4ummetr4o@ 2estin 3h A t5hj B m4hkei. -E2i g4ar 2esti s4ummetro@ 3h A t5hj B, 34ecei t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ B l4ogon, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. o2uk 24exei d4e: o2uk 24ara s4ummetr4o@ 2estin 3h A t5hj B m4hkei. -T6a 24ara 2ap6o t5wn m4hkei summ4etrwn, ka6i t6a 3ec5h@. ##9^1^Por^2##-----P4orisma -Ka6i faner6on 2ek t5wn dedeigm4enwn 24estai, 34oti a3i m4hkei s4ummetroi p4antw@ ka6i dun4amei, a3i d6e dun4amei o2u p4antw@ ka6i m4hkei <22> ^+^ <22> ^+^ <22>. ##10^1^L^2##-----L5hmma -D4edeiktai 2en to5i@ 2ariqmhtiko5i@, 34oti o3i 34omoioi 2ep4ipedoi 2ariqmo6i pr6o@ 2all4hlou@ l4ogon 24exousin, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, ka6i 34oti, 2e6an d4uo 2ariqmo6i pr6o@ 2all4hlou@ l4ogon 24exwsin, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, 34omoio4i e2isin 2ep4ipedoi. ka6i d5hlon 2ek to4utwn, 34oti o3i m6h 34omoioi 2ep4ipedoi 2ariqmo4i, tout4estin o3i m6h 2an4alogon 24exonte@ t6a@ pleur4a@, pr6o@ 2all4hlou@ l4ogon o2uk 24exousin, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. e2i g6ar 34ecousin, 34omoioi 2ep4ipedoi 24esontai: 34oper o2ux 3up4okeitai. o3i 24ara m6h 34omoioi 2ep4ipedoi pr6o@ 2all4hlou@ l4ogon o2uk 24exousin, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. $-^P213^-^L9^ <3<####BFV&####-----<00> ###10AP### ##9ALT## <00> -----24Allw@ t6o q41 -2Epe6i g6ar s4ummetr4o@ 2estin 3h A t5hj B, l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. 2ex4etw, 36on 3o G pr6o@ t6on D, ka6i 3o G 3eaut6on m6en pollaplasi4asa@ t6on E poie4itw, 3o d6e G t6on D pollaplasi4asa@ t6on Z poie4itw, 3o d6e D 3eaut6on ^+^ pollaplasi4asa@ t6on H poie4itw. 2epe6i o25un 3o G 3eaut6on m6en pollaplasi4asa@ t6on E pepo4ihken, t6on d6e D pollaplasi4asa@ t6on Z pepo4ihken, 24estin 24ara 3w@ 3o G pr6o@ t6on D, tout4estin 3w@ 3h A pr6o@ t6hn B, <22> 3o E pr6o@ t6on Z. 2all' 3w@ 3h A pr6o@ t6hn B, o34utw@ t6o 2ap6o t5h@ A pr6o@ t6o 3up6o t5wn A, B: 24estin 24ara 3w@ t6o 2ap6o t5h@ A pr6o@ t6o 3up6o t5wn A, B, o34utw@ 3o E pr6o@ t6on Z. p4alin, 2epe6i 3o D 3eaut6on pollaplasi4asa@ t6on H pepo4ihken, 3o d6e G t6on D pollaplasi4asa@ t6on Z pepo4ihken, 24estin 24ara 3w@ 3o G pr6o@ t6on D, tout4estin 3w@ 3h A pr6o@ t6hn B, o34utw@ 3o Z pr6o@ t6on H. 2all' 3w@ 3h A pr6o@ t6hn B, o34utw@ t6o 3up6o t5wn A, B pr6o@ t6o 2ap6o t5h@ B: 24estin 24ara 3w@ t6o 3up6o t5wn A, B pr6o@ t6o 2ap6o t5h@ B, o34utw@ 3o Z pr6o@ t6on H. 2all' 3w@ t6o 2ap6o t5h@ A pr6o@ t6o 3up6o t5wn A, B, o34utw@ 25hn 3o E pr6o@ t6on Z: di' 24ison 24ara 3w@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ B, o34utw@ 3o E pr6o@ t6on H. 24esti d6e 3ek4atero@ t5wn E, H tetr4agwno@: 3o m6en g6ar E 2ap6o to5u G 2estin, 3o d6e H 2ap6o to5u D: t6o 2ap6o t5h@ A 24ara pr6o@ t6o 2ap6o t5h@ B l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. 34oper 24edei de5icai. -2All6a d6h 2ex4etw t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ B l4ogon, 36on tetr4agwno@ 2ariqm6o@ 3o E pr6o@ tetr4agwnon 2ariqm6on t6on H: l4egw, 34oti s4ummetr4o@ 2estin 3h A t5hj B. -24Estw g6ar to5u m6en E pleur6a 3o G, to5u d6e H 3o D, ka6i ^+^ 3o G t6on D pollaplasi4asa@ t6on Z poie4itw: o3i E, Z, H 24ara 3ec5h@ e2isin 2an4alogon 2en t5wj to5u G pr6o@ t6on D l4ogwj. ka6i 2epe6i t5wn 2ap6o t5wn A, B m4eson 2an4alog4on 2esti t6o 3up6o t5wn A, B, t5wn d6e E, H 3o Z, 24estin 24ara 3w@ t6o 2ap6o t5h@ A pr6o@ t6o 3up6o t5wn A, B, o34utw@ 3o E pr6o@ t6on Z. 3w@ d6e t6o 3up6o t5wn A, B pr6o@ t6o 2ap6o t5h@ B, o34utw@ 3o Z pr6o@ t6on H, 2all' 3w@ t6o 2ap6o t5h@ A pr6o@ t6o 3up6o t5wn A, B, o34utw@ 3h A pr6o@ t6hn B. a3i A, B 24ara s4ummetro4i e2isin: l4ogon g6ar 24exousin, 36on 2ariqm6o@ 3o E pr6o@ 2ariqm6on t6on Z, tout4estin 36on 3o G pr6o@ t6on D: 3w@ g6ar 3o G pr6o@ t6on D, 3o E pr6o@ t6on Z: 3o g6ar G 3eaut6on m6en pollaplasi4asa@ t6on E pepo4ihken, t6on d6e D pollaplasi4asa@ t6on Z pepo4ihken: 24estin 24ara 3w@ 3o G pr6o@ t6on D, 3o E pr6o@ t6on Z.>3> $-^P17^-^L16^ ####***X#### ###PROP### ##10##-------i41 -T5hj proteqe4ishj e2uqe4iaj proseure5in d4uo e2uqe4ia@ 2asumm4etrou@, t6hn m6en m4hkei m4onon, t6hn d6e ka6i dun4amei. -24Estw 3h proteqe5isa e2uqe5ia 3h A: de5i d6h t5hj A ^-^ proseure5in d4uo e2uqe4ia@ 2asumm4etrou@, t6hn m6en m4hkei m4onon, t6hn d6e ka6i dun4amei. ^+^ -2Ekke4isqwsan g6ar d4uo 2ariqmo6i o3i B, G pr6o@ 2all4hlou@ l4ogon m6h 24exonte@, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, tout4esti m6h 34omoioi 2ep4ipedoi,, ka6i gegon4etw 3w@ 3o B pr6o@ t6on G, o34utw@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ D tetr4agwnon: 2em4aqomen g4ar: s4ummetron 24ara t6o 2ap6o t5h@ A t5wj 2ap6o t5h@ D. -ka6i 2epe6i 3o B pr6o@ t6on G l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ D l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h A t5hj D m4hkei. e2il4hfqw t5wn A, D m4esh 2an4alogon 3h E: 24estin 24ara 3w@ 3h A pr6o@ t6hn D, o34utw@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ E. 2as4ummetro@ d4e 2estin 3h A t5hj D m4hkei: 2as4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ A tetr4agwnon t5wj 2ap6o t5h@ E tetrag4wnwj: 2as4ummetro@ 24ara 2est6in 3h A t5hj E dun4amei. -T5hj 24ara proteqe4ishj e2uqe4iaj t5hj A prose4urhntai d4uo e2uqe5iai 2as4ummetroi a3i D, E, m4hkei m6en m4onon 3h D, dun4amei d6e ka6i m4hkei dhlad6h 3h E $-^P215^-^L12^ <3<####PBF&####-----<00> ###10AP### ##10## <00> -T5hj 24ara proteqe4ishj e2uqe4iaj t5hj 3rht5hj, 2af' 35h@ 24efamen t6a m4etra lamb4anesqai, o35ion t5hj A, prose4urhtai dun4amei m6en s4ummetro@ 3h D, tout4esti 3rht6h dun4amei m4onon s4ummetro@, 24alogo@ d6e 3h E. 2al4ogou@ g6ar kaq4olou kale5i t6a@ ka6i m4hkei ka6i dun4amei 2asumm4etrou@ t5hj 3rht5hj. ^+^>3> $-^P19^-^L1^ <2<34oper 24edei de5icai>2>. ^+^ ####***X#### ###PROP### ##11##-------ia41 -2E6an t4essara meg4eqh 2an4alogon 25hj, t6o d6e pr5wton t5wj deut4erwj s4ummetron 25hj, ka6i t6o tr4iton t5wj tet4artwj s4ummetron 24estai. k26an t6o pr5wton t5wj deut4erwj 2as4ummetron 25hj, ka6i ^-^ t6o tr4iton t5wj tet4artwj 2as4ummetron 24estai. -24Estwsan t4essara meg4eqh 2an4alogon t6a A, B, G, D, 3w@ t6o A pr6o@ t6o B, o34utw@ t6o G pr6o@ t6o D, t6o A d6e t5wj B s4ummetron 24estw: l4egw, 34oti ka6i t6o G t5wj D s4ummetron 24estai. -2Epe6i g6ar s4ummetr4on 2esti t6o A t5wj B, t6o A 24ara pr6o@ t6o B l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. ka4i 2estin 3w@ t6o A pr6o@ t6o B, o34utw@ t6o G pr6o@ t6o D: ka6i t6o G 24ara pr6o@ t6o D l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on: s4ummetron 24ara 2est6i t6o G t5wj D. -2All6a d6h t6o A t5wj B 2as4ummetron 24estw: l4egw, ^-^ 34oti ka6i t6o G t5wj D 2as4ummetron 24estai. 2epe6i g6ar 2as4ummetr4on 2esti t6o A t5wj B, t6o A 24ara pr6o@ t6o B l4ogon o2uk 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. ka6i 2estin 3w@ t6o A pr6o@ t6o B, o34utw@ t6o G pr6o@ t6o D: o2ud6e t6o G 24ara pr6o@ t6o D l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on: 2as4ummetron 24ara 2est6i t6o G t5wj D. -2E6an 24ara t4essara meg4eqh, ka6i t6a 3ec5h@. ^+^ ##12##-------ib41 -T6a t5wj a2ut5wj meg4eqei s4ummetra ka6i 2all4hloi@ 2est6i s4ummetra. -3Ek4ateron g6ar t5wn, A, B t5wj G 24estw s4ummetron. l4egw, 34oti ka6i t6o A t5wj B 2esti s4ummetron. -2Epe6i g6ar s4ummetr4on 2esti t6o A t5wj G, t6o A 24ara pr6o@ t6o G l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. 2ex4etw, 36on 3o D pr6o@ t6on E. p4alin, 2epe6i s4ummetr4on 2esti t6o G t5wj B, t6o G 24ara pr6o@ t6o B l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. 2ex4etw, 36on 3o Z pr6o@ t6on H. ka6i l4ogwn doq4entwn 3oposwno5un to5u te, 36on 24exei 3o D pr6o@ t6on E, ka6i 3o Z pr6o@ t6on H e2il4hfqwsan 2ariqmo6i 3ec5h@ 2en to5i@ doqe5isi l4ogoi@ o3i Q, K, L: 34wste e25inai 3w@ m6en t6on D pr6o@ t6on E, o34utw@ t6on Q pr6o@ t6on K, 3w@ d6e t6on Z pr6o@ t6on H, o34utw@ t6on K pr6o@ t6on L. -2Epe6i o25un 2estin 3w@ t6o A pr6o@ t6o G, o34utw@ 3o D pr6o@ t6on E, 2all' 3w@ 3o D pr6o@ t6on E, o34utw@ 3o Q pr6o@ t6on K, 24estin 24ara ka6i 3w@ t6o A pr6o@ t6o G, o34utw@ 3o Q pr6o@ t6on K. p4alin, 2epe6i 2estin 3w@ t6o G pr6o@ t6o B, o34utw@ 3o Z pr6o@ t6on H, 2all' 3w@ 3o Z pr6o@ t6on H, <22> 3o K pr6o@ t6on L, ka6i ^+^ 3w@ 24ara t6o G pr6o@ t6o B, o34utw@ 3o K pr6o@ t6on L. 24esti d6e ka6i 3w@ t6o A pr6o@ t6o G, o34utw@ 3o Q pr6o@ t6on K: di' 24isou 24ara 2est6in 3w@ t6o A pr6o@ t6o B, o34utw@ 3o Q pr6o@ t6on L. t6o A 24ara pr6o@ t6o B l4ogon 24exei, 36on 2ariqm6o@ 3o Q pr6o@ 2ariqm6on t6on L: s4ummetron 24ara 2est6i t6o A t5wj B. -T6a 24ara t5wj a2ut5wj meg4eqei s4ummetra ka6i 2all4hloi@ 2est6i s4ummetra: 34oper 24edei de5icai. $-^P216^-^L1^ <3<####BFV&####-----<00> ###10AP### ##13L## <00> -E2i@ t6o ig41 l5hmma 2ek t5h@ e2i@ 24atopon 2apagwg5h@. -2E6an 25hj d4uo meg4eqh, ka6i t6o m6en s4ummetron 25hj t5wj a2ut5wj, t6o d6e 34eteron 2as4ummetron, 2as4ummetra 24estai t6a meg4eqh. -24Estw g6ar d4uo meg4eqh t6a A, B, 24allo d6e t6o G, ka6i t6o m6en A t5wj G s4ummetron 24estw, t6o d6e B t5wj G 2as4ummetron. l4egw, 34oti ka6i t6o A t5wj B 2as4ummetr4on 2estin. -E2i g4ar 2esti s4ummetron t6o A t5wj B, 24esti d6e ka6i t6o G t5wj A, ka6i t6o G 24ara t5wj B s4ummetr4on 2estin: 34oper o2ux 3up4okeitai.>3> $-^P21^-^L8^ ####***X#### ###PROP### ##13##-------ig41 -2E6an 25hj d4uo meg4eqh s4ummetra, t6o d6e 34eteron a2ut5wn meg4eqei tin6i 2as4ummetron 25hj, ka6i t6o loip6on t5wj a2ut5wj 2as4ummetron 24estai. -24Estw d4uo meg4eqh s4ummetra t6a A, B, t6o d6e 34eteron a2ut5wn t6o A 24allwj tin6i t5wj G 2as4ummetron 24estw: l4egw, 34oti ka6i t6o loip6on t6o B t5wj G 2as4ummetr4on 2estin. -E2i g4ar 2esti s4ummetron t6o B t5wj G, 2all6a ka6i t6o A t5wj B s4ummetr4on 2estin, ka6i t6o A 24ara t5wj G s4ummetr4on 2estin. 2all6a ka6i 2as4ummetron: 34oper 2ad4unaton. o2uk 24ara s4ummetr4on 2esti t6o B t5wj G: 2as4ummetron 24ara. -2E6an 24ara 25hj d4uo meg4eqh s4ummetra, ka6i t6a 3ec5h@. ^+^ ##14^1^L^2##-----L5hmma -D4uo doqeis5wn e2uqei5wn 2an4iswn e3ure5in, t4ini me5izon d4unatai 3h me4izwn t5h@ 2el4assono@. -24Estwsan a3i doqe5isai d4uo 24anisoi e2uqe5iai a3i AB, G, 35wn me4izwn 24estw 3h AB: de5i d6h e3ure5in, t4ini me5izon d4unatai 3h AB t5h@ G. -Gegr4afqw 2ep6i t5h@ AB 3hmik4uklion t6o ADB, ka6i e2i@ a2ut6o 2enhrm4osqw t5hj G 24ish 3h AD, ka6i 2epeze4uxqw 3h DB. faner6on d4h, 34oti 2orq4h 2estin 3h 3up6o ADB gwn4ia, ka6i 34oti 3h AB t5h@ AD, tout4esti t5h@ G, me5izon d4unatai t5hj DB. -3Omo4iw@ d6e ka6i d4uo doqeis5wn e2uqei5wn 3h dunam4enh a2ut6a@ e3ur4isketai o34utw@. -24Estwsan a3i doqe5isai d4uo e2uqe5iai a3i AD, DB, ka6i d4eon 24estw e3ure5in t6hn dunam4enhn a2ut4a@. ke4isqwsan g4ar, 34wste 2orq6hn gwn4ian peri4exein t6hn 3up6o AD, DB, ka6i 2epeze4uxqw 3h AB: faner6on p4alin, 34oti 3h t6a@ AD, DB dunam4enh 2est6in 3h AB: 34oper 24edei de5icai. ##14##-------id41 -2E6an t4essare@ e2uqe5iai 2an4alogon 25wsin, d4unhtai d6e 3h pr4wth t5h@ deut4era@ me5izon t5wj 2ap6o summ4etrou 3eaut5hj <22>, ka6i 3h tr4ith t5h@ tet4arth@ me5izon dun4hsetai t5wj 2ap6o summ4etrou 3eaut5hj <22>. ka6i 2e6an 3h pr4wth t5h@ ^+^ deut4era@ me5izon d4unhtai t5wj 2ap6o 2asumm4etrou 3eaut5hj <22>, ka6i 3h tr4ith t5h@ tet4arth@ me5izon dun4hsetai t5wj 2ap6o 2asumm4etrou 3eaut5hj <22>. -24Estwsan t4essare@ e2uqe5iai 2an4alogon a3i A, B, G, D, 3w@ 3h A pr6o@ t6hn B, o34utw@ 3h G pr6o@ t6hn D, ka6i 3h A m6en t5h@ B me5izon dun4asqw t5wj 2ap6o t5h@ E, 3h d6e G t5h@ D me5izon dun4asqw t5wj 2ap6o t5h@ Z: l4egw, 34oti, e24ite s4ummetr4o@ 2estin 3h A t5hj E, s4ummetr4o@ 2esti ka6i 3h G t5hj Z, e24ite 2as4ummetr4o@ 2estin 3h A t5hj E, 2as4ummetr4o@ 2esti ka6i 3h G t5hj Z. -2Epe6i g4ar 2estin 3w@ 3h A pr6o@ t6hn B, o34utw@ 3h G pr6o@ t6hn D, 24estin 24ara ka6i 3w@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ B, o34utw@ t6o 2ap6o t5h@ G pr6o@ t6o 2ap6o t5h@ D. 2all6a t5wj m6en 2ap6o t5h@ A 24isa 2est6i t6a 2ap6o t5wn E, B, t5wj d6e 2ap6o t5h@ G 24isa 2est6i t6a 2ap6o t5wn D, Z. 24estin 24ara 3w@ t6a 2ap6o t5wn E, B pr6o@ t6o 2ap6o t5h@ B, o34utw@ t6a 2ap6o t5wn D, Z pr6o@ t6o 2ap6o t5h@ D: diel4onti 24ara 2est6in 3w@ t6o 2ap6o t5h@ E pr6o@ t6o 2ap6o t5h@ B, o34utw@ t6o 2ap6o t5h@ Z pr6o@ t6o 2ap6o t5h@ D: 24estin 24ara ka6i 3w@ 3h E pr6o@ t6hn B, o34utw@ 3h Z pr6o@ t6hn D: 2an4apalin 24ara 2est6in 3w@ 3h B pr6o@ t6hn E, o34utw@ 3h D pr6o@ t6hn Z. 24esti d6e ka6i 3w@ 3h A pr6o@ t6hn B, o34utw@ 3h G pr6o@ t6hn D: di' 24isou ^+^ 24ara 2est6in 3w@ 3h A pr6o@ t6hn E, o34utw@ 3h G pr6o@ t6hn Z. e24ite o25un s4ummetr4o@ 2estin 3h A t5hj E, s4ummetr4o@ 2esti ka6i 3h G t5hj Z, e24ite 2as4ummetr4o@ 2estin 3h A t5hj E, 2as4ummetr4o@ 2esti ka6i 3h G t5hj Z. -2E6an 24ara, ka6i t6a 3ec5h@. ##15##-------ie41 -2E6an d4uo meg4eqh s4ummetra sunteq5hj, ka6i t6o 34olon 3ekat4erwj a2ut5wn s4ummetron 24estai: k26an t6o 34olon 3en6i ^-^ a2ut5wn s4ummetron 25hj, ka6i t6a 2ec 2arx5h@ meg4eqh s4ummetra 24estai. -Sugke4isqw g6ar d4uo meg4eqh s4ummetra t6a AB, BG: l4egw, 34oti ka6i 34olon t6o AG 3ekat4erwj t5wn AB, BG 2esti s4ummetron. -2Epe6i g6ar s4ummetr4a 2esti t6a AB, BG, metr4hsei ti a2ut6a m4egeqo@. metre4itw, ka6i 24estw t6o D. 2epe6i o25un t6o D t6a AB, BG metre5i, ka6i 34olon t6o AG metr4hsei. metre5i d6e ka6i t6a AB, BG. t6o D 24ara t6a AB, BG, AG metre5i: s4ummetron 24ara 2est6i t6o AG 3ekat4erwj t5wn AB, BG. -2All6a d6h t6o AG 24estw s4ummetron t5wj AB: l4egw d4h, 34oti ka6i t6a AB, BG s4ummetr4a 2estin. -2Epe6i g6ar s4ummetr4a 2esti t6a AG, AB, metr4hsei ti a2ut6a m4egeqo@. metre4itw, ka6i 24estw t6o D. 2epe6i o25un t6o D ^+^ t6a GA, AB metre5i, ka6i loip6on 24ara t6o BG metr4hsei. metre5i d6e ka6i t6o AB: t6o D 24ara t6a AB, BG metr4hsei: s4ummetra 24ara 2est6i t6a AB, BG. -2E6an 24ara d4uo meg4eqh, ka6i t6a 3ec5h@. ##16##-------ist41 -2E6an d4uo meg4eqh 2as4ummetra sunteq5hj, ka6i t6o 34olon 3ekat4erwj a2ut5wn 2as4ummetron 24estai: k26an t6o 34olon 3en6i ^-^ a2ut5wn 2as4ummetron 25hj, ka6i t6a 2ec 2arx5h@ meg4eqh 2as4ummetra 24estai. -Sugke4isqw g6ar d4uo meg4eqh 2as4ummetra t6a AB, BG: -l4egw, 34oti ka6i 34olon t6o AG 3ekat4erwj t5wn AB, BG ^-^ 2as4ummetr4on 2estin. -E2i g6ar m4h 2estin 2as4ummetra t6a GA, AB, metr4hsei ti <22> m4egeqo@. metre4itw, e2i dunat4on, ka6i 24estw t6o D. 2epe6i o25un t6o D t6a GA, AB metre5i, ka6i loip6on 24ara t6o BG metr4hsei. metre5i d6e ka6i t6o AB: t6o D 24ara t6a AB, BG metre5i. s4ummetra 24ara 2est6i t6a AB, BG: 3up4ekeinto d6e ka6i 2as4ummetra: 34oper 2est6in 2ad4unaton. o2uk 24ara t6a GA, AB metr4hsei ti m4egeqo@: 2as4ummetra 24ara 2est6i t6a GA, AB. 3omo4iw@ d6h de4icomen, 34oti ka6i t6a AG, GB 2as4ummetr4a 2estin. t6o AG 24ara 3ekat4erwj t5wn AB, BG 2as4ummetr4on 2estin. -2All6a d6h t6o AG 3en6i t5wn AB, BG 2as4ummetron 24estw. 24estw d6h pr4oteron t5wj AB: l4egw 34oti ka6i t6a AB, BG 2as4ummetr4a 2estin. e2i g6ar ^+^ 24estai s4ummetra, metr4hsei ti a2ut6a m4egeqo@. metre4itw, ka6i 24estw t6o D. 2epe6i o25un t6o D t6a AB, BG metre5i, ka6i 34olon 24ara t6o AG metr4hsei. metre5i d6e ka6i t6o AB: t6o D 24ara t6a GA, AB metre5i. s4ummetra 24ara 2est6i t6a GA, AB: 3up4ekeito d6e ka6i 2as4ummetra: 34oper 2est6in 2ad4unaton. o2uk 24ara t6a AB, BG metr4hsei ti m4egeqo@: 2as4ummetra 24ara 2est6i t6a AB, BG. -2E6an 24ara d4uo meg4eqh, ka6i t6a 3ec5h@. ##17^1^L^2##-----L5hmma -2E6an par4a tina e2uqe5ian parablhq5hj parallhl4ogrammon 2elle5ipon e24idei tetrag4wnwj, t6o parablhq6en 24ison 2est6i t5wj 3up6o t5wn 2ek t5h@ parabol5h@ genom4enwn tmhm4atwn t5h@ e2uqe4ia@. -Par6a g6ar e2uqe5ian t6hn AB parabebl4hsqw parallhl4ogrammon t6o AD 2elle5ipon e24idei tetrag4wnwj t5wj DB: l4egw, 34oti 24ison 2est6i t6o AD t5wj 3up6o t5wn AG, GB. -Ka4i 2estin a2ut4oqen faner4on: 2epe6i g6ar tetr4agwn4on 2esti t6o DB, 24ish 2est6in 3h DG t5hj GB, ka4i 2esti t6o AD t6o 3up6o t5wn AG, GD, tout4esti t6o 3up6o t5wn AG, GB. -2E6an 24ara par4a tina e2uqe5ian, ka6i t6a 3ec5h@. ^+^ ##17##-----iz41 -2E6an 25wsi d4uo e2uqe5iai 24anisoi, t5wj d6e tet4artwj m4erei to5u 2ap6o t5h@ 2el4assono@ 24ison par6a t6hn me4izona parablhq5hj 2elle5ipon e24idei tetrag4wnwj ka6i e2i@ s4ummetra a2ut6hn diair5hj m4hkei, 3h me4izwn t5h@ 2el4assono@ me5izon dun4hsetai t5wj 2ap6o summ4etrou 3eaut5hj <22>. ka6i 2e6an 3h me4izwn t5h@ ^-^ 2el4assono@ me5izon d4unhtai t5wj 2ap6o summ4etrou 3eaut5hj <22>, t5wj d6e tet4artwj to5u 2ap6o t5h@ 2el4assono@ 24ison par6a t6hn me4izona parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ s4ummetra a2ut6hn diaire5i m4hkei. -24Estwsan d4uo e2uqe5iai 24anisoi a3i A, BG, 35wn me4izwn 3h BG, t5wj d6e tet4artwj m4erei to5u 2ap6o t5h@ 2el4assono@ t5h@ A, tout4esti t5wj 2ap6o t5h@ 3hmise4ia@ t5h@ A, 24ison par6a t6hn BG parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn BD, DG, s4ummetro@ d6e 24estw 3h BD t5hj DG m4hkei: l4egw, 34oti 3h BG t5h@ A me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. -Tetm4hsqw g6ar 3h BG d4ixa kat6a t6o E shme5ion, ka6i ke4isqw t5hj DE 24ish 3h EZ. loip6h 24ara 3h DG 24ish 2est6i t5hj BZ. ka6i 2epe6i e2uqe5ia 3h BG t4etmhtai e2i@ m6en 24isa kat6a t6o ^-^ E, e2i@ d6e 24anisa kat6a t6o D, t6o 24ara 3up6o BD, DG periex4omenon 2orqog4wnion met6a to5u 2ap6o t5h@ ED tetrag4wnou 24ison 2est6i ^+^ t5wj 2ap6o t5h@ EG tetrag4wnwj: ka6i t6a tetrapl4asia: t6o 24ara tetr4aki@ 3up6o t5wn BD, DG met6a to5u tetraplas4iou to5u 2ap6o t5h@ DE 24ison 2est6i t5wj tetr4aki@ 2ap6o t5h@ EG tetrag4wnwj. 2all6a t5wj m6en tetraplas4iwj to5u 3up6o t5wn BD, DG 24ison 2est6i t6o 2ap6o t5h@ A tetr4agwnon, t5wj d6e tetraplas4iwj to5u 2ap6o t5h@ DE 24ison 2est6i t6o 2ap6o t5h@ DZ tetr4agwnon: diplas4iwn g4ar 2estin 3h DZ t5h@ DE. t5wj d6e tetraplas4iwj to5u 2ap6o t5h@ EG 24ison 2est6i t6o 2ap6o t5h@ BG tetr4agwnon: diplas4iwn g4ar 2esti p4alin 3h BG t5h@ GE. t6a 24ara 2ap6o t5wn A, DZ tetr4agwna 24isa 2est6i t5wj 2ap6o t5h@ BG tetrag4wnwj: 34wste t6o 2ap6o t5h@ BG to5u 2ap6o t5h@ A me5iz4on 2esti t5wj 2ap6o t5h@ DZ: 3h BG 24ara t5h@ A me5izon d4unatai t5hj DZ. deikt4eon, 34oti ka6i s4ummetr4o@ 2estin 3h BG t5hj DZ. 2epe6i g6ar s4ummetr4o@ 2estin 3h BD t5hj DG m4hkei, s4ummetro@ 24ara 2est6i ka6i 3h BG t5hj GD m4hkei. 2all6a 3h GD ta5i@ GD, BZ 2esti s4ummetro@ m4hkei: 24ish g4ar 2estin 3h GD t5hj BZ. ka6i 3h BG 24ara s4ummetr4o@ 2esti ta5i@ BZ, GD m4hkei: 34wste ka6i loip5hj t5hj ZD s4ummetr4o@ 2estin 3h BG m4hkei: 3h BG 24ara t5h@ A me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. -2All6a d6h 3h BG t5h@ A me5izon dun4asqw t5wj 2ap6o summ4etrou 3eaut5hj, t5wj d6e tet4artwj to5u 2ap6o t5h@ A 24ison par6a t6hn BG parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn BD, DG. deikt4eon, 34oti s4ummetr4o@ 2estin 3h GD t5hj DG m4hkei. ^+^ -T5wn g6ar a2ut5wn kataskeuasq4entwn 3omo4iw@ de4icomen, 34oti 3h BG t5h@ A me5izon d4unatai t5wj 2ap6o t5h@ ZD. d4unatai d6e 3h BG t5h@ A me5izon t5wj 2ap6o summ4etrou 3eaut5hj. s4ummetro@ 24ara 2est6in 3h BG t5hj ZD m4hkei: 34wste ka6i loip5hj sunamfot4erwj t5hj BZ, DG s4ummetr4o@ 2estin 3h BG m4hkei. 2all6a sunamf4otero@ 3h BZ, DG s4ummetr4o@ 2esti t5hj DG <22>. 34wste ka6i 3h BG t5hj GD s4ummetr4o@ 2esti m4hkei: ka6i diel4onti 24ara 3h BD t5hj DG 2esti s4ummetro@ m4hkei. -2E6an 24ara 25wsi d4uo e2uqe5iai 24anisoi, ka6i t6a 3ec5h@. ##18##-------ih41 -2E6an 25wsi d4uo e2uqe5iai 24anisoi, t5wj d6e tet4artwj m4erei to5u ^-^ 2ap6o t5h@ 2el4assono@ 24ison par6a t6hn me4izona parablhq5hj 2elle5ipon e24idei tetrag4wnwj, ka6i e2i@ 2as4ummetra a2ut6hn diair5hj <22>, 3h me4izwn t5h@ 2el4assono@ me5izon dun4hsetai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka6i 2e6an 3h me4izwn t5h@ 2el4assono@ me5izon d4unhtai t5wj 2ap6o 2asumm4etrou 3eaut5hj, t5wj d6e tet4artwj to5u 2ap6o t5h@ 2el4assono@ 24ison par6a t6hn me4izona parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ 2as4ummetra a2ut6hn diaire5i <22>. ^+^ -24Estwsan d4uo e2uqe5iai 24anisoi a3i A, BG, 35wn me4izwn 3h BG, t5wj d6e tet4artwj <22> to5u 2ap6o t5h@ 2el4assono@ t5h@ A 24ison par6a t6hn BG parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn BDG, 2as4ummetro@ d6e 24estw 3h BD t5hj DG m4hkei: l4egw, 34oti 3h BG t5h@ A me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. -T5wn g6ar a2ut5wn kataskeuasq4entwn t5wj pr4oteron 3omo4iw@ de4icomen, 34oti 3h BG t5h@ A me5izon d4unatai t5wj 2ap6o t5h@ ZD, deikt4eon <22>, 34oti 2as4ummetr4o@ 2estin ^-^ 3h BG t5hj DZ m4hkei. 2epe6i g6ar 2as4ummetr4o@ 2estin 3h BD t5hj DG m4hkei, 2as4ummetro@ 24ara 2est6i ka6i 3h BG t5hj GD m4hkei. 2all6a 3h DG s4ummetr4o@ 2esti sunamfot4erai@ ta5i@ BZ, DG: ka6i 3h BG 24ara 2as4ummetr4o@ 2esti sunamfot4erai@ ta5i@ BZ, DG. 34wste ka6i loip5hj t5hj ZD 2as4ummetr4o@ 24estin 3h BG m4hkei. ka6i 3h BG t5h@ A me5izon d4unatai t5wj 2ap6o t5h@ ZD: 3h BG 24ara t5h@ A me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. -Dun4asqw d6h p4alin 3h BG t5h@ A me5izon t5wj 2ap6o 2asumm4etrou 3eaut5hj, t5wj d6e tet4artwj to5u 2ap6o t5h@ A 24ison par6a t6hn BG parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn BD, DG. deikt4eon, 34oti 2as4ummetr4o@ 2estin 3h BD t5hj DG m4hkei. -T5wn g6ar a2ut5wn kataskeuasq4entwn 3omo4iw@ de4icomen, 34oti 3h BG t5h@ A me5izon d4unatai t5wj 2ap6o t5h@ ZD. 2all6a ^+^ 3h BG t5h@ A me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. 2as4ummetro@ 24ara 2est6in 3h BG t5hj ZD m4hkei: 34wste ka6i loip5hj sunamfot4erwj t5hj BZ, DG 2as4ummetr4o@ 2estin 3h BG. 2all6a sunamf4otero@ 3h BZ, DG t5hj DG s4ummetr4o@ 2esti m4hkei: ka6i 3h BG 24ara t5hj DG 2as4ummetr4o@ 2esti m4hkei: 34wste ka6i diel4onti 3h BD t5hj DG 2as4ummetr4o@ 2esti m4hkei. -2E6an 24ara 25wsi d4uo e2uqe5iai, ka6i t6a 3ec5h@. ##19^1^L^2##-----L5hmma -2Epe6i d4edeiktai, 34oti a3i m4hkei s4ummetroi p4antw@ ka6i dun4amei <22>, a3i d6e dun4amei o2u p4antw@ ka6i m4hkei, 2all6a d6h d4unantai m4hkei ka6i s4ummetroi e25inai ka6i 2as4ummetroi, faner4on, 34oti, 2e6an t5hj 2ekkeim4enhj 3rht5hj s4ummetr4o@ ti@ 25hj m4hkei, l4egetai 3rht6h ka6i s4ummetro@ a2ut5hj o2u m4onon m4hkei, 2all6a ka6i dun4amei, 2epe6i a3i m4hkei s4ummetroi p4antw@ ka6i dun4amei. 2e6an d6e t5hj 2ekkeim4enhj 3rht5hj s4ummetr4o@ ti@ 25hj dun4amei, e2i m6en ka6i m4hkei, l4egetai ka6i o34utw@ 3rht6h ka6i s4ummetro@ a2ut5hj m4hkei ka6i dun4amei: e2i d6e t5hj 2ekkeim4enhj p4alin 3rht5hj s4ummetr4o@ ti@ o25usa dun4amei m4hkei a2ut5hj 25hj 2as4ummetro@, l4egetai ka6i o34utw@ 3rht6h dun4amei m4onon s4ummetro@. ^+^ $-^P216^-^L9^ <3<####PBF&####-----<00> ###10AP### ##18L## <00> -3Rht6a@ g6ar kale5i t6a@ t5hj 2ekkeim4enhj 3rht5hj 24htoi m4hkei ka6i dun4amei summ4etrou@ 26h ka6i dun4amei m4onon. e2is6i d6e ka6i 24allai e2uqe5iai, a36i m4hkei m6en 2as4ummetro4i e2isi t5hj 2ekkeim4enhj 3rht5hj, dun4amei d6e m4onon s4ummetroi, ka6i di6a to5uto p4alin l4egontai 3rhta6i ka6i s4ummetroi pr6o@ 2all4hla@, kaq' 36o ^+^ 3rhta4i, 2all6a s4ummetroi pr6o@ 2all4hla@ 24htoi m4hkei dhlad6h ka6i dun4amei 36h dun4amei m4onon. ka6i e2i m6en m4hkei, l4egontai ka6i a2uta6i 3rhta6i m4hkei s4ummetroi 2epakouom4enou, 34oti ka6i dun4amei: e2i d6e dun4amei m4onon pr6o@ 2all4hla@ e2is6i s4ummetroi, l4egontai ka6i a2uta6i o34utw@ 3rhta6i dun4amei m4onon s4ummetroi. 34oti d6e a3i 3rhta6i s4ummetro4i e2isin, 2ente5uqen d5hlon: 2epe6i g6ar 3rhta4i e2isin a3i t5hj 2ekkeim4enhj 3rht5hj s4ummetroi, t6a d6e t5wj a2ut5wj s4ummetra ka6i 2all4hloi@ 2est6i s4ummetra, a3i 24ara 3rhta6i s4ummetro4i e2isin.>3> $-^P32^-^L1^ ####***X#### ###PROP### ##19##-------iq41 -T6o 3up6o 3rht5wn m4hkei summ4etrwn kat4a tina t5wn proeirhm4enwn tr4opwn e2uqei5wn periex4omenon 2orqog4wnion 3rht4on 2estin. -3Up6o g6ar 3rht5wn m4hkei summ4etrwn e2uqei5wn t5wn AB, BG 2orqog4wnion periex4esqw t6o AG: l4egw, 34oti 3rht4on 2esti t6o AG. -2Anagegr4afqw g6ar 2ap6o t5h@, AB tetr4agwnon t6o AD: 3rht6on 24ara 2est6i t6o AD. ka6i 2epe6i s4ummetr4o@ 2estin 3h AB t5hj BG m4hkei, 24ish d4e 2estin 3h AB t5hj BD, s4ummetro@ 24ara 2est6in 3h BD t5hj BG m4hkei. ka4i 2estin 3w@ 3h BD pr6o@ t6hn BG, o34utw@ t6o DA pr6o@ t6o AG. s4ummetron 24ara 2est6i t6o DA t5wj AG. 3rht6on d6e t6o DA: 3rht6on 24ara 2est6i ka6i t6o AG. -T6o 24ara 3up6o 3rht5wn m4hkei summ4etrwn, ka6i t6a 3ec5h@. ##20##-------k41 -2E6an 3rht6on par6a 3rht6hn parablhq5hj, pl4ato@ poie5i 3rht6hn ka6i s4ummetron t5hj, par' 36hn par4akeitai, m4hkei. ^+^ -3Rht6on g6ar t6o AG par6a 3rht6hn kat6a tina p4alin t5wn proeirhm4enwn tr4opwn t6hn AB parabebl4hsqw pl4ato@ poio5un t6hn BG: l4egw, 34oti 3rht4h 2estin 3h BG ka6i s4ummetro@ t5hj BA m4hkei. -2Anagegr4afqw g6ar 2ap6o t5h@ AB tetr4agwnon t6o AD: 3rht6on 24ara 2est6i t6o AD. 3rht6on d6e ka6i t6o AG: s4ummetron 24ara 2est6i t6o DA t5wj AG. ka4i 2estin 3w@ t6o DA pr6o@ t6o AG, o34utw@ 3h DB pr6o@ t6hn BG. s4ummetro@ 24ara 2est6i ka6i 3h DB t5hj BG: 24ish d6e 3h DB t5hj BA: s4ummetro@ 24ara ka6i 3h AB t5hj BG. 3rht6h d4e 2estin 3h AB: 3rht6h 24ara 2est6i ka6i 3h BG ka6i s4ummetro@ t5hj AB m4hkei. -2E6an 24ara 3rht6on par6a 3rht6hn parablhq5hj, ka6i t6a 3ec5h@. $-^P217^-^L10^ <3<####PBF&####-----<00> ###10AP### <00> ##20L## -----L5hmma -3H dunam4enh 24alogon xwr4ion 24alog4o@ 2estin. -Dun4asqw g6ar 3h A 24alogon xwr4ion, tout4esti t6o 2ap6o t5h@ A tetr4agwnon 24ison 24estw 2al4ogwj xwr4iwj. l4egw, 34oti 3h A 24alog4o@ 2estin. -E2i g6ar 24estai 3rht6h 3h A, 3rht6on 24estai ka6i t6o 2ap' a2ut5h@ tetr4agwnon: o34utw@ g6ar <2<2estin>2> 2en to5i@ 34oroi@. o2uk 24esti d4e: 24alogo@ 24ara 2est6in 3h A: 34oper 24edei de5icai. ^+^>3> $-^P33^-^L15^ ####***X#### ###PROP### ##21##-------ka41 -T6o 3up6o 3rht5wn dun4amei m4onon summ4etrwn e2uqei5wn periex4omenon 2orqog4wnion 24alog4on 2estin, ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin, kale4isqw d6e m4esh. -3Up6o g6ar 3rht5wn dun4amei m4onon summ4etrwn e2uqei5wn t5wn AB, BG 2orqog4wnion periex4esqw t6o AG: l4egw, 34oti 24alog4on 2esti t6o AG, ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin, kale4isqw d6e m4esh. ^+^ -2Anagegr4afqw g6ar 2ap6o t5h@ AB tetr4agwnon t6o AD: 3rht6on 24ara 2est6i t6o AD. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h AB t5hj BG m4hkei: dun4amei g6ar m4onon 3up4okeintai s4ummetroi: 24ish d6e 3h AB t5hj BD, 2as4ummetro@ 24ara 2est6i ka6i 3h DB t5hj BG m4hkei. ka4i 2estin 3w@ 3h DB pr6o@ t6hn BG, o34utw@ t6o AD pr6o@ t6o AG: 2as4ummetron 24ara <2<2est6i>2> t6o DA t5wj AG. 3rht6on d6e t6o DA: 24alogon 24ara 2est6i t6o AG: 34wste ka6i 3h dunam4enh t6o AG <22> 24alog4o@ 2estin, kale4isqw d6e m4esh: 34oper 24edei de5icai. ##22^1^L^2##-----L5hmma -2E6an 25wsi d4uo e2uqe5iai, 24estin 3w@ 3h pr4wth pr6o@ t6hn deut4eran, o34utw@ t6o 2ap6o t5h@ pr4wth@ pr6o@ t6o 3up6o t5wn d4uo e2uqei5wn. -24Estwsan d4uo e2uqe5iai a3i ZE, EH. l4egw, 34oti 2est6in 3w@ 3h ZE pr6o@ t6hn EH, o34utw@ t6o 2ap6o t5h@ ZE pr6o@ t6o 3up6o t5wn ZE, EH. -2Anagegr4afqw g6ar 2ap6o t5h@ ZE tetr4agwnon t6o DZ, ka6i sumpeplhr4wsqw t6o HD. 2epe6i o25un 2estin 3w@ 3h ZE ^+^ pr6o@ t6hn EH, o34utw@ t6o ZD pr6o@ t6o DH, ka4i 2esti t6o m6en ZD t6o 2ap6o t5h@ ZE, t6o d6e DH t6o 3up6o t5wn DE, EH, tout4esti t6o 3up6o t5wn ZE, EH, 24estin 24ara 3w@ 3h ZE t6hn EH, o34utw@ t6o 2ap6o t5h@ ZE pr6o@ t6o 3up6o t5wn ZE, EH. 3omo4iw@ d6e ka6i 3w@ t6o 3up6o t5wn HE, EZ pr6o@ t6o 2ap6o t5h@ EZ, tout4estin 3w@ t6o HD pr6o@ t6o ZD, o34utw@ 3h HE pr6o@ t6hn EZ: 34oper 24edei de5icai. ##22##-------kb41 -T6o 2ap6o m4esh@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 3rht6hn ka6i 2as4ummetron t5hj, par' 36hn par4akeitai, m4hkei. -24Estw m4esh m6en 3h A, 3rht6h d6e 3h GB, ka6i t5wj 2ap6o t5h@ A 24ison par6a t6hn BG parabebl4hsqw xwr4ion 2orqog4wnion t6o BD pl4ato@ poio5un t6hn GD: l4egw, 34oti 3rht4h 2estin 3h GD ka6i 2as4ummetro@ t5hj GB m4hkei. -2Epe6i g6ar m4esh 2est6in 3h A, d4unatai xwr4ion periex4omenon 3up6o 3rht5wn dun4amei m4onon summ4etrwn. dun4asqw t6o HZ. d4unatai d6e ka6i t6o BD: 24ison 24ara 2est6i t6o BD t5wj HZ. 24esti d6e a2ut5wj ka6i 2isog4wnion: t5wn d6e 24iswn te ka6i 2isogwn4iwn parallhlogr4ammwn 2antipep4onqasin a3i pleura6i a3i per6i t6a@ 24isa@ gwn4ia@: 2an4alogon 24ara 2est6in 3w@ 3h BG pr6o@ t6hn EH, o34utw@ 3h EZ pr6o@ t6hn GD. 24estin 24ara ka6i 3w@ t6o 2ap6o t5h@ ^+^ BG pr6o@ t6o 2ap6o t5h@ EH, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ GD. s4ummetron d4e 2esti t6o 2ap6o t5h@ GB t5wj 2ap6o t5h@ EH: 3rht6h g4ar 2estin 3ekat4era a2ut5wn: s4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ EZ t5wj 2ap6o t5h@ GD. 3rht6on d4e 2esti t6o 2ap6o t5h@ EZ: 3rht6on 24ara 2est6i ka6i t6o 2ap6o t5h@ GD: 3rht6h 24ara 2est6in 3h GD. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h EZ t5hj EH m4hkei: dun4amei g6ar m4onon e2is6i s4ummetroi: 3w@ d6e 3h EZ pr6o@ t6hn EH, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 3up6o t5wn ZE, EH, 2as4ummetron 24ara <2<2est6i>2> t6o 2ap6o t5h@ EZ t5wj 3up6o t5wn ZE, EH. 2all6a t5wj m6en 2ap6o t5h@ EZ s4ummetr4on 2esti t6o 2ap6o t5h@ GD: 3rhta6i g4ar e2isi dun4amei: t5wj d6e 3up6o t5wn ZE, EH s4ummetr4on 2esti t6o 3up6o t5wn AG, GB: 24isa g4ar 2esti t5wj 2ap6o t5h@ A: 2as4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ GD t5wj 3up6o t5wn DG, GB. 3w@ d6e t6o 2ap6o t5h@ GD pr6o@ t6o 3up6o t5wn DG, GB, o34utw@ 2est6in 3h DG pr6o@ t6hn GB: 2as4ummetro@ 24ara 2est6in 3h DG t5hj GB m4hkei. 3rht6h 24ara 2est6in 3h GD ka6i 2as4ummetro@ t5hj GB m4hkei: 34oper 24edei de5icai. ##23##-------kg41 -3H t5hj m4eshj s4ummetro@ m4esh 2est4in. -24Estw m4esh 3h A, ka6i t5hj A s4ummetro@ 24estw 3h B: l4egw, 34oti ka6i 3h B m4esh 2est4in. ^+^ -2Ekke4isqw g6ar 3rht6h 3h GD, ka6i t5wj m6en 2ap6o t5h@ A 24ison par6a t6hn GD parabebl4hsqw xwr4ion 2orqog4wnion t6o GE pl4ato@ poio5un t6hn ED: 3rht6h 24ara 2est6in 3h ED ka6i 2as4ummetro@ t5hj GD m4hkei. t5wj d6e 2ap6o t5h@ B 24ison par6a t6hn GD parabebl4hsqw xwr4ion 2orqog4wnion t6o GZ pl4ato@ poio5un t6hn DZ. 2epe6i o25un s4ummetr4o@ 2estin 3h A t5hj B, s4ummetr4on 2esti ka6i t6o 2ap6o t5h@ A t5wj 2ap6o t5h@ B. 2all6a t5wj m6en 2ap6o t5h@ A 24ison 2est6i t6o EG, t5wj d6e 2ap6o t5h@ B 24ison 2est6i t6o GZ: s4ummetron 24ara 2est6in t6o EG t5wj GZ. ka4i 2estin 3w@ t6o EG pr6o@ t6o GZ, o34utw@ 3h ED pr6o@ t6hn DZ: s4ummetro@ 24ara 2est6in 3h ED t5hj DZ m4hkei. 3rht6h d4e 2estin 3h ED ka6i 2as4ummetro@ t5hj DG m4hkei: 3rht6h 24ara 2est6i ka6i 3h DZ ka6i 2as4ummetro@ t5hj DG m4hkei: a3i GD, DZ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. 3h d6e t6o 3up6o 3rht5wn dun4amei m4onon summ4etrwn dunam4enh m4esh 2est4in. 3h 24ara t6o 3up6o t5wn GD, DZ dunam4enh m4esh 2est4in: ka6i d4unatai t6o 3up6o t5wn GD, DZ 3h B: m4esh 24ara 2est6in 3h B. ##23^1^Por^2##-----P4orisma -2Ek d6h to5utou faner4on, 34oti t6o t5wj m4eswj xwr4iwj s4ummetron m4eson 2est4in. <22> -3Wsa4utw@ d6e to5i@ 2ep6i t5wn 3rht5wn e2irhm4enoi@ ka6i 2ep6i t5wn m4eswn 2ecakolouqe5i, t6hn t5hj m4eshj m4hkei s4ummetron l4egesqai m4eshn ka6i s4ummetron a2ut5hj m6h m4onon m4hkei, 2all6a ka6i dun4amei, 2epeid4hper kaq4olou a3i m4hkei s4ummetroi p4antw@ ka6i dun4amei. 2e6an d6e t5hj m4eshj s4ummetr4o@ ti@ 25hj dun4amei, e2i m6en ka6i m4hkei, l4egontai ka6i o34utw@ m4esai ka6i s4ummetroi m4hkei ka6i dun4amei, e2i d6e dun4amei m4onon, l4egontai m4esai dun4amei m4onon s4ummetroi. $-^P218^-^L1^ <3<####**PV####-----<00> ###10AP### ##23Por## <00> -E2is6i d6e p4alin ka6i 24allai e2uqe5iai, a36i m4hkei m6en 2as4ummetro4i e2isi t5hj m4eshj, dun4amei d6e m4onon s4ummetroi, ka6i l4egontai p4alin m4esai di6a t6o s4ummetroi e25inai dun4amei t5hj m4eshj ka6i s4ummetroi pr6o@ 2all4hla@, kaq6o m4esai, 2all6a s4ummetroi pr6o@ 2all4hla@ 24htoi m4hkei dhlad6h ka6i dun4amei 26h dun4amei m4onon. ka6i e2i m6en m4hkei, l4egontai ka6i a34utai m4esai m4hkei s4ummetroi 3epom4enou to5u, 34oti ka6i dun4amei: e2i d6e dun4amei m4onon e2is6i s4ummetroi, l4egontai ka6i o34utw@ m4esai dun4amei m4onon s4ummetroi. -34Oti d6e a3i m4esai s4ummetro4i e2isin, o34utw@ deikt4eon. 2epe6i a3i m4esai m4eshj tin6i s4ummetro4i e2isin, t6a d6e t5wj a2ut5wj s4ummetra ka6i 2all4hloi@ 2est6i s4ummetra, a3i 24ara m4esai s4ummetro4i e2isin.>3> $-^P38^-^L11^ ####***X#### ###PROP### ##24##-------kd41 -T6o 3up6o m4eswn m4hkei summ4etrwn e2uqei5wn kat4a tina t5wn e2irhm4enwn tr4opwn periex4omenon 2orqog4wnion m4eson 2est4in. -3Up6o g6ar m4eswn m4hkei summ4etrwn e2uqei5wn t5wn AB, BG periex4esqw 2orqog4wnion t6o AG: l4egw, 34oti t6o AG m4eson 2est4in. -2Anagegr4afqw g6ar 2ap6o t5h@ AB tetr4agwnon t6o AD: m4eson 24ara 2est6i t6o AD. ka6i 2epe6i s4ummetr4o@ 2estin 3h AB t5hj BG m4hkei, 24ish d6e 3h AB t5hj BD, s4ummetro@ 24ara 2est6i ka6i 3h DB t5hj BG m4hkei: 34wste ka6i t6o DA t5wj AG s4ummetr4on 2estin. m4eson d6e t6o DA: m4eson 24ara ka6i t6o AG: 34oper 24edei de5icai. ^+^ ##25##-------ke41 -T6o 3up6o m4eswn dun4amei m4onon summ4etrwn e2uqei5wn periex4omenon 2orqog4wnion 24htoi 3rht6on 26h m4eson 2est4in. -3Up6o g6ar m4eswn dun4amei m4onon summ4etrwn e2uqei5wn t5wn AB, BG 2orqog4wnion periex4esqw t6o AG: l4egw, 34oti t6o AG 24htoi 3rht6on 26h m4eson 2est4in. -2Anagegr4afqw g6ar 2ap6o t5wn AB, BG tetr4agwna t6a AD, BE: m4eson 24ara 2est6in 3ek4ateron t5wn AD, BE. ka6i 2ekke4isqw 3rht6h 3h ZH, ka6i t5wj m6en AD 24ison par6a t6hn ZH parabebl4hsqw 2orqog4wnion parallhl4ogrammon t6o HQ pl4ato@ poio5un t6hn ZQ, t5wj d6e AG 24ison par6a t6hn QM parabebl4hsqw 2orqog4wnion parallhl4ogrammon t6o MK pl4ato@ poio5un t6hn QK, ka6i 24eti t5wj BE 24ison 3omo4iw@ par6a t6hn KN parabebl4hsqw t6o NL pl4ato@ poio5un t6hn KL: 2ep' e2uqe4ia@ 24ara e2is6in a3i ZQ, QK, KL. 2epe6i o25un m4eson 2est6in 3ek4ateron t5wn AD, BE, ka4i 2estin 24ison t6o m6en AD t5wj HQ, t6o d6e BE t5wj NL, m4eson 24ara ka6i 3ek4ateron t5wn HQ, NL. ka6i par6a 3rht6hn t6hn ZH par4akeitai: 3rht6h 24ara 2est6in 3ekat4era t5wn ZQ, KL ka6i 2as4ummetro@ t5hj ZH m4hkei. ka6i 2epe6i s4ummetr4on 2esti t6o AD t5wj BE, s4ummetron 24ara 2est6i ka6i t6o HQ t5wj NL. ka4i 2estin 3w@ t6o HQ pr6o@ ^+^ t6o NL, o34utw@ 3h ZQ pr6o@ t6hn KL: s4ummetro@ 24ara 2est6in 3h ZQ t5hj KL m4hkei. a3i ZQ, KL 24ara 3rhta4i e2isi m4hkei s4ummetroi: 3rht6on 24ara 2est6i t6o 3up6o t5wn ZQ, KL. ka6i 2epe6i 24ish 2est6in 3h m6en DB t5hj BA, 3h d6e CB t5hj BG, 24estin 24ara 3w@ 3h DB pr6o@ t6hn BG, o34utw@ 3h AB pr6o@ t6hn BC. 2all' 3w@ m6en 3h DB pr6o@ t6hn BG, o34utw@ t6o DA pr6o@ t6o AG: 3w@ d6e 3h AB pr6o@ t6hn BC, o34utw@ t6o AG pr6o@ t6o GC: 24estin 24ara 3w@ t6o DA pr6o@ t6o AG, o34utw@ t6o AG pr6o@ t6o GC. 24ison d4e 2esti t6o m6en AD t5wj HQ, t6o d6e AG t5wj MK, t6o d6e GC t5wj NL: 24estin 24ara 3w@ t6o HQ pr6o@ t6o MK, o34utw@ t6o MK pr6o@ t6o NL: 24estin 24ara ka6i 3w@ 3h ZQ pr6o@ t6hn QK, o34utw@ 3h QK pr6o@ t6hn KL: t6o 24ara 3up6o t5wn ZQ, KL 24ison 2est6i t5wj 2ap6o t5h@ QK. 3rht6on d6e t6o 3up6o t5wn ZQ, KL: 3rht6on 24ara 2est6i ka6i t6o 2ap6o t5h@ QK: 3rht6h 24ara 2est6in 3h QK. ka6i e2i m6en s4ummetr4o@ 2esti t5hj ZH m4hkei, 3rht4on 2esti t6o QN: e2i d6e 2as4ummetr4o@ 2esti t5hj ZH m4hkei, a3i KQ, QM 3rhta4i e2isi dun4amei m4onon s4ummetroi: m4eson 24ara t6o QN. t6o QN 24ara 24htoi 3rht6on 26h m4eson 2est4in. 24ison d6e t6o QN t5wj AG: t6o AG 24ara 24htoi 3rht6on 26h m4eson 2est4in. -T6o 24ara 3up6o m4eswn dun4amei m4onon summ4etrwn, ka6i t6a 3ec5h@. ^+^ ##26##-------kst41 -M4eson m4esou o2ux 3uper4exei 3rht5wj. -E2i g6ar dunat4on, m4eson t6o AB m4esou to5u AG 3uperex4etw 3rht5wj t5wj DB, ka6i 2ekke4isqw 3rht6h 3h EZ, ka6i t5wj AB 24ison par6a t6hn EZ parabebl4hsqw parallhl4ogrammon 2orqog4wnion t6o ZQ pl4ato@ poio5un t6hn EQ, t5wj d6e AG 24ison 2afhjr4hsqw t6o ZH: loip6on 24ara t6o BD loip5wj t5wj KQ 2estin 24ison. 3rht6on d4e 2esti t6o DB: 3rht6on 24ara 2est6i ka6i t6o KQ. 2epe6i o25un m4eson 2est6in 3ek4ateron t5wn AB, AG, ka4i 2esti t6o m6en AB t5wj ZQ 24ison, t6o d6e AG t5wj ZH, m4eson 24ara ka6i 3ek4ateron t5wn ZQ, ZH. ka6i par6a 3rht6hn t6hn EZ par4akeitai: 3rht6h 24ara 2est6in 3ekat4era t5wn QE, EH ka6i 2as4ummetro@ t5hj EZ m4hkei. ka6i 2epe6i 3rht4on 2esti t6o DB ka4i 2estin 24ison t5wj KQ, 3rht6on 24ara 2est6i ka6i t6o KQ. ka6i par6a 3rht6hn t6hn EZ par4akeitai: 3rht6h 24ara 2est6in 3h HQ ka6i s4ummetro@ t5hj EZ m4hkei. 2all6a ka6i 3h EH 3rht4h 2esti ka6i 2as4ummetro@ t5hj EZ m4hkei: 2as4ummetro@ 24ara 2est6in 3h EH t5hj HQ m4hkei. ka4i 2estin 3w@ 3h EH pr6o@ t6hn HQ, o34utw@ t6o 2ap6o t5h@ EH pr6o@ t6o 3up6o t5wn EH, HQ: 2as4ummetron 24ara 2est6i t6o 2ap6o t5h@ EH t5wj 3up6o t5wn EH, HQ. 2all6a t5wj m6en 2ap6o t5h@ EH s4ummetr4a 2esti t6a 2ap6o t5wn EH, HQ tetr4agwna: 3rht6a g6ar 2amf4otera: t5wj d6e 3up6o t5wn EH, HQ s4ummetr4on 2esti t6o ^+^ d6i@ 3up6o t5wn EH, HQ: dipl4asion g4ar 2estin a2uto5u: 2as4ummetra 24ara 2est6i t6a 2ap6o t5wn EH, HQ t5wj d6i@ 3up6o t5wn EH, HQ: ka6i sunamf4otera 24ara t4a te 2ap6o t5wn EH, HQ ka6i t6o d6i@ 3up6o t5wn EH, HQ, 34oper 2est6i t6o 2ap6o t5h@ EQ, 2as4ummetr4on 2esti to5i@ 2ap6o t5wn EH, HQ. 3rht6a d6e t6a 2ap6o t5wn EH, HQ: 24alogon 24ara t6o 2ap6o t5h@ EQ. 24alogo@ 24ara 2est6in 3h EQ. 2all6a ka6i 3rht4h: 34oper 2est6in 2ad4unaton. -M4eson 24ara m4esou o2ux 3uper4exei 3rht5wj: 34oper 24edei ^-^ de5icai. ##27##-------kz41 -M4esa@ e3ure5in dun4amei m4onon summ4etrou@ 3rht6on peri* exo4usa@. -2Ekke4isqwsan d4uo 3rhta6i dun4amei m4onon s4ummetroi a3i A, B, ka6i e2il4hfqw t5wn A, B m4esh 2an4alogon 3h G, ka6i gegon4etw 3w@ 3h A pr6o@ t6hn B, o34utw@ 3h G pr6o@ t6hn D. -Ka6i 2epe6i a3i A, B 3rhta4i e2isi dun4amei m4onon s4ummetroi, t6o 24ara 3up6o t5wn A, B, tout4esti t6o 2ap6o t5h@ G, m4eson 2est4in. m4esh 24ara 3h G. ka6i 2epe4i 2estin 3w@ 3h A pr6o@ t6hn B, <22> 3h G pr6o@ t6hn D, a3i d6e A, B dun4amei m4onon <22> s4ummetroi, ka6i a3i G, D 24ara dun4amei m4onon e2is6i s4ummetroi. ka4i 2esti m4esh 3h G: m4esh 24ara ka6i 3h D. a3i G, D 24ara m4esai ^+^ e2is6i dun4amei m4onon s4ummetroi. l4egw, 34oti ka6i 3rht6on peri4exousin. 2epe6i g4ar 2estin 3w@ 3h A pr6o@ t6hn B, o34utw@ 3h G pr6o@ t6hn D, 2enall6ac 24ara 2est6in 3w@ 3h A pr6o@ t6hn G, 3h B pr6o@ t6hn D. 2all' 3w@ 3h A pr6o@ t6hn G, 3h G pr6o@ t6hn B: ka6i 3w@ 24ara 3h G pr6o@ t6hn B, o34utw@ 3h B pr6o@ t6hn D: t6o 24ara 3up6o t5wn G, D 24ison 2est6i t5wj 2ap6o t5h@ B. 3rht6on d6e t6o 2ap6o t5h@ B: 3rht6on 24ara <2<2est6i>2> ka6i t6o 3up6o t5wn G, D. -E34urhntai 24ara m4esai dun4amei m4onon s4ummetroi 3rht6on peri4exousai: 34oper 24edei de5icai. $-^P218^-^L13^ <3<####***V####-----<00> ###10AP### ##27L## <00> -----L5hmma -D4uo 2ariqm5wn doq4entwn 2en l4ogwj 3opoiwjo5un ka6i 24allou tin6o@ d4eon poi5hsai 3w@ t6on 2ariqm6on pr6o@ t6on 2ariqm6on o34utw@ to5uton pr6o@ 24allon tin4a. -24Estwsan o3i doq4ente@ d4uo 2ariqmo6i o3i AB, GD l4ogon 24exonte@ pr6o@ 2all4hlou@ 3opoiono5un, 24allo@ d4e ti@ 3o GE. de5i poi5hsai t6o proke4imenon. ^+^ -2Anagegr4afqw g6ar 3up6o t5wn DG, GE parallhl4ogrammon 2orqog4wnion t6o DE, ka6i t5wj DE 24ison par6a t6on AB parabebl4hsqw parallhl4ogrammon t6o BZ pl4ato@ poio5un t6hn AZ. 2epe6i o25un 24ison 2est6i t6o DE parallhl4ogrammon t5wj BZ parallhlogr4ammwj, 24esti d6e a2ut5wj ka6i 2isog4wnion, t5wn d6e 24iswn ka6i 2isogwn4iwn parallhlogr4ammwn 2antipep4onqasin a3i pleura6i a3i per6i t6a@ 24isa@ gwn4ia@, 2an4alogon 24ara 2est6in 3w@ 3o AB pr6o@ t6on GD, o34utw@ 3o GE pr6o@ t6on AZ: 34oper 24edei de5icai.>3> $-^P43^-^L12^ ####***X#### ###PROP### ##28##-------kh41 -M4esa@ e3ure5in dun4amei m4onon summ4etrou@ m4eson peri* exo4usa@. -2Ekke4isqwsan <22> 3rhta6i dun4amei m4onon s4ummetroi a3i, A, B, G, ka6i e2il4hfqw t5wn A, B m4esh 2an4alogon 3h D, ka6i gegon4etw 3w@ 3h B pr6o@ t6hn G, 3h D pr6o@ t6hn E. -2Epe6i a3i A, B 3rhta4i e2isi dun4amei m4onon s4ummetroi, t6o 24ara 3up6o t5wn A, B, tout4esti t6o 2ap6o t5h@ D, m4eson 2est4in. ^+^ m4esh 24ara 3h D. ka6i 2epe6i a3i B, G dun4amei m4onon e2is6i s4ummetroi, ka6i 2estin 3w@ 3h B pr6o@ t6hn G, 3h D pr6o@ t6hn E, ka6i a3i D, E 24ara dun4amei m4onon e2is6i s4ummetroi. m4esh d6e 3h D: m4esh 24ara ka6i 3h E: a3i D, E 24ara m4esai e2is6i dun4amei m4onon s4ummetroi. l4egw d4h, 34oti ka6i m4eson peri4exousin. 2epe6i g4ar 2estin 3w@ 3h B pr6o@ t6hn G, 3h D pr6o@ t6hn E, 2enall6ac 24ara 3w@ 3h B pr6o@ t6hn D, 3h G pr6o@ t6hn E. 3w@ d6e 3h B pr6o@ t6hn D, 3h D pr6o@ t6hn A: ka6i 3w@ 24ara 3h D pr6o@ t6hn A, 3h G pr6o@ t6hn E: t6o 24ara 3up6o t5wn A, G 24ison 2est6i t5wj 3up6o t5wn D, E. m4eson d6e t6o 3up6o t5wn A, G: m4eson 24ara ka6i t6o 3up6o t5wn D, E. -E34urhntai 24ara m4esai dun4amei m4onon s4ummetroi m4eson peri4exousai: 34oper 24edei de5icai. ##29^1^L2^2##-----L5hmma -E3ure5in d4uo tetrag4wnou@ 2ariqmo4u@, 34wste ka6i t6on sugke4imenon 2ec a2ut5wn e25inai tetr4agwnon. -2Ekke4isqwsan d4uo 2ariqmo6i o3i AB, BG, 24estwsan d6e 24htoi 24artioi 26h peritto4i. ka6i 2epe4i, 2e4an te 2ap6o 2art4iou ^-^ 24artio@ 2afaireq5hj, 2e4an te 2ap6o perisso5u periss4o@, 3o loip6o@ 24arti4o@ 2estin, 3h loip6o@ 24ara 3o AG 24arti4o@ 2estin. tetm4hsqw 3o AG d4ixa kat6a t6o D. 24estwsan d6e ka6i o3i AB, BG 24htoi 34omoioi 2ep4ipedoi 26h tetr4agwnoi, o36i ka6i a2uto6i 34omoio4i e2isin ^+^ 2ep4ipedoi: 3o 24ara 2ek t5wn AB, BG met6a to5u 2ap6o <22> GD tetrag4wnou 24iso@ 2est6i t5wj 2ap6o to5u BD tetrag4wnwj. ka6i 2esti tetr4agwno@ 3o 2ek t5wn AB, BG, 2epeid4hper 2ede4ixqh, 34oti, 2e6an d4uo 34omoioi 2ep4ipedoi pollaplasi4asante@ 2all4hlou@ poi5ws4i tina, 3o gen4omeno@ tetr4agwn4o@ 2estin. e34urhntai 24ara d4uo tetr4agwnoi 2ariqmo6i 34o te 2ek t5wn AB, BG ka6i 3o 2ap6o to5u GD, o36i sunteq4ente@ poio5usi t6on 2ap6o to5u BD tetr4a* gwnon. -Ka6i faner4on, 34oti e34urhntai p4alin d4uo tetr4agwnoi 34o te 2ap6o to5u BD ka6i 3o 2ap6o to5u GD, 34wste t6hn 3uperox6hn a2ut5wn t6on 3up6o AB, BG e25inai tetr4agwnon, 34otan o3i AB, BG 34omoioi 25wsin 2ep4ipedoi. 34otan d6e m6h 25wsin 34omoioi 2ep4ipedoi, e34urhntai d4uo tetr4agwnoi 34o te 2ap6o to5u BD ka6i 3o 2ap6o to5u DG, 35wn 3h 3uperox6h 3o 3up6o t5wn AB, BG o2uk 24esti tetr4agwno@: 34oper 24edei de5icai. ##30^1^L2^2##-----L5hmma -E3ure5in d4uo tetrag4wnou@ 2ariqmo4u@, 34wste t6on 2ec a2ut5wn sugke4imenon m6h e25inai tetr4agwnon. -24Estw g6ar 3o 2ek t5wn AB, BG, 3w@ 24efamen, tetr4agwno@, ka6i 24artio@ 3o GA, ka6i tetm4hsqw 3o GA d4ixa t5wj D. faner6on d4h, 34oti 3o 2ek t5wn AB, BG tetr4agwno@ met6a to5u 2ap6o <22> ^+^ GD tetrag4wnou 24iso@ 2est6i t5wj 2ap6o <22> BD tetrag4wnwj: 2afhjr4hsqw mon6a@ 3h DE: 3o 24ara 2ek t5wn AB, BG met6a to5u 2ap6o <22> GE 2el4asswn 2est6i to5u 2ap6o <22> BD tetrag4wnou. l4egw o25un, 34oti 3o 2ek t5wn AB, BG tetr4agwno@ met6a to5u 2ap6o <22> GE o2uk 24estai tetr4agwno@. -E2i g6ar 24estai tetr4agwno@, 24htoi 24iso@ 2est6i t5wj 2ap6o <22> BE 26h 2el4asswn to5u 2ap6o <22> BE, o2uk4eti d6e ka6i me4izwn, 34ina m6h tmhq5hj 3h mon4a@. 24estw, e2i dunat4on, pr4oteron 3o 2ek t5wn AB, BG met6a to5u 2ap6o GE 24iso@ t5wj 2ap6o BE, ka6i 24estw t5h@ DE mon4ado@ diplas4iwn 3o HA. 2epe6i o25un 34olo@ 3o AG 34olou to5u GD 2esti diplas4iwn, 35wn 3o AH to5u DE 2esti diplas4iwn, ka6i loip6o@ 24ara 3o HG loipo5u to5u EG 2esti diplas4iwn: d4ixa 24ara t4etmhtai 3o HG t5wj E. 3o 24ara 2ek t5wn HB, BG met6a to5u 2ap6o GE 24iso@ 2est6i t5wj 2ap6o BE tetrag4wnwj. 2all6a ka6i 3o 2ek t5wn AB, BG met6a to5u 2ap6o GE 24iso@ 3up4okeitai t5wj 2ap6o <22> BE tetrag4wnwj: 3o 24ara 2ek t5wn ^+^ HB, BG met6a to5u 2ap6o GE 24iso@ 2est6i t5wj 2ek t5wn AB, BG met6a to5u 2ap6o GE. ka6i koino5u 2afaireq4ento@ to5u 2ap6o GE sun4agetai 3o AB 24iso@ t5wj HB: 34oper 24atopon. o2uk 24ara 3o 2ek t5wn AB, BG met6a to5u 2ap6o <22> GE 24iso@ 2est6i t5wj 2ap6o BE. l4egw d4h, 34oti o2ud6e 2el4asswn to5u 2ap6o BE. e2i g6ar dunat4on, 24estw t5wj 2ap6o BZ 24iso@, ka6i to5u DZ diplas4iwn 3o QA. ka6i sunaxq4hsetai p4alin diplas4iwn 3o QG to5u GZ: 34wste ka6i t6on GQ d4ixa tetm5hsqai kat6a t6o Z, ka6i di6a to5uto t6on 2ek t5wn QB, BG met6a to5u 2ap6o ZG 24ison g4inesqai t5wj 2ap6o BZ. 3up4okeitai d6e ka6i 3o 2ek t5wn AB, BG met6a to5u 2ap6o GE 24iso@ t5wj 2ap6o BZ. 34wste ka6i 3o 2ek t5wn QB, BG met6a to5u 2ap6o GZ 24iso@ 24estai t5wj 2ek t5wn AB, BG met6a to5u 2ap6o GE: 34oper 24atopon. o2uk 24ara 3o 2ek t5wn AB, BG met6a to5u 2ap6o GE 24iso@ 2est6i <22> 2el4assoni to5u 2ap6o BE. 2ede4ixqh d4e, 34oti o2ud6e <22> t5wj 2ap6o BE. o2uk 24ara 3o ^-^ 2ek t5wn AB, BG met6a to5u 2ap6o GE tetr4agwn4o@ 2estin. <22> ^+^ <22> 34oper 24edei de5icai. ##29##-------kq41 -E3ure5in d4uo 3rht6a@ dun4amei m4onon summ4etrou@, 34wste t6hn me4izona t5h@ 2el4assono@ me5izon d4unasqai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. -2Ekke4isqw g4ar ti@ 3rht6h 3h AB ka6i d4uo tetr4agwnoi 2ariqmo6i o3i GD, DE, 34wste t6hn 3uperox6hn a2ut5wn t6on GE m6h e25inai tetr4agwnon, ka6i gegr4afqw 2ep6i t5h@ AB 3hmik4uklion t6o AZB, ka6i pepoi4hsqw 3w@ 3o DG pr6o@ t6on GE, o34utw@ t6o 2ap6o t5h@ BA tetr4agwnon pr6o@ t6o 2ap6o t5h@ AZ tetr4agwnon ka6i 2epeze4uxqw 3h ZB. -2Epe6i <22> 2estin 3w@ t6o 2ap6o t5h@ BA pr6o@ t6o 2ap6o t5h@ AZ, o34utw@ 3o DG pr6o@ t6on GE, t6o 2ap6o t5h@ BA 24ara pr6o@ t6o 2ap6o t5h@ AZ l4ogon 24exei, 36on 2ariqm6o@ 3o DG pr6o@ 2ariqm6on t6on GE: s4ummetron 24ara 2est6i t6o 2ap6o t5h@ BA t5wj 2ap6o t5h@ AZ. 3rht6on d6e t6o 2ap6o t5h@ AB: 3rht6on 24ara ka6i t6o 2ap6o t5h@ AZ: 3rht6h 24ara ka6i 3h AZ. ka6i 2epe6i 3o DG pr6o@ t6on GE l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o 2ap6o t5h@ BA 24ara pr6o@ t6o 2ap6o t5h@ ^+^ AZ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h AB t5hj AZ m4hkei: a3i BA, AZ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. ka6i 2epe4i <2<2estin>2> 3w@ 3o DG pr6o@ t6on GE, o34utw@ t6o 2ap6o t5h@ BA pr6o@ t6o 2ap6o t5h@ AZ, 2anastr4eyanti 24ara 3w@ 3o GD pr6o@ t6on DE, o34utw@ t6o 2ap6o t5h@ AB pr6o@ t6o 2ap6o t5h@ BZ. 3o d6e GD pr6o@ t6on DE l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i t6o 2ap6o t5h@ AB 24ara pr6o@ t6o 2ap6o t5h@ BZ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: s4ummetro@ 24ara 2est6in 3h AB t5hj BZ m4hkei. ka6i 2esti t6o 2ap6o t5h@ AB 24ison to5i@ 2ap6o t5wn AZ, ZB: 3h AB 24ara t5h@ AZ me5izon d4unatai t5hj BZ summ4etrwj 3eaut5hj. -E34urhntai 24ara d4uo 3rhta6i dun4amei m4onon s4ummetroi a3i BA, AZ, 34wste t6hn me4izona t6hn AB t5h@ 2el4assono@ t5h@ AZ me5izon d4unasqai t5wj 2ap6o t5h@ BZ summ4etrou 3eaut5hj m4hkei: 34oper 24edei de5icai. $-^P219^-^L12^ <3<####***V####-----<00> ###10AP### ##29L## <00> -----L5hmma e2i@ t6o kq41 -D4uo 2ariqm5wn doq4entwn ka6i e2uqe4ia@ d4eon poi5hsai 3w@ t6on 2ariqm6on pr6o@ t6on 2ariqm4on, o34utw@ t6o 2ap6o t5h@ e2uqe4ia@ tetr4agwnon pr6o@ t6o 2ap' 24allh@ tin4o@. -24Estwsan o3i doq4ente@ d4uo 2ariqmo6i o3i A, B, e2uqe5ia d6e 3h G, ka6i d4eon 2est6i poi5hsai t6o proke4imenon. pepoi4hsqw g6ar 3w@ 3o A pr6o@ t6on B, 3h G e2uqe5ia pr6o@ 24allhn tin6a t6hn D, ka6i e2il4hfqw t5wn G, D m4esh 2an4alogon 3h E. 2epe6i o25un 2estin 3w@ 3o A pr6o@ t6on B, 3h G e2uqe5ia pr6o@ t6hn D, 2all' 3w@ 3h G pr6o@ t6hn D, t6o 2ap6o t5h@ G pr6o@ t6o 2ap6o t5h@ E, 3w@ 24ara 3o A pr6o@ t6on B, t6o 2ap6o t5h@ G pr6o@ t6o 2ap6o t5h@ E tetr4agwnon. ^+^>3> $-^P49^-^L17^ ####***X#### ###PROP### ##30##-------l41 -E3ure5in d4uo 3rht6a@ dun4amei m4onon summ4etrou@, 34wste t6hn me4izona t5h@ 2el4assono@ me5izon d4unasqai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei. -2Ekke4isqw 3rht6h 3h AB ka6i d4uo tetr4agwnoi 2ariqmo6i o3i GE, ED, 34wste t6on sugke4imenon 2ec a2ut5wn t6on GD m6h ^+^ e25inai tetr4agwnon, ka6i gegr4afqw 2ep6i t5h@ AB 3hmik4uklion t6o AZB, ka6i pepoi4hsqw 3w@ 3o DG pr6o@ t6on GE, o34utw@ t6o 2ap6o t5h@ BA pr6o@ t6o 2ap6o t5h@ AZ, ka6i 2epeze4uxqw 3h ZB. -3Omo4iw@ d6h de4icomen t5wj pr6o to4utou, 34oti a3i BA, AZ 3rhta4i e2isi dun4amei m4onon s4ummetroi. ka6i 2epe4i 2estin 3w@ 3o DG pr6o@ t6on GE, o34utw@ t6o 2ap6o t5h@ BA pr6o@ t6o 2ap6o t5h@ AZ, 2anastr4eyanti 24ara 3w@ 3o GD pr6o@ t6on DE, o34utw@ t6o 2ap6o t5h@ AB pr6o@ t6o 2ap6o t5h@ BZ. 3o d6e GD pr6o@ t6on DE l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ AB pr6o@ t6o 2ap6o t5h@ BZ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h AB t5hj BZ m4hkei. ka6i d4unatai 3h AB t5h@ AZ me5izon t5wj 2ap6o t5h@ ZB 2asumm4etrou 3eaut5hj. -A3i AB, AZ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h AB t5h@ AZ me5izon d4unatai t5wj 2ap6o t5h@ ZB 2asumm4etrou 3eaut5hj m4hkei: 34oper 24edei de5icai. ^+^ ##31##-------la41 -E3ure5in d4uo m4esa@ dun4amei m4onon summ4etrou@ 3rht6on periexo4usa@, 34wste t6hn me4izona t5h@ 2el4assono@ me5izon d4unasqai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. -2Ekke4isqwsan d4uo 3rhta6i dun4amei m4onon s4ummetroi a3i A, B, 34wste t6hn A me4izona o25usan t5h@ 2el4assono@ t5h@ B me5izon d4unasqai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. ka6i t5wj 3up6o t5wn A, B 24ison 24estw t6o 2ap6o t5h@ G. m4eson d6e t6o 3up6o t5wn A, B: m4eson 24ara ka6i t6o 2ap6o t5h@ G: m4esh 24ara ka6i 3h G. t5wj d6e 2ap6o t5h@ B 24ison 24estw t6o 3up6o t5wn G, D. 3rht6on d6e t6o 2ap6o t5h@ B: 3rht6on 24ara ka6i t6o 3up6o t5wn G, D. ka6i 2epe4i 2estin 3w@ 3h A pr6o@ t6hn B, o34utw@ t6o 3up6o t5wn A, B pr6o@ t6o 2ap6o t5h@ B, 2all6a t5wj m6en 3up6o t5wn A, B 24ison 2est6i t6o 2ap6o t5h@ G, t5wj d6e 2ap6o t5h@ B 24ison t6o 3up6o t5wn G, D, 3w@ 24ara 3h A pr6o@ t6hn B, o34utw@ t6o 2ap6o t5h@ G pr6o@ t6o 3up6o t5wn G, D. 3w@ d6e t6o 2ap6o t5h@ G pr6o@ t6o 3up6o t5wn G, D, o34utw@ 3h G pr6o@ t6hn D: ka6i 3w@ 24ara 3h A pr6o@ t6hn B, o34utw@ 3h G pr6o@ t6hn D. s4ummetro@ d6e 3h A t5hj B dun4amei m4onon: s4ummetro@ 24ara ka6i 3h G t5hj D dun4amei m4onon. ka4i 2esti m4esh 3h G: m4esh 24ara ka6i 3h D. ka6i 2epe4i 2estin 3w@ 3h A pr6o@ t6hn B, 3h G pr6o@ t6hn D, 3h d6e A t5h@ B me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h G 24ara t5h@ D me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. ^+^ -E34urhntai 24ara d4uo m4esai dun4amei m4onon s4ummetroi a3i G, D 3rht6on peri4exousai, ka6i 3h G t5h@ D me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. -3Omo4iw@ d6h deixq4hsetai ka6i t5wj 2ap6o 2asumm4etrou, 34otan 3h A t5h@ B me5izon d4unhtai t5wj 2ap6o 2asumm4etrou 3eaut5hj. $-^P220^-^L0^ <3<####***V####-----<00> ###10AP### ##31L## <00> -----L5hmma e2i@ t6o la41 -2E6an 25wsi d4uo e2uqe5iai 2en l4ogwj tin4i, 24estai 3w@ 3h e2uqe5ia pr6o@ t6hn e2uqe5ian, o34utw@ t6o 3up6o t5wn d4uo pr6o@ t6o 2ap6o t5h@ 2elax4isth@. -24Estwsan d6h d4uo e2uqe5iai a3i AB, BG 2en l4ogwj tin4i: l4egw, 34oti 2est6in 3w@ 3h AB pr6o@ t6hn BG, o34utw@ t6o 3up6o t5wn AB, BG pr6o@ t6o 2ap6o t5h@ BG. 2anagegr4afqw g6ar 2ap6o t5h@ BG tetr4agwnon t6o BDEG, ka6i sumpeplhr4wsqw t6o AD parallhl4ogrammon. faner6on d4h, 34oti 2est6in 3w@ 3h AB pr6o@ t6hn BG, o34utw@ t6o AD parallhl4ogrammon pr6o@ t6o BE parallhl4ogrammon. ka4i 2esti t6o m6en AD t6o 3up6o t5wn AB, BG: 24ish g6ar 3h BG t5hj BD: t6o d6e BE t6o 2ap6o t5h@ BG: 3w@ 24ara 3h AB pr6o@ t6hn BG, o34utw@ t6o 3up6o t5wn AB, BG pr6o@ t6o 2ap6o t5h@ BG: 34oper 24edei de5icai.>3> $-^P52^-^L6^ ####***X#### ###PROP### ##32##-------lb41 -E3ure5in d4uo m4esa@ dun4amei m4onon summ4etrou@ m4eson periexo4usa@, 34wste t6hn me4izona t5h@ 2el4assono@ me5izon d4unasqai t5wj 2ap6o summ4etrou 3eaut5hj. -2Ekke4isqwsan tre5i@ 3rhta6i dun4amei m4onon s4ummetroi a3i A, B, G, 34wste t6hn A t5h@ G me5izon d4unasqai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i t5wj m6en 3up6o t5wn A, B 24ison 24estw t6o 2ap6o t5h@ D. m4eson 24ara t6o 2ap6o t5h@ D: ka6i 3h D 24ara m4esh 2est4in. t5wj d6e 3up6o t5wn B, G 24ison 24estw t6o 3up6o t5wn D,E. ka6i 2epe4i 2estin 3w@ t6o 3up6o t5wn A, B pr6o@ t6o 3up6o t5wn B, G, o34utw@ 3h A pr6o@ t6hn G, 2all6a t5wj m6en 3up6o t5wn A, B 24ison 2est6i t6o 2ap6o t5h@ D, t5wj d6e 3up6o t5wn B, G 24ison t6o 3up6o t5wn D, E, 24estin 24ara 3w@ 3h A pr6o@ t6hn G, ^+^ o34utw@ t6o 2ap6o t5h@ D pr6o@ t6o 3up6o t5wn D, E. 3w@ d6e t6o 2ap6o t5h@ D pr6o@ t6o 3up6o t5wn D, E, o34utw@ 3h D pr6o@ t6hn E: ka6i 3w@ 24ara 3h A pr6o@ t6hn G, o34utw@ 3h D pr6o@ t6hn E: s4ummetro@ d6e 3h A t5hj G dun4amei <22>. s4ummetro@ 24ara ka6i 3h D t5hj E dun4amei m4onon. m4esh d6e 3h D: m4esh 24ara ka6i 3h E. ka6i 2epe4i 2estin 3w@ 3h A pr6o@ t6hn G, 3h D pr6o@ t6hn E, 3h d6e A t5h@ G me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h D 24ara t5h@ E me5izon dun4hsetai t5wj 2ap6o summ4etrou 3eaut5hj. l4egw d4h, 34oti ka6i m4eson 2est6i t6o 3up6o t5wn D, E. 2epe6i g6ar 24ison 2est6i t6o 3up6o t5wn B, G t5wj 3up6o t5wn D, E, m4eson d6e t6o 3up6o t5wn B, G <22>, m4eson 24ara ka6i t6o 3up6o t5wn D, E. -E34urhntai 24ara d4uo m4esai dun4amei m4onon s4ummetroi a3i D, E m4eson peri4exousai, 34wste t6hn me4izona t5h@ 2el4assono@ me5izon d4unasqai t5wj 2ap6o summ4etrou 3eaut5hj. -3Omo4iw@ d6h p4alin deixq4hsetai ka6i t5wj 2ap6o 2asumm4etrou, 34otan 3h A t5h@ G me5izon d4unhtai t5wj 2ap6o 2asumm4etrou 3eaut5hj. $-^P220^-^L16^ <3<####***V####-----<00> ###10AP### ##32L## <00> -----L5hmma e2i@ t6o lb41 -2E6an 25wsi tre5i@ e2uqe5iai 2en l4ogwj tin4i, 24estai 3w@ 3h pr4wth pr6o@ t6hn tr4ithn, o34utw@ t6o 3up6o t5h@ pr4wth@ ka6i m4esh@ pr6o@ t6o 3up6o t5h@ m4esh@ ka6i 2elax4isth@. ^+^ -24Estwsan tre5i@ e2uqe5iai 2en l4ogwj tin6i a3i AB, BG, GD: l4egw, 34oti 2est6in 3w@ 3h AB pr6o@ t6hn GD, o34utw@ t6o 3up6o t5wn AB, BG pr6o@ t6o 3up6o t5wn BG, GD. -24Hxqw g6ar 2ap6o to5u A shme4iou t5hj AB pr6o@ 2orq6a@ 3h AE, ka6i ke4isqw t5hj BG 24ish 3h AE, ka6i di6a to5u E shme4iou t5hj AD e2uqe4iaj par4allhlo@ 24hxqw 3h EK, di6a d6e t5wn B, G, D shme4iwn t5hj AE par4allhloi 24hxqwsan a3i ZB, GQ, DK. ka6i 2epe4i 2estin 3w@ 3h AB pr6o@ t6hn BG, o34utw@ t6o AZ parallhl4ogrammon pr6o@ t6o BQ parallhl4ogrammon, 3w@ d6e 3h BG pr6o@ t6hn GD, o34utw@ t6o BQ pr6o@ t6o GK, di' 24isou 24ara 3w@ 3h AB pr6o@ t6hn GD, o34utw@ t6o AZ parallhl4ogrammon pr6o@ t6o GK parallhl4ogrammon. ka4i 2esti t6o m6en AZ t6o 3up6o t5wn AB, BG: 24ish g6ar 3h AE t5hj BG: t6o d6e GK t6o 3up6o t5wn BG, GD: 24ish g6ar 3h BG t5hj GQ. -2E6an 24ara tre5i@ 25wsin e2uqe5iai 2en l4ogwj tin4i, 24estai 3w@ 3h pr4wth pr6o@ t6hn tr4ithn, o34utw@ t6o 3up6o t5h@ pr4wth@ ka6i m4esh@ pr6o@ t6o 3up6o t5h@ m4esh@ ka6i tr4ith@: 34oper 24edei de5icai. ^+^>3> $-^P53^-^L19^ ####***X#### ###PROP### ##32^1^L^2##-----L5hmma -24Estw tr4igwnon 2orqog4wnion t6o ABG 2orq6hn 24exon t6hn A, ka6i 24hxqw k4aqeto@ 3h AD: l4egw, 34oti t6o m6en 3up6o t5wn ^+^ GBD 24ison 2est6i t5wj 2ap6o t5h@ BA, t6o d6e 3up6o t5wn BGD 24ison t5wj 2ap6o t5h@ GA, ka6i t6o 3up6o t5wn BD, DG 24ison t5wj 2ap6o t5h@ AD, ka6i 24eti t6o 3up6o t5wn BG, AD 24ison <2<2est6i>2> t5wj 3up6o t5wn BA, AG. -Ka6i pr5wton, 34oti t6o 3up6o t5wn GBD 24ison <2<2est6i>2> t5wj ^-^ 2ap6o t5h@ BA. -2Epe6i g6ar 2en 2orqogwn4iwj trig4wnwj 2ap6o t5h@ 2orq5h@ gwn4ia@ 2ep6i t6hn b4asin k4aqeto@ 25hktai 3h AD, t6a ABD, ADG 24ara tr4igwna 34omoi4a 2esti t5wj te 34olwj t5wj ABG ka6i 2all4hloi@. ka6i 2epe6i 34omoi4on 2esti t6o ABG tr4igwnon t5wj ABD trig4wnwj, 24estin 24ara 3w@ 3h GB pr6o@ t6hn BA, o34utw@ 3h BA pr6o@ t6hn BD: t6o 24ara 3up6o t5wn GBD 24ison 2est6i t5wj 2ap6o t5h@ AB. -Di6a t6a a2ut6a d6h ka6i t6o 3up6o t5wn BGD 24ison 2est6i t5wj 2ap6o t5h@ AG. -Ka6i 2epe4i, 2e6an 2en 2orqogwn4iwj trig4wnwj 2ap6o t5h@ 2orq5h@ gwn4ia@ 2ep6i t6hn b4asin k4aqeto@ 2axq5hj, 3h 2axqe5isa t5wn t5h@ b4asew@ tmhm4atwn m4esh 2an4alog4on 2estin, 24estin 24ara 3w@ 3h BD pr6o@ t6hn DA, o34utw@ 3h AD pr6o@ t6hn DG: t6o 24ara 3up6o t5wn BD, DG 24ison 2est6i t5wj 2ap6o t5h@ DA. -L4egw, 34oti ka6i t6o 3up6o t5wn BG, AD 24ison 2est6i t5wj 3up6o t5wn BA, AG. 2epe6i g4ar, 3w@ 24efamen, 34omoi4on 2esti t6o ABG ^+^ t5wj ABD, 24estin 24ara 3w@ 3h BG pr6o@ t6hn GA, o34utw@ 3h BA pr6o@ t6hn AD. <2<2e6an d6e t4essare@ e2uqe5iai 2an4alogon 25wsin, t6o 3up6o t5wn 24akrwn 24ison 2est6i t5wj 3up6o t5wn m4eswn.>2> t6o ^-^ 24ara 3up6o t5wn BG, AD 24ison 2est6i t5wj 3up6o t5wn BA, AG: $-^P222^-^L0^ <3<####PBF&####-----<00> ###10AP### ##32LALT## <00> -26H ka6i 34oti, 2e6an 2anagr4aywmen t6o EG 2orqog4wnion parallhl4ogrammon ka6i sumplhr4wswmen t6o AZ, 24ison 24estai t6o EG t5wj AZ: 3ek4ateron g6ar a2ut5wn dipl4asi4on 2esti to5u ABG trig4wnou. ka4i 2esti t6o m6en EG t6o 3up6o t5wn BG, AD, t6o d6e AZ t6o 3up6o t5wn BA, AG. t6o 24ara 3up6o t5wn BG, AD 24ison 2est6i t5wj 3up6o t5wn BA, AG.>3> $-^P55^-^L4^ ####***X#### ###PROP### 34oper 24edei de5icai. ##33##-------lg41 -E3ure5in d4uo e2uqe4ia@ dun4amei 2asumm4etrou@ poio4usa@ t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d' 3up' a2ut5wn m4eson. -2Ekke4isqwsan d4uo 3rhta6i dun4amei m4onon s4ummetroi a3i AB, BG, 34wste t6hn me4izona t6hn AB t5h@ 2el4assono@ t5h@ BG me5izon d4unasqai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i tetm4hsqw 3h BG d4ixa kat6a t6o D, ka6i t5wj 2af' 3opot4era@ t5wn BD, DG 24ison par6a t6hn AB parabebl4hsqw parallhl4ogrammon 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn AEB, ka6i gegr4afqw 2ep6i t5h@ AB 3hmik4uklion t6o AZB, ka6i 24hxqw t5hj AB pr6o@ 2orq6a@ 3h EZ, ka6i 2epeze4uxqwsan a3i AZ, ZB. -Ka6i 2epe6i <22> e2uqe5iai 24aniso4i e2isin a3i AB, BG, ka6i ^-^ 3h ^+^ AB t5h@ BG me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj, t5wj d6e tet4artwj to5u 2ap6o t5h@ BG, tout4esti t5wj 2ap6o t5h@ 3hmise4ia@ a2ut5h@, 24ison par6a t6hn AB parab4eblhtai parallhl4ogrammon 2elle5ipon e24idei tetrag4wnwj ka6i poie5i t6o 3up6o t5wn AEB, 2as4ummetro@ 24ara 2est6in 3h AE t5hj EB. ka4i 2estin 3w@ 3h AE pr6o@ EB, o34utw@ t6o 3up6o t5wn BA, AE pr6o@ t6o 3up6o t5wn AB, BE, 24ison d6e t6o m6en 3up6o t5wn BA, AE t5wj 2ap6o t5h@ AZ, t6o d6e 3up6o t5wn AB, BE t5wj 2ap6o t5h@ BZ: 2as4ummetron 24ara 2est6i t6o 2ap6o t5h@ AZ t5wj 2ap6o t5h@ ZB: a3i AZ, ZB 24ara dun4amei e2is6in 2as4ummetroi. ka6i 2epe6i 3h AB 3rht4h 2estin, 3rht6on 24ara 2est6i ka6i t6o 2ap6o t5h@ AB: 34wste ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AZ, ZB 3rht4on 2estin. ka6i 2epe6i p4alin t6o 3up6o t5wn AE, EB 24ison 2est6i t5wj 2ap6o t5h@ EZ, 3up4okeitai d6e t6o 3up6o t5wn AE, EB ka6i t5wj 2ap6o t5h@ BD 24ison, 24ish 24ara 2est6in 3h ZE t5hj BD: dipl5h 24ara 3h BG t5h@ ZE: 34wste ka6i t6o 3up6o t5wn AB, BG s4ummetr4on 2esti t5wj 3up6o t5wn AB, EZ. m4eson d6e t6o 3up6o t5wn AB, BG: m4eson 24ara ka6i t6o 3up6o t5wn AB, EZ. 24ison d6e t6o 3up6o t5wn AB, EZ t5wj 3up6o t5wn AZ, ZB: m4eson 24ara ka6i t6o 3up6o ^+^ t5wn AZ, ZB. 2ede4ixqh d6e ka6i 3rht6on t6o sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn. -E34urhntai 24ara d4uo e2uqe5iai dun4amei 2as4ummetroi a3i AZ, ZB poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d6e 3up' a2ut5wn m4eson: 34oper 24edei de5icai. $-^P222^-^L6^ <3<####***V####-----<00> ###10AP### ##33L## <00> -----L5hmma e2i@ t6o lg41 -2E6an e2uqe5ia gramm6h tmhq5hj e2i@ 24anisa, 24estai 3w@ 3h e2uqe5ia pr6o@ t6hn e2uqe5ian, o34utw@ t6o 3up6o t5h@ 34olh@ ka6i t5h@ me4izono@ pr6o@ t6o 3up6o t5h@ 34olh@ ka6i t5h@ 2el4attono@. -E2uqe5ia g4ar ti@ 3h AB tetm4hsqw e2i@ 24anisa kat6a t6o E: l4egw, 34oti 3w@ 3h AE pr6o@ t6hn EB, o34utw@ t6o 3up6o t5wn BA, AE pr6o@ t6o 3up6o t5wn AB, BE. -2Anagegr4afqw g6ar 2ap6o t5h@ AB tetr4agwnon t6o AGDB, ka6i di6a to5u E shme4iou 3opot4eraj t5wn AG, BD par4allhlo@ 24hxqw 3h EZ. faner6on o25un, 34oti 3w@ 3h AE pr6o@ ^+^ t6hn EB, o34utw@ t6o AZ parallhl4ogrammon pr6o@ t6o ZB parallhl4ogrammon. ka4i 2esti t6o m6en AZ t6o 3up6o t5wn BA, AE: 24ish g6ar 3h AG t5hj AB: t6o d6e ZB t6o 3up6o t5wn AB, BE: 24ish g6ar 3h BD t5hj AB. 3w@ 24ara 3h AE pr6o@ t6hn EB, o34utw@ t6o 3up6o t5wn BA, AE pr6o@ t6o 3up6o t5wn AB, BE: 34oper 24edei de5icai.>3> $-^P57^-^L7^ ####***X#### ###PROP### ##34##-------ld41 -E3ure5in d4uo e2uqe4ia@ dun4amei 2asumm4etrou@ poio4usa@ t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on. -2Ekke4isqwsan d4uo m4esai dun4amei m4onon s4ummetroi a3i AB, BG 3rht6on peri4exousai t6o 3up' a2ut5wn, 34wste t6hn AB t5h@ BG me5izon d4unasqai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i gegr4afqw 2ep6i t5h@ AB t6o ADB 3hmik4uklion, ka6i tetm4hsqw 3h BG d4ixa kat6a t6o E, ka6i parabebl4hsqw par6a t6hn AB t5wj 2ap6o t5h@ BE 24ison parallhl4ogrammon 2elle5ipon e24idei tetrag4wnwj t6o 3up6o t5wn AZB: 2as4ummetro@ 24ara <2<2est6in>2> 3h AZ t5hj ZB m4hkei. ka6i 24hxqw 2ap6o to5u Z t5hj AB pr6o@ 2orq6a@ 3h ZD, ka6i 2epeze4uxqwsan a3i AD, DB. ^+^ -2Epe6i 2as4ummetr4o@ 2estin 3h AZ t5hj ZB, 2as4ummetron 24ara 2est6i ka6i t6o 3up6o t5wn BA, AZ t5wj 3up6o t5wn AB, BZ. 24ison d6e t6o m6en 3up6o t5wn BA, AZ t5wj 2ap6o t5h@ AD, t6o d6e 3up6o t5wn AB, BZ t5wj 2ap6o t5h@ DB: 2as4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ AD t5wj 2ap6o t5h@ DB. ka6i 2epe6i m4eson 2est6i t6o 2ap6o t5h@ AB, m4eson 24ara ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AD, DB. ka6i 2epe6i dipl5h 2estin 3h BG t5h@ DZ, dipl4asion 24ara ka6i t6o 3up6o t5wn AB, BG to5u 3up6o t5wn AB, ZD. 3rht6on d6e t6o 3up6o t5wn AB, BG: 3rht6on 24ara ka6i t6o 3up6o t5wn AB, ZD. t6o d6e 3up6o t5wn AB, ZD 24ison t5wj 3up6o t5wn AD, DB: 34wste ka6i t6o 3up6o t5wn AD, DB 3rht4on 2estin. -E34urhntai 24ara d4uo e2uqe5iai dun4amei 2as4ummetroi a3i AD, DB poio5usai t6o <22> sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on: 34oper 24edei de5icai. $-^P223^-^L6^ <3<####***V####-----<00> ###10AP### <00> ##34L## <00> ##34L##-----L5hmma -2E6an 25wsi d4uo e2uqe5iai 24anisoi, tmhq5hj d6e 3h 2elax4isth a2ut5wn e2i@ 24isa, t6o 3up6o t5wn d4uo e2uqei5wn dipl4asion 24estai to5u t5h@ me4izono@ ka6i t5h@ 3hmise4ia@ t5h@ 2elax4isth@. -24Estwsan d4uo e2uqe5iai 24anisoi a3i AB, BG, 35wn me4izwn 24estw 3h AB, ka6i tetm4hsqw 3h BG d4ixa kat6a t6o D: l4egw, 34oti t6o 3up6o t5wn AB, BG dipl4asi4on 2esti to5u 3up6o t5wn AB, BD. -24Hxqw g6ar 2ap6o to5u B shme4iou t5hj BG pr6o@ 2orq6a@ 3h BE, ka6i ke4isqw t5hj BA 24ish 3h BE, ka6i katagegr4afqw t6o sx5hma. 2epe6i o25un 2estin 3w@ 3h DB pr6o@ t6hn DG, o34utw@ t6o BZ pr6o@ t6o DH, sunq4enti 24ara 3w@ 3h BG pr6o@ t6hn DG, o34utw@ t6o BH pr6o@ t6o DH: diplas4iwn d4e 2estin 3h BG t5h@ DG: dipl4asion 24ara 2est6i ka6i t6o BH to5u DH. ka4i 2esti t6o m6en BH t6o 3up6o t5wn AB, BG: 24ish g6ar 3h AB t5hj BE: t6o d6e DH t6o 3up6o t5wn AB, BD: 24ish g6ar t5hj m6en BD 3h DG, t5hj d6e AB 3h DZ: 34oper 24edei de5icai. ^+^>3> $-^P58^-^L16^ ####***X#### ###PROP### ##35##-------le41 -E3ure5in d4uo e2uqe4ia@ dun4amei 2asumm4etrou@ poio4usa@ t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson ka6i t6o 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t5wj sugkeim4enwj 2ek t5wn 2ap' a2ut5wn tetrag4wnwj. ^+^ -2Ekke4isqwsan d4uo m4esai dun4amei m4onon s4ummetroi a3i AB, BG m4eson peri4exousai, 34wste t6hn AB t5h@ BG me5izon d4unasqai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i gegr4afqw 2ep6i t5h@ AB 3hmik4uklion t6o ADB, ka6i t6a loip6a gegon4etw to5i@ 2ep4anw 3omo4iw@. -Ka6i 2epe6i 2as4ummetr4o@ 2estin 3h AZ t5hj ZB m4hkei, 2as4ummetr4o@ 2esti ka6i 3h AD t5hj DB dun4amei. ka6i 2epe6i m4eson 2est6i t6o 2ap6o t5h@ AB, m4eson 24ara ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AD, DB. ka6i 2epe6i t6o 3up6o t5wn AZ, ZB 24ison 2est6i t5wj 2af' 3ekat4era@ t5wn BE, DZ, 24ish 24ara 2est6in 3h BE t5hj DZ: dipl5h 24ara 3h BG t5h@ ZD: 34wste ka6i t6o 3up6o t5wn AB, BG dipl4asi4on 2esti to5u 3up6o t5wn AB, ZD. m4eson d6e t6o 3up6o t5wn AB, BG: m4eson 24ara ka6i t6o 3up6o t5wn AB, ZD. ka4i 2estin 24ison t5wj 3up6o t5wn AD, DB: m4eson 24ara ka6i t6o 3up6o t5wn AD, DB. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h AB t5hj BG m4hkei, s4ummetro@ d6e 3h GB t5hj BE, 2as4ummetro@ 24ara ka6i 3h AB t5hj BE m4hkei: 34wste ka6i t6o 2ap6o t5h@ AB t5wj 3up6o t5wn AB, BE 2as4ummetr4on 2estin. 2all6a t5wj m6en 2ap6o t5h@ AB 24isa 2est6i t6a 2ap6o t5wn AD, DB, t5wj d6e 3up6o t5wn AB, ^+^ BE 24ison 2est6i t6o 3up6o t5wn AB, ZD, tout4esti t6o 3up6o t5wn AD, DB: 2as4ummetron 24ara 2est6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AD, DB t5wj 3up6o t5wn AD, DB. -E34urhntai 24ara d4uo e2uqe5iai a3i AD, DB dun4amei 2as4ummetroi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn m4eson ka6i t6o 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t5wj sugkeim4enwj 2ek t5wn 2ap' a2ut5wn tetrag4wnwn: 34oper 24edei de5icai. ##36##-------lst41 -2E6an d4uo 3rhta6i dun4amei m4onon s4ummetroi sunteq5wsin, 3h 34olh 24alog4o@ 2estin, kale4isqw d6e 2ek d4uo 2onom4atwn. -Sugke4isqwsan g6ar d4uo 3rhta6i dun4amei m4onon s4ummetroi a3i AB, BG: l4egw, 34oti 34olh 3h AG 24alog4o@ 2estin. -2Epe6i g6ar 2as4ummetr4o@ 2estin 3h AB t5hj BG m4hkei: dun4amei g6ar m4onon e2is6i s4ummetroi: 3w@ d6e 3h AB pr6o@ t6hn BG, o34utw@ t6o 3up6o t5wn ABG pr6o@ t6o 2ap6o t5h@ BG, 2as4ummetron 24ara 2est6i t6o 3up6o t5wn AB, BG t5wj 2ap6o t5h@ BG. 2all6a t5wj m6en 3up6o t5wn AB, BG s4ummetr4on 2esti t6o ^+^ d6i@ 3up6o t5wn AB, BG, t5wj d6e 2ap6o t5h@ BG s4ummetr4a 2esti t6a 2ap6o t5wn AB, BG: a3i g6ar AB, BG 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2as4ummetron 24ara 2est6i t6o d6i@ 3up6o t5wn AB, BG to5i@ 2ap6o t5wn AB, BG. ka6i sunq4enti t6o d6i@ 3up6o t5wn AB, BG met6a t5wn 2ap6o t5wn AB, BG, tout4esti t6o 2ap6o t5h@ AG, 2as4ummetr4on 2esti t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn AB, BG. 3rht6on d6e t6o sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG: 24alogon 24ara <2<2est6i>2> t6o 2ap6o t5h@ AG: 34wste ka6i 3h AG 24alog4o@ 2estin, kale4isqw d6e 2ek d4uo 2onom4atwn: $-^P224^-^L0^ <3<####PBFb####-----<00> ###10AP### ##36## <00> -2Ek4alese d6e a2ut6hn 2ek d4uo 2onom4atwn di6a t6o 2ek d4uo 3rht5wn a2ut6hn sugke5isqai k4urion 24onoma kal5wn t6o 3rht4on, kaq' 36o 3rht4on.>3> $-^P61^-^L10^ ####***X#### ###PROP### 34oper 24edei de5icai. ##37##-------lz41 -2E6an d4uo m4esai dun4amei m4onon s4ummetroi sunteq5wsi 3rht6on peri4exousai, 3h 34olh 24alog4o@ 2estin, kale4isqw d6e 2ek d4uo m4eswn pr4wth. -Sugke4isqwsan g6ar d4uo m4esai dun4amei m4onon s4ummetroi a3i AB, BG 3rht6on peri4exousai: l4egw, 34oti 34olh 3h AG 24alog4o@ 2estin. -2Epe6i g6ar 2as4ummetr4o@ 2estin 3h AB t5hj BG m4hkei, ka6i t6a 2ap6o t5wn AB, BG 24ara 2as4ummetr4a 2esti t5wj d6i@ 3up6o t5wn ^+^ AB, BG: ka6i sunq4enti t6a 2ap6o t5wn AB, BG met6a to5u d6i@ 3up6o t5wn AB, BG, 34oper 2est6i t6o 2ap6o t5h@ AG, 2as4ummetr4on 2esti t5wj 3up6o t5wn AB, BG. 3rht6on d6e t6o 3up6o t5wn AB, BG: 3up4okeintai g6ar a3i AB, BG 3rht6on peri4exousai: 24alogon 24ara t6o 2ap6o t5h@ AG: 24alogo@ 24ara 3h AG, kale4isqw d6e 2ek d4uo m4eswn pr4wth: $-^P224^-^L3^ <3<####PBFb####-----<00> ###10AP### ##37## <00> -2Ek4alese d6e a2ut6hn 2ek d4uo m4eswn pr4wthn di6a t6o 3rht6on peri4exein ka6i protere5in t6o 3rht4on.>3> $-^P62^-^L7^ ####***X#### 34oper 24edei de5icai. ###PROP### ##38##-------lh41 -2E6an d4uo m4esai dun4amei m4onon s4ummetroi sunteq5wsi m4eson peri4exousai, 3h 34olh 24alog4o@ 2estin, kale4isqw d6e 2ek d4uo m4eswn deut4era. -Sugke4isqwsan g6ar d4uo m4esai dun4amei m4onon s4ummetroi a3i AB, BG m4eson peri4exousai: l4egw, 34oti 24alog4o@ 2estin 3h AG. -2Ekke4isqw g6ar 3rht6h 3h DE, ka6i t5wj 2ap6o t5h@ AG 24ison par6a t6hn DE parabebl4hsqw t6o DZ pl4ato@ poio5un t6hn DH. ka6i 2epe6i t6o 2ap6o t5h@ AG 24ison 2est6i to5i@ te 2ap6o t5wn AB, BG ka6i t5wj d6i@ 3up6o t5wn AB, BG,parabebl4hsqw ^+^ d6h to5i@ 2ap6o t5wn AB, BG par6a t6hn DE 24ison t6o EQ: loip6on 24ara t6o QZ 24ison 2est6i t5wj d6i@ 3up6o t5wn AB, BG. ka6i 2epe6i m4esh 2est6in 3ekat4era t5wn AB, BG, m4esa 24ara 2est6i ka6i t6a 2ap6o t5wn AB, BG. m4eson d6e 3up4okeitai ka6i t6o d6i@ 3up6o t5wn AB, BG. ka4i 2esti to5i@ m6en 2ap6o t5wn AB, BG 24ison t6o EQ, t5wj d6e d6i@ 3up6o t5wn AB, BG 24ison t6o ZQ: m4eson 24ara 3ek4ateron t5wn EQ, QZ. ka6i par6a 3rht6hn t6hn DE par4akeitai: 3rht6h 24ara 2est6in 3ekat4era t5wn DQ, QH ka6i 2as4ummetro@ t5hj DE m4hkei. 2epe6i o25un 2as4ummetr4o@ 2estin 3h AB t5hj BG m4hkei, ka4i 2estin 3w@ 3h AB pr6o@ t6hn BG, o34utw@ t6o 2ap6o t5h@ AB pr6o@ t6o 3up6o t5wn AB, BG, 2as4ummetron 24ara 2est6i t6o 2ap6o t5h@ AB t5wj 3up6o t5wn AB, BG. 2all6a t5wj m6en 2ap6o t5h@ AB s4ummetr4on 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG tetrag4wnwn, t5wj d6e 3up6o t5wn AB, BG s4ummetr4on 2esti t6o d6i@ 3up6o t5wn AB, BG. 2as4ummetron 24ara ^+^ 2est6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG. 2all6a to5i@ m6en 2ap6o t5wn AB, BG 24ison 2est6i t6o EQ, t5wj d6e d6i@ 3up6o t5wn AB, BG 24ison 2est6i t6o QZ. 2as4ummetron 24ara 2est6i t6o EQ t5wj QZ: 34wste ka6i 3h DQ t5hj QH 2estin 2as4ummetro@ m4hkei. a3i DQ, QH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. 34wste 3h DH 24alog4o@ 2estin. 3rht6h d6e 3h DE: t6o d6e 3up6o 2al4ogou ka6i 3rht5h@ periex4omenon 2orqog4wnion 24alog4on 2estin: 24alogon 24ara 2est6i t6o DZ xwr4ion, ka6i 3h dunam4enh <22> 24alog4o@ 2estin. d4unatai d6e t6o DZ 3h AG: 24alogo@ 24ara 2est6in 3h AG, kale4isqw d6e 2ek d4uo m4eswn deut4era. $-^P224^-^L5^ <3<####PBF&####-----<00> ###10AP### ##38## <00> -2Ek4alese d6e a2ut6hn 2ek d4uo m4eswn deut4eran di6a t6o m4eson peri4exein t6o 3up' a2ut5wn ka6i m6h 3rht4on, deutere4uein d6e t6o m4eson to5u 3rhto5u. 34oti d6e t6o 3up6o 3rht5h@ ka6i 2al4ogou periex4omenon 24alog4on 2estin, d5hlon. e2i g6ar 24estai 3rht6on ka6i parab4eblhtai par6a 3rht4hn, e24ih 26an ka6i 3h 3et4era a2uto5u pleur6a 3rht4h. 2all6a ka6i 24alogo@: 34oper 24atopon. t6o 24ara 3up6o 3rht5h@ ka6i 2al4ogou 24alog4on 2estin. ^+^>3> $-^P64^-^L12^ ####***X#### ###PROP### 34oper 24edei de5icai. ##39##-------lq41 -2E6an d4uo e2uqe5iai dun4amei 2as4ummetroi sunteq5wsi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d' 3up' a2ut5wn m4eson, 3h 34olh e2uqe5ia 24alog4o@ 2estin, kale4isqw d6e me4izwn. -Sugke4isqwsan g6ar d4uo e2uqe5iai dun4amei 2as4ummetroi a3i AB, BG poio5usai t6a proke4imena: l4egw, 34oti 24alog4o@ 2estin 3h AG. -2Epe6i g6ar t6o 3up6o t5wn AB, BG m4eson 2est4in, ka6i t6o d6i@ <2<24ara>2> 3up6o t5wn AB, BG m4eson 2est4in. t6o d6e sugke4imenon 2ek ^+^ t5wn 2ap6o t5wn AB, BG 3rht4on: 2as4ummetron 24ara 2est6i t6o d6i@ 3up6o t5wn AB, BG t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn AB, BG: 34wste ka6i t6a 2ap6o t5wn AB, BG met6a to5u d6i@ 3up6o t5wn AB, BG, 34oper 2est6i t6o 2ap6o t5h@ AG, 2as4ummetr4on 2esti t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn AB, BG <2<3rht6on d6e t6o sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG>2>: 24alogon 24ara 2est6i t6o 2ap6o t5h@ AG. 34wste ka6i 3h AG 24alog4o@ 2estin, kale4isqw d6e me4izwn. $-^P225^ <3<####PBF&####-----<00> ###10AP### <00> ##39A##-2Ek4alese d6e a2ut6hn me4izona di6a t6o t6a 2ap6o t5wn AB, BG 3rht6a me4izona e25inai to5u d6i@ 3up6o t5wn AB, BG m4esou, ka6i d4eon e25inai 2ap6o t5h@ t5wn 3rht5wn o2ikei4othto@ t6hn 2onomas4ian t4attesqai. 34oti d6e me4izon4a 2esti t6a 2ap6o t5wn AB, BG to5u d6i@ 3up6o t5wn AB, BG, o34utw@ deikt4eon. -Faner6on m6en o25un, 34oti 24aniso4i e2isin a3i AB, BG. e2i g6ar 25hsan 24isai, 24isa 26an 25hn ka6i t6a 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG, ka6i 25hn 26an ka6i t6o 3up6o t5wn AB, BG 3rht4on: 35oper o2ux 3up4okeitai: 24anisoi 24ara e2is6in a3i AB, BG. 3upoke4isqw me4izwn 3h AB, ka6i ke4isqw t5hj BG 24ish 3h BD: t6a 24ara 2ap6o t5wn AB, BD 24isa 2est6i t5wj te d6i@ 3up6o t5wn AB, BD ka6i t5wj 2ap6o t5h@ DA. 24ish d6e 3h DB t5hj BG: t6a 24ara 2ap6o t5wn AB, BG 24isa 2est6i t5wj te d6i@ 3up6o t5wn AB, BG ka6i t5wj 2ap6o t5h@ AD: 34wste t6a 2ap6o t5wn AB, BG me4izona e25inai to5u d6i@ 3up6o t5wn AB, BG t5wj 2ap6o DA.>3> $-^P65^-^L8^ ####***X#### ###PROP### ##40##-------m41 34oper 24edei de5icai. -2E6an d4uo e2uqe5iai dun4amei 2as4ummetroi sunteq5wsi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on, 3h 34olh e2uqe5ia 24alog4o@ 2estin, kale4isqw d6e 3rht6on ka6i m4eson dunam4enh. -Sugke4isqwsan g6ar d4uo e2uqe5iai dun4amei 2as4ummetroi a3i AB, BG poio5usai t6a proke4imena: l4egw, 34oti 24alog4o@ 2estin 3h AG. -2Epe6i g6ar t6o sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG m4eson 2est4in, t6o d6e d6i@ 3up6o t5wn AB, BG 3rht4on, 2as4ummetron 24ara 2est6i t6o sugke4imenon 2ek t5wn ^+^ 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG: 34wste ka6i t6o 2ap6o t5h@ AG 2as4ummetr4on 2esti t5wj d6i@ 3up6o t5wn AB, BG. 3rht6on d6e t6o d6i@ 3up6o t5wn AB, BG: 24alogon 24ara t6o 2ap6o t5h@ AG. 24alogo@ 24ara 3h AG, kale4isqw d6e 3rht6on ka6i m4eson dunam4enh. $-^P226^ <3<####PBF&####-----<00> ###10AP### <00> ##40A##-3Rht6on d6e ka6i m4eson dunam4enh kale5itai a34uth di6a t6o d4unasqai d4uo xwr4ia, t6o m6en 3rht6on, t6o d6e m4eson: ka6i di6a t6hn to5u 3rhto5u pro4uparcin pr5wton 2ek4alesen.>3> $-^P66^-^L5^ 34oper 24edei de5icai. ####***X#### ###PROP### ##41##-------ma41 -2E6an d4uo e2uqe5iai dun4amei 2as4ummetroi sunteq5wsi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson ka6i t6o 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t5wj sugkeim4enwj 2ek t5wn 2ap' a2ut5wn tetrag4wnwn, 3h 34olh e2uqe5ia 24alog4o@ 2estin, kale4isqw d6e d4uo m4esa dunam4enh. -Sugke4isqwsan g6ar d4uo e2uqe5iai dun4amei 2as4ummetroi a3i AB, BG poio5usai t6a proke4imena. l4egw, 34oti 3h AG 24alog4o@ 2estin. -2Ekke4isqw 3rht6h 3h DE, ka6i parabebl4hsqw par6a t6hn DE to5i@ m6en 2ap6o t5wn AB, BG 24ison t6o DZ, t5wj d6e d6i@ 3up6o t5wn AB, BG 24ison t6o HQ: 34olon 24ara t6o DQ 24ison 2est6i t5wj 2ap6o t5h@ AG tetrag4wnwj. ka6i 2epe6i m4eson 2est6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG, ka4i 2estin 24ison ^+^ t5wj DZ, m4eson 24ara 2est6i ka6i t6o DZ. ka6i par6a 3rht6hn t6hn DE par4akeitai: 3rht6h 24ara 2est6in 3h DH ka6i 2as4ummetro@ t5hj DE m4hkei. di6a t6a a2ut6a d6h ka6i 3h HK 3rht4h 2esti ka6i 2as4ummetro@ t5hj HZ, tout4esti t5hj DE, m4hkei. ka6i 2epe6i 2as4ummetr4a 2esti t6a 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG, 2as4ummetr4on 2esti t6o DZ t5wj HQ: 34wste ka6i 3h DH t5hj HK 2as4ummetr4o@ 2estin. ka4i e2isi 3rhta4i: a3i DH, HK 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 24alogo@ 24ara 2est6in 3h DK 3h kaloum4enh 2ek d4uo 2onom4atwn. 3rht6h d6e 3h DE: 24alogon 24ara 2est6i t6o DQ ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin. d4unatai d6e t6o QD 3h AG: 24alogo@ 24ara 2est6in 3h AG, kale4isqw d6e d4uo m4esa dunam4enh. $-^P226^-^L4^ <3<####PBF&####-----<00> ###10AP### <00> ##41A##-Kale5i d6e a2ut6hn d4uo m4esa dunam4enhn di6a t6o d4unasqai a2ut6hn d4uo m4esa xwr4ia t4o te sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG ka6i t6o d6i@ 3up6o t5wn AB, BG.>3> $-^P67^-^L13^ ####***X#### 34oper 24edei de5icai. ###PROP### ##42^1^L^2## -----L5hmma -34Oti d6e a3i e2irhm4enai 24alogoi monax5w@ diairo5untai e2i@ t6a@ e2uqe4ia@, 2ec 35wn s4ugkeintai poious5wn t6a proke4imena e24idh, de4icomen 24hdh proekq4emenoi lhmm4ation toio5uton. -2Ekke4isqw e2uqe5ia 3h AB ka6i tetm4hsqw 3h 34olh e2i@ 24anisa kaq' 3ek4ateron t5wn G, D, 3upoke4isqw d6e me4izwn 3h AG t5h@ DB: l4egw, 34oti t6a 2ap6o t5wn AG, GB me4izon4a 2esti t5wn 2ap6o t5wn AD, DB. ^+^ -Tetm4hsqw g6ar 3h AB d4ixa kat6a t6o E. ka6i 2epe6i me4izwn 2est6in 3h AG t5h@ DB, koin6h 2afhjr4hsqw 3h DG: loip6h 24ara 3h AD loip5h@ t5h@ GB me4izwn 2est4in. 24ish d6e 3h AE t5hj EB: 2el4attwn 24ara 3h DE t5h@ EG: t6a G, D 24ara shme5ia o2uk 24ison 2ap4exousi t5h@ dixotom4ia@. ka6i 2epe6i t6o 3up6o t5wn AG, GB met6a to5u 2ap6o t5h@ EG 24ison 2est6i t5wj 2ap6o t5h@ EB, 2all6a m6hn ka6i t6o 3up6o t5wn AD, DB met6a to5u 2ap6o DE 24ison 2est6i t5wj 2ap6o t5h@ EB, t6o 24ara 3up6o t5wn AG, GB met6a to5u 2ap6o t5h@ EG 24ison 2est6i t5wj 3up6o t5wn AD, DB met6a to5u 2ap6o t5h@ DE: 35wn t6o 2ap6o t5h@ DE 24elass4on 2esti to5u 2ap6o t5h@ EG: ka6i loip6on 24ara t6o 3up6o t5wn AG, GB 24elass4on 2esti to5u 3up6o t5wn AD, DB. 34wste ka6i t6o d6i@ 3up6o t5wn AG, GB 24elass4on 2esti to5u d6i@ 3up6o AD, DB. ka6i loip6on 24ara t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB me5iz4on 2esti to5u sugkeim4enou 2ek t5wn 2ap6o t5wn AD, DB: 34oper 24edei de5icai. ##42##-------mb41 -3H 2ek d4uo 2onom4atwn kat6a 36en m4onon shme5ion diaire5itai e2i@ t6a 2on4omata. -24Estw 2ek d4uo 2onom4atwn 3h AB dihjrhm4enh e2i@ t6a 2on4omata kat6a t6o G: a3i AG, GB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. l4egw, 34oti 3h AB kat' 24allo shme5ion o2u diaire5itai e2i@ d4uo 3rht6a@ dun4amei m4onon summ4etrou@. ^+^ -E2i g6ar dunat4on, dihjr4hsqw ka6i kat6a t6o D, 34wste ka6i t6a@ AD, DB 3rht6a@ e25inai dun4amei m4onon summ4etrou@. faner6on d4h, 34oti 3h AG t5hj DB o2uk 24estin 3h a2ut4h. e2i g6ar dunat4on, 24estw. 24estai d6h ka6i 3h AD t5hj GB 3h a2ut4h: ka6i 24estai 3w@ 3h AG pr6o@ t6hn GB, o34utw@ 3h BD pr6o@ t6hn DA, ka6i 24estai 3h AB kat6a t6o a2ut6o t5hj kat6a t6o G diair4esei diaireqe5isa ka6i kat6a t6o D: 34oper o2ux 3up4okeitai. o2uk 24ara 3h AG t5hj DB 2estin 3h a2ut4h. di6a d6h to5uto ka6i t6a G, D shme5ia o2uk 24ison 2ap4exousi t5h@ dixotom4ia@. 35wj 24ara diaf4erei t6a 2ap6o t5wn AG, GB t5wn 2ap6o t5wn AD, DB, to4utwj diaf4erei ka6i t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB di6a t6o ka6i t6a 2ap6o t5wn AG, GB met6a to5u d6i@ 3up6o t5wn AG, GB ka6i t6a 2ap6o t5wn AD, DB met6a to5u d6i@ 3up6o t5wn AD, DB 24isa e25inai t5wj 2ap6o t5h@ AB. 2all6a t6a 2ap6o t5wn AG, GB t5wn 2ap6o t5wn AD, DB diaf4erei 3rht5wj: 3rht6a g6ar 2amf4otera: ka6i t6o d6i@ 24ara 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB diaf4erei 3rht5wj m4esa 24onta: 34oper 24atopon: m4eson g6ar m4esou o2ux 3uper4exei 3rht5wj. -O2uk 24ara 3h 2ek d4uo 2onom4atwn kat' 24allo ka6i 24allo shme5ion diaire5itai: kaq' 36en 24ara m4onon: 34oper 24edei de5icai. ^+^ ##43##-------mg41 -3H 2ek d4uo m4eswn pr4wth kaq' 36en m4onon shme5ion diaire5itai. -24Estw 2ek d4uo m4eswn pr4wth 3h AB dihjrhm4enh kat6a t6o G, 34wste t6a@ AG, GB m4esa@ e25inai dun4amei m4onon summ4etrou@ 3rht6on periexo4usa@: l4egw, 34oti 3h AB kat' 24allo shme5ion o2u diaire5itai. -E2i g6ar dunat4on, dihjr4hsqw ka6i kat6a t6o D, 34wste ka6i t6a@ AD, DB m4esa@ e25inai dun4amei m4onon summ4etrou@ 3rht6on periexo4usa@. 2epe6i o25un, 35wj diaf4erei t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB, to4utwj diaf4erei t6a 2ap6o t5wn AG, GB t5wn 2ap6o t5wn AD, DB, 3rht5wj d6e diaf4erei t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB: 3rht6a g6ar 2amf4otera: 3rht5wj 24ara diaf4erei ka6i t6a 2ap6o t5wn AG, GB t5wn 2ap6o t5wn AD, DB m4esa 24onta: 34oper 24atopon. -o2uk 24ara 3h 2ek d4uo m4eswn pr4wth kat' 24allo ka6i 24allo shme5ion diaire5itai e2i@ t6a 2on4omata: kaq' 36en 24ara m4onon: 34oper 24edei de5icai. ##44##-------md41 -3H 2ek m4eswn deut4era kaq' 36en m4onon shme5ion diaire5itai. -24Estw 2ek d4uo m4eswn deut4era 3h AB dihjrhm4enh kat6a t6o G, 34wste t6a@ AG, GB m4esa@ e25inai dun4amei m4onon ^+^ summ4etrou@ m4eson periexo4usa@: faner6on d4h, 34oti t6o G o2uk 24esti kat6a t5h@ dixotom4ia@, 34oti o2uk e2is6i m4hkei s4ummetroi. l4egw, 34oti 3h AB kat' 24allo shme5ion o2u diaire5itai. -E2i g6ar dunat4on, dihjr4hsqw ka6i kat6a t6o D, 34wste t6hn AG t5hj DB m6h e25inai t6hn a2ut4hn, 2all6a me4izona kaq' 3up4oqesin t6hn AG: d5hlon d4h, 34oti ka6i t6a 2ap6o t5wn AD, DB, 3w@ 2ep4anw 2ede4icamen, 2el4assona t5wn 2ap6o t5wn AG, GB: ka6i t6a@ AD, DB m4esa@ e25inai dun4amei m4onon summ4etrou@ m4eson periexo4usa@. ka6i 2ekke4isqw 3rht6h 3h EZ, ka6i t5wj m6en 2ap6o t5h@ AB 24ison par6a t6hn EZ parallhl4ogrammon 2orqog4wnion parabebl4hsqw t6o EK, to5i@ d6e 2ap6o t5wn AG, BG 24ison 2afhjr4hsqw t6o EH: loip6on 24ara t6o QK 24ison 2est6i t5wj d6i@ 3up6o t5wn AG, GB. p4alin d6h to5i@ 2ap6o t5wn AD, DB, 34aper 2el4assona 2ede4ixqh t5wn 2ap6o t5wn AG, GB, 24ison 2afhjr4hsqw t6o EL: ka6i loip6on 24ara t6o MK 24ison t5wj d6i@ 3up6o t5wn AD, DB. ka6i 2epe6i m4esa 2est6i t6a 2ap6o t5wn AG, GB, m4eson 24ara <22> t6o EH. ka6i par6a 3rht6hn t6hn EZ par4akeitai: ^+^ 3rht6h 24ara 2est6in 3h EQ ka6i 2as4ummetro@ t5hj EZ m4hkei. di6a t6a a2ut6a d6h ka6i 3h QN 3rht4h 2esti ka6i 2as4ummetro@ t5hj EZ m4hkei. ka6i 2epe6i a3i AG, GB m4esai e2is6i dun4amei m4onon s4ummetroi, 2as4ummetro@ 24ara 2est6in 3h AG t5hj GB m4hkei. 3w@ d6e 3h AG pr6o@ t6hn GB, o34utw@ t6o 2ap6o t5h@ AG pr6o@ t6o 3up6o t5wn AG, GB: 2as4ummetron 24ara 2est6i t6o 2ap6o t5h@ AG t5wj 3up6o t5wn AG, GB. 2all6a t5wj m6en 2ap6o t5h@ AG s4ummetr4a 2esti t6a 2ap6o t5wn AG, GB: dun4amei g4ar e2isi s4ummetroi a3i AG, GB. t5wj d6e 3up6o t5wn AG, GB s4ummetr4on 2esti t6o d6i@ 3up6o t5wn AG, GB. ka6i t6a 2ap6o t5wn AG, GB 24ara 2as4ummetr4a 2esti t5wj d6i@ 3up6o t5wn AG, GB. 2all6a to5i@ m6en 2ap6o t5wn AG, GB 24ison 2est6i t6o EH, t5wj d6e d6i@ 3up6o t5wn AG, GB 24ison t6o QK: 2as4ummetron 24ara 2est6i t6o EH t5wj QK: 34wste ka6i 3h EQ t5hj QN 2as4ummetr4o@ 2esti m4hkei. ka4i e2isi 3rhta4i: a3i EQ, QN 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. 2e6an d6e d4uo 3rhta6i dun4amei m4onon s4ummetroi sunteq5wsin, 3h 34olh 24alog4o@ 2estin 3h kaloum4enh 2ek d4uo 2onom4atwn: 3h EN 24ara 2ek d4uo 2onom4atwn 2est6i dihjrhm4enh kat6a t6o Q. kat6a t6a a2ut6a d6h deixq4hsontai ka6i a3i EM, MN 3rhta6i dun4amei m4onon s4ummetroi: ka6i 24estai 3h EN 2ek d4uo 2onom4atwn kat' 24allo ka6i 24allo dihjrhm4enh t4o te Q ka6i t6o M, ka6i o2uk 24estin 3h EQ t5hj MN 3h a2ut4h, 34oti ^+^ t6a 2ap6o t5wn AG, GB me4izon4a 2esti t5wn 2ap6o t5wn AD, DB. 2all6a t6a 2ap6o t5wn AD, DB me4izon4a 2esti to5u d6i@ 3up6o AD, DB: poll5wj 24ara ka6i t6a 2ap6o t5wn AG, GB, tout4esti t6o EH, me5iz4on 2esti to5u d6i@ 3up6o t5wn AD, DB, tout4esti to5u MK: 34wste ka6i 3h EQ t5h@ MN me4izwn 2est4in. 3h 24ara EQ t5hj MN o2uk 24estin 3h a2ut4h: 34oper 24edei de5icai. ##45##-------me41 -3H me4izwn kat6a t6o a2ut6o m4onon shme5ion diaire5itai. -24Estw me4izwn 3h AB dihjrhm4enh kat6a t6o G, 34wste t6a@ AG, GB dun4amei 2asumm4etrou@ e25inai poio4usa@ t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB tetrag4wnwn 3rht4on, t6o d' 3up6o t5wn AG, GB m4eson: l4egw, 34oti 3h AB kat' 24allo shme5ion o2u diaire5itai. -E2i g6ar dunat4on, dihjr4hsqw ka6i kat6a t6o D, 34wste ka6i t6a@ AD, DB dun4amei 2asumm4etrou@ e25inai poio4usa@ t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AD, DB 3rht4on, t6o d' 3up' a2ut5wn m4eson. ka6i 2epe4i, 35wj diaf4erei t6a 2ap6o t5wn AG, GB t5wn 2ap6o t5wn AD, DB, to4utwj ^+^ diaf4erei ka6i t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB, 2all6a t6a 2ap6o t5wn AG, GB t5wn 2ap6o t5wn AD, DB 3uper4exei 3rht5wj: 3rht6a g6ar 2amf4otera: ka6i t6o d6i@ 3up6o t5wn AD, DB 24ara to5u d6i@ 3up6o t5wn AG, GB 3uper4exei 3rht5wj m4esa 24onta: 34oper 2est6in 2ad4unaton. o2uk 24ara 3h me4izwn kat' 24allo ka6i 24allo shme5ion diaire5itai: kat6a t6o a2ut6o 24ara m4onon diaire5itai: 34oper 24edei de5icai. ##46##-------mst41 -3H 3rht6on ka6i m4eson dunam4enh kaq' 36en m4onon shme5ion diaire5itai. -24Estw 3rht6on ka6i m4eson dunam4enh 3h AB dihjrhm4enh kat6a t6o G, 34wste t6a@ AG, GB dun4amei 2asumm4etrou@ e25inai poio4usa@ t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB m4eson, t6o d6e d6i@ 3up6o t5wn AG, GB 3rht4on: l4egw, 34oti 3h AB kat' 24allo shme5ion o2u diaire5itai. -E2i g6ar dunat4on, dihjr4hsqw ka6i kat6a t6o D, 34wste ka6i t6a@ AD, DB dun4amei 2asumm4etrou@ e25inai poio4usa@ t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AD, DB m4eson, t6o d6e d6i@ 3up6o t5wn AD, DB 3rht4on. 2epe6i o25un, 35wj diaf4erei t6o d6i@ 3up6o t5wn AG, GB to5u d6i@ 3up6o t5wn AD, DB, to4utwj diaf4erei ka6i t6a 2ap6o t5wn AD, DB t5wn 2ap6o t5wn AG, GB, t6o d6e d6i@ 3up6o t5wn AG, GB to5u d6i@ 3up6o t5wn AD, DB 3uper4exei 3rht5wj, ^+^ ka6i t6a 2ap6o t5wn AD, DB 24ara t5wn 2ap6o t5wn AG, GB 3uper4exei 3rht5wj m4esa 24onta: 34oper 2est6in 2ad4unaton. o2uk 24ara 3h 3rht6on ka6i m4eson dunam4enh kat' 24allo ka6i 24allo shme5ion diaire5itai. kat6a 36en 24ara shme5ion diaire5itai: 34oper 24edei de5icai. ##47##-------mz41 -3H d4uo m4esa dunam4enh kaq' 36en m4onon shme5ion diaire5itai. -24Estw <22> 3h AB dihjrhm4enh kat6a t6o G, 34wste t6a@ AG, GB dun4amei 2asumm4etrou@ e25inai poio4usa@ t4o te sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB m4eson ka6i t6o 3up6o t5wn AG, GB m4eson ka6i 24eti 2as4ummetron t5wj sugkeim4enwj 2ek t5wn 2ap' a2ut5wn. l4egw, 34oti 3h AB kat' 24allo shme5ion o2u diaire5itai poio5usa t6a proke4imena. -E2i g6ar dunat4on, dihjr4hsqw kat6a t6o D, 34wste p4alin dhlon4oti t6hn AG t5hj DB m6h e25inai t6hn a2ut4hn, 2all6a me4izona kaq' 3up4oqesin t6hn AG, ka6i 2ekke4isqw 3rht6h 3h EZ, ka6i parabebl4hsqw par6a t6hn EZ to5i@ m6en 2ap6o t5wn AG, GB 24ison t6o EH, t5wj d6e d6i@ 3up6o t5wn AG, GB 24ison t6o QK: 34olon 24ara t6o EK 24ison 2est6i t5wj 2ap6o t5h@ AB tetrag4wnwj. p4alin d6h parabebl4hsqw par6a t6hn EZ to5i@ ^+^ 2ap6o t5wn AD, DB 24ison t6o EL: loip6on 24ara t6o d6i@ 3up6o t5wn AD, DB loip5wj t5wj MK 24ison 2est4in. ka6i 2epe6i m4eson 3up4okeitai t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB, m4eson 24ara 2est6i ka6i t6o EH. ka6i par6a 3rht6hn t6hn EZ par4akeitai: 3rht6h 24ara 2est6in 3h QE ka6i 2as4ummetro@ t5hj EZ m4hkei. di6a t6a a2ut6a d6h ka6i 3h QN 3rht4h 2esti ka6i 2as4ummetro@ t5hj EZ m4hkei. ka6i 2epe6i 2as4ummetr4on 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB t5wj d6i@ 3up6o t5wn AG, GB, ka6i t6o EH 24ara t5wj HN 2as4ummetr4on 2estin: 34wste ka6i 3h EQ t5hj QN 2as4ummetr4o@ 2estin. ka4i e2isi 3rhta4i: a3i EQ, QN 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h EN 24ara 2ek d4uo 2onom4atwn 2est6i dihjrhm4enh kat6a t6o Q. 3omo4iw@ d6h de4icomen, 34oti ka6i kat6a t6o M di4hjrhtai. ka6i o2uk 24estin 3h EQ t5hj MN 3h a2ut4h: 3h 24ara 2ek d4uo 2onom4atwn kat' 24allo ka6i 24allo shme5ion di4hjrhtai: 34oper 2est6in 24atopon. o2uk 24ara 3h d4uo m4esa dunam4enh kat' 24allo ka6i 24allo shme5ion diaire5itai: kaq' 36en 24ara m4onon <22> diaire5itai. ###DEF2###-----<00> -----34Oroi de4uteroi ##1##-a41 3Upokeim4enh@ 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn dihjrhm4enh@ e2i@ t6a 2on4omata, 35h@ t6o me5izon 24onoma to5u 2el4assono@ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei, 2e6an m6en t6o me5izon 24onoma s4ummetron 25hj m4hkei t5hj 2ekkeim4enhj 3rht5hj, kale4isqw <2<3h 34olh>2> 2ek d4uo 2onom4atwn pr4wth. ^+^ ##2##-b41 2E6an d6e t6o 24elasson 24onoma s4ummetron 25hj m4hkei t5hj 2ekkeim4enhj 3rht5hj, kale4isqw 2ek d4uo 2onom4atwn deut4era. ##3##-g41 2E6an d6e mhd4eteron t5wn 2onom4atwn s4ummetron 25hj m4hkei t5hj 2ekkeim4enhj 3rht5hj, kale4isqw 2ek d4uo 2onom4atwn tr4ith. ##4##-d41 P4alin d6h 2e6an t6o me5izon 24onoma <22> me5izon d4unhtai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei, 2e6an m6en t6o me5izon 24onoma s4ummetron 25hj m4hkei t5hj 2ekkeim4enhj 3rht5hj, kale4isqw 2ek d4uo 2onom4atwn tet4arth. ##5##-e41 2E6an d6e t6o 24elasson, p4empth. ##6##-st41 2E6an d6e mhd4eteron, 34ekth. $-^P226^-^L7^ <3<####PBF&####-----<00> ###10AP### <00> ##2DEF7##-36Ec o25un o2us5wn t5wn o34utw@ katalambanom4enwn e2uqei5wn t4attei pr4wta@ t5hj t4acei tre5i@, 2ef' 35wn 3h me4izwn t5h@ 2el4assono@ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, deut4era@ d6e t5hj t4acei t6a@ loip6a@ tre5i@, 2ef' 35wn t5wj 2ap6o 2asumm4etrou, di6a t6o protere5in t6o s4ummetron to5u 2asumm4etrou: ^+^ ka6i 24eti pr4wthn m4en, 2ef' 35h@ t6o me5izon 24onoma s4ummetr4on 2esti t5hj 2ekkeim4enhj 3rht5hj, deut4eran d4e, 2ef' 35h@ t6o 24elasson, di6a t6o p4alin protere5in t6o me5izon to5u 2el4assono@ t5wj 2emperi4exein t6o 24elasson, tr4ithn d4e, 2ef' 35wn mhd4eteron t5wn 2onom4atwn s4ummetr4on 2esti t5hj 2ekkeim4enhj 3rht5hj. ka6i 2ep6i t5wn 3ec5h@ tri5wn 3omo4iw@ t6hn pr4wthn t5h@ e2irhm4enh@ deut4era@ t4acew@ tet4arthn kal5wn ka6i t6hn deut4eran p4empthn ka6i t6hn tr4ithn 34ekthn.>3> $-^P77^-^L12^ ####***X#### ###PROP### ##48##-------mh41 -E3ure5in t6hn 2ek d4uo 2onom4atwn pr4wthn. -2Ekke4isqwsan d4uo 2ariqmo6i o3i AG, GB, 34wste t6on sugke4imenon 2ec a2ut5wn t6on AB pr6o@ m6en t6on BG l4ogon 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, pr6o@ d6e t6on GA l4ogon m6h 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, ka6i 2ekke4isqw ti@ 3rht6h 3h D, ka6i t5hj D s4ummetro@ 24estw m4hkei 3h EZ. 3rht6h 24ara 2est6i ^+^ ka6i 3h EZ. ka6i gegon4etw 3w@ 3o BA 2ariqm6o@ pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH. 3o d6e AB pr6o@ t6on AG l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on: ka6i t6o 2ap6o t5h@ EZ 24ara pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on: 34wste s4ummetr4on 2esti t6o 2ap6o t5h@ EZ t5wj 2ap6o t5h@ ZH. ka4i 2esti 3rht6h 3h EZ: 3rht6h 24ara ka6i 3h ZH. ka6i 2epe6i 3o BA pr6o@ t6on AG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o 2ap6o t5h@ EZ 24ara pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h EZ t5hj ZH m4hkei. a3i EZ, ZH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h EH. -L4egw 34oti ka6i pr4wth. -2Epe6i g4ar 2estin 3w@ 3o BA 2ariqm6o@ pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH, me4izwn d6e 3o BA to5u AG, me5izon 24ara ka6i t6o 2ap6o t5h@ EZ to5u 2ap6o t5h@ ZH. 24estw o25un t5wj 2ap6o t5h@ EZ 24isa t6a 2ap6o t5wn ZH, Q. ka6i 2epe4i 2estin 3w@ 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH, 2anastr4eyanti 24ara 2est6in 3w@ 3o AB pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ Q. 3o d6e AB pr6o@ t6on BG l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i t6o 2ap6o t5h@ EZ 24ara pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. s4ummetro@ 24ara 2est6in ^+^ 3h EZ t5hj Q m4hkei: 3h EZ 24ara t5h@ ZH me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. ka4i e2isi 3rhta6i a3i EZ, ZH, ka6i s4ummetro@ 3h EZ t5hj D m4hkei. -3H EH 24ara 2ek d4uo 2onom4atwn 2est6i pr4wth: 34oper 24edei de5icai. ##49##-------mq41 -E3ure5in t6hn 2ek d4uo 2onom4atwn deut4eran. -2Ekke4isqwsan d4uo 2ariqmo6i o3i AG, GB, 34wste t6on sugke4imenon 2ec a2ut5wn t6on AB pr6o@ m6en t6on BG l4ogon 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, pr6o@ d6e t6on AG l4ogon m6h 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, ka6i 2ekke4isqw 3rht6h 3h D, ka6i t5hj D s4ummetro@ 24estw 3h EZ m4hkei: 3rht6h 24ara 2est6in 3h EZ. gegon4etw d6h ka6i 3w@ 3o GA 2ariqm6o@ pr6o@ t6on AB, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH: s4ummetron 24ara 2est6i t6o 2ap6o t5h@ EZ t5wj 2ap6o t5h@ ZH. 3rht6h 24ara 2est6i ka6i 3h ZH. ka6i 2epe6i 3o GA 2ariqm6o@ pr6o@ t6on AB l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o ^+^ 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. 2as4ummetro@ 24ara 2est6in 3h EZ t5hj ZH m4hkei: a3i EZ, ZH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h EH. -Deikt4eon d4h, 34oti ka6i deut4era. -2Epe6i g6ar 2an4apal4in 2estin 3w@ 3o BA 2ariqm6o@ pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ HZ pr6o@ t6o 2ap6o t5h@ ZE, me4izwn d6e 3o BA to5u AG, me5izon 24ara <22> t6o 2ap6o t5h@ HZ to5u 2ap6o t5h@ ZE. 24estw t5wj 2ap6o t5h@ HZ 24isa t6a 2ap6o t5wn EZ, Q: 2anastr4eyanti 24ara 2est6in 3w@ 3o AB pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ Q. 2all' 3o AB pr6o@ t6on BG l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i t6o 2ap6o t5h@ ZH 24ara pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. s4ummetro@ 24ara 2est6in 3h ZH t5hj Q m4hkei: 34wste 3h ZH t5h@ ZE me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. ka4i e2isi 3rhta6i a3i ZH, ZE dun4amei m4onon s4ummetroi, ka6i t6o EZ 24elasson 24onoma t5hj 2ekkeim4enhj 3rht5hj s4ummetr4on 2esti t5hj D m4hkei. -3H EH 24ara 2ek d4uo 2onom4atwn 2est6i deut4era: 34oper ^-^ 24edei de5icai. ^+^ ##50##-------n41 -E3ure5in t6hn 2ek d4uo 2onom4atwn tr4ithn. -2Ekke4isqwsan d4uo 2ariqmo6i o3i AG, GB, 34wste t6on sugke4imenon 2ec a2ut5wn t6on AB pr6o@ m6en t6on BG l4ogon 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, pr6o@ d6e t6on AG l4ogon m6h 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. 2ekke4isqw d4e ti@ ka6i 24allo@ m6h tetr4agwno@ 2ariqm6o@ 3o D, ka6i pr6o@ 3ek4ateron t5wn BA, AG l4ogon m6h 2ex4etw, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i 2ekke4isqw ti@ 3rht6h e2uqe5ia 3h E, ka6i gegon4etw 3w@ 3o D pr6o@ t6on AB, o34utw@ t6o 2ap6o t5h@ E pr6o@ t6o 2ap6o t5h@ ZH: s4ummetron 24ara 2est6i t6o 2ap6o t5h@ E t5wj 2ap6o t5h@ ZH. ka4i 2esti 3rht6h 3h E: 3rht6h 24ara 2est6i ka6i 3h ZH. ka6i 2epe6i 3o D pr6o@ t6on AB l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o 2ap6o t5h@ E pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h E t5hj ZH m4hkei. gegon4etw d6h p4alin 3w@ 3o BA 2ariqm6o@ pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ: s4ummetron 24ara 2est6i t6o 2ap6o t5h@ ZH t5wj 2ap6o t5h@ HQ. 3rht6h d6e 3h ZH: 3rht6h 24ara ka6i 3h HQ. ka6i 2epe6i 3o BA pr6o@ t6on AG l4ogon o2uk 24exei, 36on tetr4agwno@ ^+^ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ QH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h ZH t5hj HQ m4hkei. a3i ZH, HQ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h ZQ 24ara 2ek d4uo 2onom4atwn 2est4in. -L4egw d4h, 34oti ka6i tr4ith. -2Epe6i g4ar 2estin 3w@ 3o D pr6o@ t6on AB, o34utw@ t6o 2ap6o t5h@ E pr6o@ t6o 2ap6o t5h@ ZH, 3w@ d6e 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, di' 24isou 24ara 2est6in 3w@ 3o D pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ E pr6o@ t6o 2ap6o t5h@ HQ. 3o d6e D pr6o@ t6on AG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud6e t6o 2ap6o t5h@ E 24ara pr6o@ t6o 2ap6o t5h@ HQ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h E t5hj HQ m4hkei. ka6i 2epe4i 2estin 3w@ 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, me5izon 24ara t6o 2ap6o t5h@ ZH to5u 2ap6o t5h@ HQ. 24estw o25un t5wj 2ap6o t5h@ ZH 24isa t6a 2ap6o t5wn HQ, K: 2anastr4eyanti 24ara <2<2est6in>2> 3w@ 3o AB pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ K. 3o d6e AB pr6o@ t6on BG l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i t6o 2ap6o t5h@ ZH 24ara pr6o@ t6o 2ap6o t5h@ K l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: s4ummetro@ 24ara <2<2est6in>2> 3h ZH t5hj K m4hkei. 3h ZH ^+^ 24ara t5h@ HQ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. ka4i e2isin a3i ZH, HQ 3rhta6i dun4amei m4onon s4ummetroi, ka6i o2udet4era a2ut5wn s4ummetr4o@ 2esti t5hj E m4hkei. -3H ZQ 24ara 2ek d4uo 2onom4atwn 2est6i tr4ith: 34oper 24edei de5icai. ##51##-------na41 -E3ure5in t6hn 2ek d4uo 2onom4atwn tet4arthn. -2Ekke4isqwsan d4uo 2ariqmo6i o3i AG, GB, 34wste t6on AB pr6o@ t6on BG l4ogon m6h 24exein m4hte m6hn pr6o@ t6on AG, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. ka6i 2ekke4isqw 3rht6h 3h D, ka6i t5hj D s4ummetro@ 24estw m4hkei 3h EZ: 3rht6h 24ara 2est6i ka6i 3h EZ. ka6i gegon4etw 3w@ 3o BA 2ariqm6o@ pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ QH: s4ummetron 24ara 2est6i t6o 2ap6o t5h@ EZ t5wj 2ap6o t5h@ ZH: 3rht6h 24ara 2est6i ka6i 3h ZH. ka6i 2epe6i 3o BA pr6o@ t6on AG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara ^+^ 2est6in 3h EZ t5hj ZH m4hkei. a3i EZ, ZH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 34wste 3h EH 2ek d4uo 2onom4atwn 2est4in. -L4egw d4h, 34oti ka6i tet4arth. -2Epe6i g4ar 2estin 3w@ 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH <22>, me5izon 24ara t6o 2ap6o t5h@ EZ to5u 2ap6o t5h@ ZH. 24estw o25un t5wj 2ap6o t5h@ EZ 24isa t6a 2ap6o t5wn ZH, Q: 2anastr4eyanti 24ara 3w@ 3o AB 2ariqm6o@ pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ Q. 3o d6e AB pr6o@ t6on BG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. 2as4ummetro@ 24ara 2est6in 3h EZ t5hj Q m4hkei: 3h EZ 24ara t5h@ HZ me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i e2isin a3i EZ, ZH 3rhta6i dun4amei m4onon s4ummetroi, ka6i 3h EZ t5hj D s4ummetr4o@ 2esti m4hkei. -3H EH 24ara 2ek d4uo 2onom4atwn 2est6i tet4arth: 34oper ^-^ 24edei de5icai. ##52##-------nb41 -E3ure5in t6hn 2ek d4uo 2onom4atwn p4empthn. -2Ekke4isqwsan d4uo 2ariqmo6i o3i AG, GB, 34wste t6on AB pr6o@ 3ek4ateron a2ut5wn l4ogon m6h 24exein, 36on tetr4agwno@ ^+^ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, ka6i 2ekke4isqw 3rht4h ti@ e2uqe5ia 3h D, ka6i t5hj D s4ummetro@ 24estw <22> 3h EZ: 3rht6h 24ara 3h EZ. ka6i gegon4etw 3w@ 3o GA pr6o@ t6on AB, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH. 3o d6e GA pr6o@ t6on AB l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud6e t6o 2ap6o t5h@ EZ 24ara pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. a3i EZ,ZH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h EH. -L4egw d4h, 34oti ka6i p4empth. -2Epe6i g4ar 2estin 3w@ 3o GA pr6o@ t6on AB, o34utw@ t6o 2ap6o t5h@ EZ pr6o@ t6o 2ap6o t5h@ ZH, 2an4apalin 3w@ 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ ZE: me5izon 24ara t6o 2ap6o t5h@ HZ to5u 2ap6o t5h@ ZE. 24estw o25un ^+^ t5wj 2ap6o t5h@ HZ 24isa t6a 2ap6o t5wn EZ, Q: 2anastr4eyanti 24ara 2est6in 3w@ 3o AB 2ariqm6o@ pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ HZ pr6o@ t6o 2ap6o t5h@ Q. 3o d6e AB pr6o@ t6on BG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. 2as4ummetro@ 24ara 2est6in 3h ZH t5hj Q m4hkei: 34wste 3h ZH t5h@ ZE me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka6i e2isin a3i HZ, ZE 3rhta6i dun4amei m4onon s4ummetroi ka6i t6o EZ 24elatton 24onoma s4ummetr4on 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj D m4hkei. -3H EH 24ara 2ek d4uo 2onom4atwn 2est6i p4empth: 34oper 24edei de5icai. ##53##-------ng41 -E3ure5in t6hn 2ek d4uo 2onom4atwn 34ekthn. -2Ekke4isqwsan d4uo 2ariqmo6i o3i AG, GB, 34wste t6on AB pr6o@ 3ek4ateron a2ut5wn l4ogon m6h 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 24estw d6e ka6i 34etero@ 2ariqm6o@ 3o D m6h tetr4agwno@ 26wn mhd6e pr6o@ 3ek4ateron t5wn BA, AG l4ogon 24exwn, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i 2ekke4isqw ti@ 3rht6h e2uqe5ia ^+^ 3h E, ka6i gegon4etw 3w@ 3o D pr6o@ t6on AB, o34utw@ t6o 2ap6o t5h@ E pr6o@ t6o 2ap6o t5h@ ZH: s4ummetron 24ara t6o 2ap6o t5h@ E t5wj 2ap6o t5h@ ZH. ka4i 2esti 3rht6h 3h E: 3rht6h 24ara ka6i 3h ZH. ka6i 2epe6i o2uk 24exei 3o D pr6o@ t6on AB l4ogon, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o 2ap6o t5h@ E 24ara pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 3h E t5hj ZH m4hkei. gegon4etw d6h p4alin 3w@ 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ. s4ummetron 24ara t6o 2ap6o t5h@ ZH t5wj 2ap6o t5h@ QH. 3rht6on 24ara t6o 2ap6o t5h@ QH: 3rht6h 24ara 3h QH. ka6i 2epe6i 3o BA pr6o@ t6on AG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud6e t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h ZH t5hj HQ m4hkei. a3i ZH, HQ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h ZQ. -Deikt4eon d4h, 34oti ka6i 34ekth. -2Epe6i g4ar 2estin 3w@ 3o D pr6o@ t6on AB, o34utw@ t6o 2ap6o t5h@ E pr6o@ t6o 2ap6o t5h@ ZH, 24esti d6e ka6i 3w@ 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, di' 24isou 24ara 2est6in 3w@ 3o D pr6o@ t6on AG, o34utw@ t6o 2ap6o ^+^ t5h@ E pr6o@ t6o 2ap6o t5h@ HQ. 3o d6e D pr6o@ t6on AG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud6e t6o 2ap6o t5h@ E 24ara pr6o@ t6o 2ap6o t5h@ HQ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h E t5hj HQ m4hkei. 2ede4ixqh d6e ka6i t5hj ZH 2as4ummetro@: 3ekat4era 24ara t5wn ZH, HQ 2as4ummetr4o@ 2esti t5hj E m4hkei. ka6i 2epe4i 2estin 3w@ 3o BA pr6o@ t6on AG, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, me5izon 24ara t6o 2ap6o t5h@ ZH to5u 2ap6o t5h@ HQ. 24estw o25un t5wj 2ap6o <22> ZH 24isa t6a 2ap6o t5wn HQ, K: 2anastr4eyanti 24ara 3w@ 3o AB pr6o@ BG, o34utw@ t6o 2ap6o ZH pr6o@ t6o 2ap6o t5h@ K. 3o d6e AB pr6o@ t6on BG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 34wste o2ud6e t6o 2ap6o ZH pr6o@ t6o 2ap6o t5h@ K l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. 2as4ummetro@ 24ara 2est6in 3h ZH t5hj K m4hkei: 3h ZH 24ara t5h@ HQ me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i e2isin a3i ZH, HQ 3rhta6i dun4amei m4onon s4ummetroi, ka6i o2udet4era a2ut5wn s4ummetr4o@ 2esti m4hkei t5hj 2ekkeim4enhj 3rht5hj t5hj E. -3H ZQ 24ara 2ek d4uo 2onom4atwn 2est6in 34ekth: 34oper ^-^ 24edei de5icai. ##54^1^L^2##-----L5hmma -24Estw d4uo tetr4agwna t6a AB, BG ka6i ke4isqwsan 34wste 2ep' e2uqe4ia@ e25inai t6hn DB t5hj BE: 2ep' e2uqe4ia@ 24ara 2est6i ^+^ ka6i 3h ZB t5hj BH. ka6i sumpeplhr4wsqw t6o AG parallhl4ogrammon: l4egw, 34oti tetr4agwn4on 2esti t6o AG, ka6i 34oti t5wn AB, BG m4eson 2an4alog4on 2esti t6o DH, ka6i 24eti t5wn AG, GB m4eson 2an4alog4on 2esti t6o DG. -2Epe6i g6ar 24ish 2est6in 3h m6en DB t5hj BZ, 3h d6e BE t5hj BH, 34olh 24ara 3h DE 34olhj t5hj ZH 2estin 24ish. 2all' 3h m6en DE 3ekat4eraj t5wn AQ, KG 2estin 24ish, 3h d6e ZH 3ekat4eraj t5wn AK, QG 2estin 24ish: ka6i 3ekat4era 24ara t5wn AQ, KG 3ekat4eraj t5wn AK, QG 2estin 24ish. 2is4opleuron 24ara 2est6i t6o AG parallhl4ogrammon: 24esti d6e ka6i 2orqog4wnion: tetr4agwnon 24ara 2est6i t6o AG. -Ka6i 2epe4i 2estin 3w@ 3h ZB pr6o@ t6hn BH, o34utw@ 3h DB pr6o@ t6hn BE, 2all' 3w@ m6en 3h ZB pr6o@ t6hn BH, o34utw@ t6o AB pr6o@ t6o DH, 3w@ d6e 3h DB pr6o@ t6hn BE, o34utw@ t6o DH pr6o@ t6o BG, ka6i 3w@ 24ara t6o AB pr6o@ t6o DH, o34utw@ t6o DH pr6o@ t6o BG. t5wn AB, BG 24ara m4eson 2an4alog4on 2esti t6o DH. -L4egw d4h, 34oti ka6i t5wn AG, GB m4eson 2an4alog4on <2<2esti>2> t6o DG. -2Epe6i g4ar 2estin 3w@ 3h AD pr6o@ t6hn DK, o34utw@ 3h KH pr6o@ t6hn HG: 24ish g4ar <2<2estin>2> 3ekat4era 3ekat4eraj: ka6i sunq4enti 3w@ 3h AK pr6o@ KD, o34utw@ 3h KG pr6o@ GH, 2all' 3w@ m6en 3h AK pr6o@ KD, o34utw@ t6o AG pr6o@ t6o ^+^ GD, 3w@ d6e 3h KG pr6o@ GH, o34utw@ t6o DG pr6o@ GB, ka6i 3w@ 24ara t6o AG pr6o@ DG, o34utw@ t6o DG pr6o@ t6o BG. t5wn AG, GB 24ara m4eson 2an4alog4on 2esti t6o DG: 36a ^-^ pro4ekeito de5icai. ##54##-------nd41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn pr4wth@, 3h t6o xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh 2ek d4uo 2onom4atwn. -Xwr4ion g6ar t6o AG periex4esqw 3up6o 3rht5h@ t5h@ AB ka6i t5h@ 2ek d4uo 2onom4atwn pr4wth@ t5h@ AD: l4egw, 34oti 3h t6o AG xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh 2ek d4uo 2onom4atwn. -2Epe6i g6ar 2ek d4uo 2onom4atwn 2est6i pr4wth 3h AD, dihjr4hsqw e2i@ t6a 2on4omata kat6a t6o E, ka6i 24estw t6o me5izon 24onoma t6o AE, faner6on d4h, 34oti a3i AE, ED 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h AE t5h@ ED me5izon ^+^ d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h AE s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj AB m4hkei. tetm4hsqw d6h 3h ED d4ixa kat6a t6o Z shme5ion. ka6i 2epe6i 3h AE t5h@ ED me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, 2e6an 24ara t5wj tet4artwj m4erei to5u 2ap6o t5h@ 2el4assono@, tout4esti t5wj 2ap6o t5h@ EZ, 24ison par6a t6hn me4izona t6hn AE parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ s4ummetra a2ut6hn diaire5i. parabebl4hsqw o25un par6a t6hn AE t5wj 2ap6o t5h@ EZ 24ison t6o 3up6o AH, HE: s4ummetro@ 24ara 2est6in 3h AH t5hj EH m4hkei. ka6i 24hxqwsan 2ap6o t5wn H, E, Z 3opot4eraj t5wn AB, GD par4allhloi a3i HQ, EK, ZL: ka6i t5wj m6en AQ parallhlogr4ammwj 24ison tetr4agwnon sunest4atw t6o SN, t5wj d6e HK 24ison t6o NP, ka6i ke4isqw 34wste 2ep' e2uqe4ia@ e25inai t6hn MN t5hj NC: 2ep' e2uqe4ia@ 24ara 2est6i ka6i 3h RN t5hj NO. ka6i sumpeplhr4wsqw t6o SP parallhl4ogrammon: tetr4agwnon 24ara 2est6i t6o SP. ka6i 2epe6i t6o 3up6o t5wn AH, HE 24ison 2est6i t5wj 2ap6o t5h@ EZ, 24estin 24ara 3w@ 3h AH pr6o@ EZ, o34utw@ 3h ZE pr6o@ EH: ka6i 3w@ 24ara t6o AQ pr6o@ EL, t6o EL pr6o@ KH: t5wn AQ, HK 24ara m4eson 2an4alog4on 2esti t6o EL. 2all6a t6o m6en AQ 24ison 2est6i t5wj SN, t6o d6e HK 24ison t5wj NP: t5wn SN, NP 24ara m4eson 2an4alog4on ^+^ 2esti t6o EL. 24esti d6e t5wn a2ut5wn t5wn SN, NP m4eson 2an4alogon ka6i t6o MR: 24ison 24ara 2est6i t6o EL t5wj MR: 34wste ka6i t5wj OC 24ison 2est4in. 24esti d6e ka6i t6a AQ, HK to5i@ SN, NP 24isa: 34olon 24ara t6o AG 24ison 2est6in 34olwj t5wj SP, tout4esti t5wj 2ap6o t5h@ MC tetrag4wnwj: t6o AG 24ara d4unatai 3h MC. -L4egw, 34oti 3h MC 2ek d4uo 2onom4atwn 2est4in. -2Epe6i g6ar s4ummetr4o@ 2estin 3h AH t5hj HE, s4ummetr4o@ 2esti ka6i 3h AE 3ekat4eraj t5wn AH, HE. 3up4okeitai d6e ka6i 3h AE t5hj AB s4ummetro@: ka6i a3i AH, HE 24ara t5hj AB s4ummetro4i e2isin. ka4i 2esti 3rht6h 3h AB: 3rht6h 24ara 2est6i ka6i 3ekat4era t5wn AH, HE: 3rht6on 24ara 2est6in 3ek4ateron t5wn AQ, HK, ka4i 2esti s4ummetron t6o AQ t5wj HK. 2all6a t6o m6en AQ t5wj SN 24ison 2est4in, t6o d6e HK t5wj NP: ka6i t6a SN, NP 24ara, tout4esti t6a 2ap6o t5wn MN, NC, 3rht4a 2esti ka6i s4ummetra. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h AE t5hj ED m4hkei, 2all' 3h m6en AE t5hj AH 2esti s4ummetro@, 3h d6e DE t5hj EZ s4ummetro@, 2as4ummetro@ 24ara ka6i 3h AH t5hj EZ: 34wste ka6i t6o AQ t5wj EL 2as4ummetr4on 2estin. 2all6a t6o m6en AQ t5wj SN 2estin 24ison, t6o d6e EL t5wj MR: ka6i t6o SN 24ara t5wj MR 2as4ummetr4on 2estin. ^+^ 2all' 3w@ t6o SN pr6o@ MR, 3h ON pr6o@ t6hn NR: 2as4ummetro@ 24ara 2est6in 3h ON t5hj NR. 24ish d6e 3h m6en ON t5hj MN, 3h d6e NR t5hj NC: 2as4ummetro@ 24ara 2est6in 3h MN t5hj NC. ka4i 2esti t6o 2ap6o t5h@ MN s4ummetron t5wj 2ap6o t5h@ NC, ka6i 3rht6on 3ek4ateron: a3i MN, NC 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. -3H MC 24ara 2ek d4uo 2onom4atwn 2est6i ka6i d4unatai t6o AG: 34oper 24edei de5icai. ##55##-------ne41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn deut4era@, 3h t6o xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh 2ek d4uo m4eswn pr4wth. -Periex4esqw g6ar xwr4ion t6o ABGD 3up6o 3rht5h@ t5h@ AB ka6i t5h@ 2ek d4uo 2onom4atwn deut4era@ t5h@ AD: l4egw, 34oti 3h t6o AG xwr4ion dunam4enh 2ek d4uo m4eswn pr4wth 2est4in. -2Epe6i g6ar 2ek d4uo 2onom4atwn deut4era 2est6in 3h AD, dihjr4hsqw e2i@ t6a 2on4omata kat6a t6o E, 34wste t6o me5izon 24onoma e25inai t6o AE: a3i AE, ED 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h AE t5h@ ED me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i t6o 24elatton 24onoma 3h ED s4ummetr4on 2esti t5hj AB m4hkei. tetm4hsqw 3h ED d4ixa kat6a t6o Z, ka6i t5wj 2ap6o t5h@ EZ 24ison par6a t6hn AE parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj t6o 3up6o t5wn AHE: ^+^ s4ummetro@ 24ara 3h AH t5hj HE m4hkei. ka6i di6a t5wn H, E, Z par4allhloi 24hxqwsan ta5i@ AB, GD a3i HQ, EK, ZL, ka6i t5wj m6en AQ parallhlogr4ammwj 24ison tetr4agwnon sunest4atw t6o SN, t5wj d6e HK 24ison tetr4agwnon t6o NP, ka6i ke4isqw 34wste 2ep' e2uqe4ia@ e25inai t6hn MN t5hj NC: 2ep' e2uqe4ia@ 24ara <2<2est6i>2> ka6i 3h RN t5hj NO. ka6i sumpeplhr4wsqw t6o SP tetr4agwnon: faner6on d6h 2ek to5u prodedeigm4enou, 34oti t6o MR m4eson 2an4alog4on 2esti t5wn SN, NP, ka6i 24ison t5wj EL, ka6i 34oti t6o AG xwr4ion d4unatai 3h MC. deikt4eon d4h, 34oti 3h MC 2ek d4uo m4eswn 2est6i pr4wth. 2epe6i 2as4ummetr4o@ 2estin 3h AE t5hj ED m4hkei, s4ummetro@ d6e 3h ED t5hj AB, 2as4ummetro@ 24ara 3h AE t5hj AB. ka6i 2epe6i s4ummetr4o@ 2estin 3h AH t5hj EH, s4ummetr4o@ 2esti ka6i 3h AE 3ekat4eraj t5wn AH, HE. 2all6a 3h AE ^+^ 2as4ummetro@ t5hj AB m4hkei: ka6i a3i AH, HE 24ara 2as4ummetro4i e2isi t5hj AB. a3i BA, AH, HE 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 34wste m4eson 2est6in 3ek4ateron t5wn AQ, HK. 34wste ka6i 3ek4ateron t5wn SN, NP m4eson 2est4in. ka6i a3i MN, NC 24ara m4esai e2is4in. ka6i 2epe6i s4ummetro@ 3h AH t5hj HE m4hkei, s4ummetr4on 2esti ka6i t6o AQ t5wj HK, tout4esti t6o SN t5hj NP, tout4esti t6o 2ap6o t5h@ MN t5wj 2ap6o t5h@ NC <2<34wste dun4amei e2is6i s4ummetroi a3i MN, NC>2>. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h AE t5hj ED m4hkei, 2all' 3h m6en AE s4ummetr4o@ 2esti t5hj AH, 3h d6e ED t5hj EZ s4ummetro@, 2as4ummetro@ 24ara 3h AH t5hj EZ: 34wste ka6i t6o AQ t5wj EL 2as4ummetr4on 2estin, tout4esti t6o SN t5wj MR, tout4estin 3h ON t5hj NR, tout4estin 3h MN t5hj NC 2as4ummetr4o@ 2esti m4hkei. 2ede4ixqhsan d6e a3i MN, NC ka6i m4esai o25usai ka6i dun4amei s4ummetroi: a3i MN, NC 24ara m4esai e2is6i dun4amei m4onon s4ummetroi. l4egw d4h, 34oti ka6i 3rht6on peri4exousin. 2epe6i g6ar 3h DE 3up4okeitai 3ekat4eraj t5wn AB, EZ s4ummetro@, s4ummetro@ 24ara ka6i 3h EZ t5hj EK. ka6i 3rht6h 3ekat4era a2ut5wn: 3rht6on 24ara t6o EL, tout4esti t6o MR: t6o d6e MR 2esti t6o 3up6o t5wn MNC. 2e6an d6e d4uo m4esai dun4amei m4onon s4ummetroi sunteq5wsi ^+^ 3rht6on peri4exousai, 3h 34olh 24alog4o@ 2estin, kale5itai d6e 2ek d4uo m4eswn pr4wth. -3H 24ara MC 2ek d4uo m4eswn 2est6i pr4wth: 34oper 24edei de5icai. ##56##-----nst41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn tr4ith@, 3h t6o xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh 2ek d4uo m4eswn deut4era. -Xwr4ion g6ar t6o ABGD periex4esqw 3up6o 3rht5h@ t5h@ AB ka6i t5h@ 2ek d4uo 2onom4atwn tr4ith@ t5h@ AD dihjrhm4enh@ e2i@ t6a 2on4omata kat6a t6o E, 35wn me5iz4on 2esti t6o AE: l4egw, 34oti 3h t6o AG xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh 2ek d4uo m4eswn deut4era. -Kateskeu4asqw g6ar t6a a2ut6a to5i@ pr4oteron. ka6i 2epe6i 2ek d4uo 2onom4atwn 2est6i tr4ith 3h AD, a3i AE, ED 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h AE t5h@ ED me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i o2udet4era ^+^ t5wn AE, ED s4ummetr4o@ <2<2esti>2> t5hj AB m4hkei. 3omo4iw@ d6h to5i@ prodedeigm4enoi@ de4icomen, 34oti 3h MC 2estin 3h t6o AG xwr4ion dunam4enh, ka6i a3i MN, NC m4esai e2is6i dun4amei m4onon s4ummetroi: 34wste 3h MC 2ek d4uo m4eswn 2est4in. -Deikt4eon d4h, 34oti ka6i deut4era. -<22> 2epe6i 2as4ummetr4o@ 2estin 3h DE t5hj AB m4hkei, tout4esti t5hj EK, s4ummetro@ d6e 3h DE t5hj EZ, 2as4ummetro@ 24ara 2est6in 3h EZ t5hj EK m4hkei. ka4i e2isi 3rhta4i: a3i ZE, EK 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. m4eson 24ara <2<2est6i>2> t6o EL, tout4esti t6o MR: ka6i peri4exetai 3up6o t5wn MNC: m4eson 24ara 2est6i t6o 3up6o t5wn MNC. -3H MC 24ara 2ek d4uo m4eswn 2est6i deut4era: 34oper 24edei de5icai. ##57##-------nz41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn tet4arth@, 3h t6o xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh me4izwn. -Xwr4ion g6ar t6o AG periex4esqw 3up6o 3rht5h@ t5h@ AB ka6i t5h@ 2ek d4uo 2onom4atwn tet4arth@ t5h@ AD dihjrhm4enh@ e2i@ t6a 2on4omata kat6a t6o E, 35wn me5izon 24estw t6o AE: l4egw, 34oti 3h t6o AG xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh me4izwn. ^+^ -2Epe6i g6ar 3h AD 2ek d4uo 2onom4atwn 2est6i tet4arth, a3i AE, ED 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h AE t5h@ ED me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i 3h AE t5hj AB s4ummetr4o@ <2<2esti>2> m4hkei. tetm4hsqw 3h DE d4ixa kat6a t6o Z, ka6i t5wj 2ap6o t5h@ EZ 24ison par6a t6hn AE parabebl4hsqw parallhl4ogrammon t6o 3up6o AH, HE: 2as4ummetro@ 24ara 2est6in 3h AH t5hj HE m4hkei. 24hxqwsan par4allhloi t5hj AB a3i HQ, EK, ZL, ka6i t6a loip6a t6a a2ut6a to5i@ pr6o to4utou gegon4etw: faner6on d4h, 34oti 3h t6o AG xwr4ion dunam4enh 2est6in 3h MC. deikt4eon d4h, 34oti 3h MC 24alog4o@ 2estin 3h kaloum4enh me4izwn. 2epe6i 2as4ummetr4o@ 2estin 3h AH t5hj EH m4hkei, 2as4ummetr4on 2esti ka6i t6o AQ t5wj HK, tout4esti t6o SN t5wj NP: a3i MN, NC 24ara dun4amei e2is6in 2as4ummetroi. ka6i 2epe6i s4ummetr4o@ ^+^ 2estin 3h AE t5hj AB m4hkei, 3rht4on 2esti t6o AK: ka6i 2estin 24ison to5i@ 2ap6o t5wn MN, NC: 3rht6on 24ara <2<2est6i>2> ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn MN, NC. ka6i 2epe6i 2as4ummetr4o@ <2<2estin>2> 3h DE t5hj AB m4hkei, tout4esti t5hj EK, 2all6a 3h DE s4ummetr4o@ 2esti t5hj EZ, 2as4ummetro@ 24ara 3h EZ t5hj EK m4hkei. a3i EK, EZ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: m4eson 24ara t6o LE, tout4esti t6o MR. ka6i peri4exetai 3up6o t5wn MN, NC: m4eson 24ara 2est6i t6o 3up6o t5wn MN, NC. ka6i 3rht6on t6o <22> 2ek t5wn 2ap6o t5wn MN, NC, ka4i e2isin 2as4ummetroi a3i MN, NC dun4amei. 2e6an d6e d4uo e2uqe5iai dun4amei 2as4ummetroi sunteq5wsi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d' 3up' a2ut5wn m4eson, 3h 34olh 24alog4o@ 2estin, kale5itai d6e me4izwn. -3H MC 24ara 24alog4o@ 2estin 3h kaloum4enh me4izwn, ka6i d4unatai t6o AG xwr4ion: 34oper 24edei de5icai. ##58##-------nh41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn p4empth@, 3h t6o xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh 3rht6on ka6i m4eson dunam4enh. -Xwr4ion g6ar t6o AG periex4esqw 3up6o 3rht5h@ t5h@ AB ka6i t5h@ 2ek d4uo 2onom4atwn p4empth@ t5h@ AD dihjrhm4enh@ e2i@ t6a 2on4omata kat6a t6o E, 34wste t6o me5izon 24onoma e25inai t6o AE: l4egw <22>, 34oti 3h t6o AG xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh 3rht6on ka6i m4eson dunam4enh. ^+^ -Kateskeu4asqw g6ar t6a a2ut6a to5i@ pr4oteron dedeigm4enoi@: faner6on d4h, 34oti 3h t6o AG xwr4ion dunam4enh 2est6in 3h MC. deikt4eon d4h, 34oti 3h MC 2estin 3h 3rht6on ka6i m4eson dunam4enh. 2epe6i g6ar 2as4ummetr4o@ 2estin 3h AH t5hj HE, 2as4ummetron 24ara 2est6i ka6i t6o AQ t5wj QE, tout4esti t6o 2ap6o t5h@ MN t5wj 2ap6o t5h@ NC: a3i MN, NC 24ara dun4amei e2is6in 2as4ummetroi. ka6i 2epe6i 3h AD 2ek d4uo 2onom4atwn 2est6i p4empth, ka4i <2<2estin>2> 24elasson a2ut5h@ tm5hma t6o ED, s4ummetro@ 24ara 3h ED t5hj AB m4hkei. 2all6a 3h AE t5hj ED 2estin 2as4ummetro@: ka6i 3h AB 24ara t5hj AE 2estin 2as4ummetro@ m4hkei. <22> m4eson 24ara 2est6i t6o AK, tout4esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn MN, NC. ka6i 2epe6i s4ummetr4o@ 2estin 3h DE t5hj AB m4hkei, tout4esti t5hj EK, 2all6a 3h DE ^+^ t5hj EZ s4ummetr4o@ 2estin, ka6i 3h EZ 24ara t5hj EK s4ummetr4o@ 2estin. ka6i 3rht6h 3h EK: 3rht6on 24ara ka6i t6o EL, tout4esti t6o MR, tout4esti t6o 3up6o MNC: a3i MN, NC 24ara dun4amei 2as4ummetro4i e2isi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on. -3H MC 24ara 3rht6on ka6i m4eson dunam4enh 2est6i ka6i d4unatai t6o AG xwr4ion: 34oper 24edei de5icai. ##59##-------nq41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn 34ekth@, 3h t6o xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh d4uo m4esa dunam4enh. -Xwr4ion g6ar t6o ABGD periex4esqw 3up6o 3rht5h@ t5h@ AB ka6i t5h@ 2ek d4uo 2onom4atwn 34ekth@ t5h@ AD dihjrhm4enh@ e2i@ t6a 2on4omata kat6a t6o E, 34wste t6o me5izon 24onoma e25inai t6o AE: l4egw, 34oti 3h t6o AG dunam4enh 3h d4uo m4esa dunam4enh 2est4in. -Kateskeu4asqw <22> t6a a2ut6a to5i@ prodedeigm4enoi@. faner6on d4h, 34oti <2<3h>2> t6o AG dunam4enh 2est6in 3h MC, ka6i 34oti 2as4ummetr4o@ 2esti 3h MN t5hj NC dun4amei. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h EA t5hj AB m4hkei, a3i EA, AB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: m4eson 24ara 2est6i ^+^ t6o AK, tout4esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn MN, NC. p4alin, 2epe6i 2as4ummetr4o@ 2estin 3h ED t5hj AB m4hkei, 2as4ummetro@ 24ara 2est6i ka6i 3h ZE t5hj EK: a3i ZE, EK 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: m4eson 24ara 2est6i t6o EL, tout4esti t6o MR, tout4esti t6o 3up6o t5wn MNC. ka6i 2epe6i 2as4ummetro@ 3h AE t5hj EZ, ka6i t6o AK t5wj EL 2as4ummetr4on 2estin. 2all6a t6o m6en AK 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn MN, NC, t6o d6e EL 2esti t6o 3up6o t5wn MNC: 2as4ummetron 24ara 2est6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn MNC t5wj 3up6o t5wn MNC. ka4i 2esti m4eson 3ek4ateron a2ut5wn, ka6i a3i MN, NC dun4amei e2is6in 2as4um* metroi. -3H MC 24ara d4uo m4esa dunam4enh 2est6i ka6i d4unatai t6o AG: 34oper 24edei de5icai. ^+^ ##44^1^L^2##-----<22> t5wn 2ap6o t5wn AD, DG: t6a 24ara 2ap6o t5wn AG, GB me4izon4a 2esti to5u d6i@ 3up6o t5wn AG, GB: 34oper 24edei de5icai.>2> ##60##-------c41 -T6o 2ap6o t5h@ 2ek d4uo 2onom4atwn par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn pr4wthn. -24Estw 2ek d4uo 2onom4atwn 3h AB dihjrhm4enh e2i@ t6a 2on4omata kat6a t6o G, 34wste t6o me5izon 24onoma e25inai t6o AG, ka6i ^+^ 2ekke4isqw 3rht6h 3h DE, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn DE parabebl4hsqw t6o DEZH pl4ato@ poio5un t6hn DH. l4egw, 34oti 3h DH 2ek d4uo 2onom4atwn 2est6i pr4wth. -Parabebl4hsqw g6ar par6a t6hn DE t5wj m6en 2ap6o t5h@ AG 24ison t6o DQ, t5wj d6e 2ap6o t5h@ BG 24ison t6o KL: loip6on 24ara t6o d6i@ 3up6o t5wn AG, GB 24ison 2est6i t5wj MZ. tetm4hsqw 3h MH d4ixa kat6a t6o N, ka6i par4allhlo@ 24hxqw 3h NC <2<3ekat4eraj t5wn ML, HZ>2>. 3ek4ateron 24ara t5wn MC, NZ 24ison 2est6i t5wj 34apac 3up6o t5wn AGB. ka6i 2epe6i 2ek d4uo 2onom4atwn 2est6in 3h AB dihjrhm4enh e2i@ t6a 2on4omata kat6a t6o G, a3i AG, GB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: t6a 24ara 2ap6o t5wn AG, GB 3rht4a 2esti ka6i s4ummetra 2all4hloi@: 34wste ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB <22>. ka4i 2estin 24ison t5wj DL: 3rht6on 24ara 2est6i t6o DL. ka6i par6a 3rht6hn t6hn DE par4akeitai: 3rht6h 24ara 2est6in 3h DM ka6i s4ummetro@ t5hj DE m4hkei. p4alin, 2epe6i a3i AG, GB 3rhta4i e2isi dun4amei m4onon s4ummetroi, m4eson 24ara 2est6i t6o d6i@ 3up6o t5wn AG, GB, tout4esti t6o MZ. ka6i par6a 3rht6hn t6hn ML par4akeitai: 3rht6h 24ara ka6i 3h MH 2esti ka6i 2as4ummetro@ ^+^ t5hj ML, tout4esti t5hj DE, m4hkei. 24esti d6e ka6i 3h MD 3rht6h ka6i t5hj DE m4hkei s4ummetro@: 2as4ummetro@ 24ara 2est6in 3h DM t5hj MH m4hkei. ka4i e2isi 3rhta4i: a3i DM, MH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h DH. -Deikt4eon d4h, 34oti ka6i pr4wth. -2Epe6i t5wn 2ap6o t5wn AG, GB m4eson 2an4alog4on 2esti t6o 3up6o t5wn AGB, ka6i t5wn DQ, KL 24ara m4eson 2an4alog4on 2esti t6o MC. 24estin 24ara 3w@ t6o DQ pr6o@ t6o MC, o34utw@ t6o MC pr6o@ t6o KL, tout4estin 3w@ 3h DK pr6o@ t6hn MN, 3h MN pr6o@ t6hn MK: t6o 24ara 3up6o t5wn DK, KM 24ison 2est6i t5wj 2ap6o t5h@ MN, ka6i 2epe6i s4ummetr4on 2esti t6o 2ap6o t5h@ AG t5wj 2ap6o t5h@ GB, s4ummetr4on 2esti ka6i t6o DQ t5wj KL: 34wste ka6i 3h DK t5hj KM s4ummetr4o@ 2estin. ka6i 2epe6i me4izon4a 2esti t6a 2ap6o t5wn AG, GB to5u d6i@ 3up6o t5wn AG, GB, me5izon 24ara ka6i t6o DL to5u MZ: 34wste ka6i 3h DM t5h@ MH me4izwn 2est4in. ka4i 2estin 24ison t6o 3up6o t5wn DK, KM t5wj 2ap6o t5h@ MN, tout4esti t5wj tet4artwj to5u 2ap6o t5h@ MH, ka6i s4ummetro@ 3h DK t5hj KM. 2e6an d6e 25wsi d4uo e2uqe5iai 24anisoi, t5wj d6e tet4artwj m4erei to5u 2ap6o t5h@ 2el4assono@ 24ison par6a t6hn me4izona parablhq5hj 2elle5ipon e24idei tetrag4wnwj ka6i e2i@ s4ummetra a2ut6hn diair5hj, 3h me4izwn t5h@ 2el4assono@ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj: 3h DM 24ara t5h@ MH me5izon d4unatai t5wj ^+^ 2ap6o summ4etrou 3eaut5hj. ka4i e2isi 3rhta6i a3i DM, MH, ka6i 3h DM me5izon 24onoma s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj DE m4hkei. -3H DH 24ara 2ek d4uo 2onom4atwn 2est6i pr4wth: 34oper 24edei de5icai. ##61##-------ca41 -T6o 2ap6o t5h@ 2ek d4uo m4eswn pr4wth@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn deut4eran. -24Estw 2ek d4uo m4eswn pr4wth 3h AB dihjrhm4enh e2i@ t6a@ m4esa@ kat6a t6o G, 34wn me4izwn 3h AG, ka6i 2ekke4isqw 3rht6h 3h DE, ka6i parabebl4hsqw par6a t6hn DE t5wj 2ap6o t5h@ AB 24ison parallhl4ogrammon t6o DZ pl4ato@ poio5un t6hn DH: l4egw, 34oti 3h DH 2ek d4uo 2onom4atwn 2est6i deut4era. -Kateskeu4asqw g6ar t6a a2ut6a to5i@ pr6o to4utou. ka6i 2epe6i 3h AB 2ek d4uo m4eswn 2est6i pr4wth dihjrhm4enh kat6a t6o G, a3i AG, GB 24ara m4esai e2is6i dun4amei m4onon s4ummetroi 3rht6on peri4exousai: 34wste ka6i t6a 2ap6o t5wn AG, GB m4esa 2est4in. m4eson 24ara 2est6i t6o DL. ka6i par6a 3rht6hn t6hn DE parab4eblhtai: 3rht6h 24ara 2est6in 3h MD ka6i 2as4ummetro@ t5hj DE m4hkei. p4alin, 2epe6i 3rht4on 2esti t6o d6i@ 3up6o t5wn AG, GB, 3rht4on 2esti ka6i t6o MZ. ka6i par6a 3rht6hn t6hn ML par4akeitai: 3rht6h 24ara <2<2est6i>2> ka6i 3h MH ^+^ ka6i m4hkei s4ummetro@ t5hj ML, tout4esti t5hj DE: 2as4ummetro@ 24ara 2est6in 3h DM t5hj MH m4hkei. ka4i e2isi 3rhta4i: a3i DM, MH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h DH. -Deikt4eon d4h, 34oti ka6i deut4era. -2Epe6i g6ar t6a 2ap6o t5wn AG, GB me4izon4a 2esti to5u d6i@ 3up6o t5wn AG, GB, me5izon 24ara ka6i t6o DL to5u MZ: 34wste ka6i 3h DM t5h@ MH. ka6i 2epe6i s4ummetr4on 2esti t6o 2ap6o t5h@ AG t5wj 2ap6o t5h@ GB, s4ummetr4on 2esti ka6i t6o DQ t5wj KL: 34wste ka6i 3h DK t5hj KM s4ummetr4o@ 2estin ka4i 2esti t6o 3up6o t5wn DKM 24ison t5wj 2ap6o t5h@ MN: 3h DM 24ara t5h@ MH me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. ka4i 2estin 3h MH s4ummetro@ t5hj DE m4hkei. -3H DH 24ara 2ek d4uo 2onom4atwn 2est6i deut4era. ##62##-------cb41 -T6o 2ap6o t5h@ 2ek d4uo m4eswn deut4era@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn tr4ithn. -24Estw 2ek d4uo m4eswn deut4era 3h AB dihjrhm4enh e2i@ t6a@ m4esa@ kat6a t6o G, 34wste t6o me5izon tm5hma e25inai t6o AG, 3rht6h d4e ti@ 24estw 3h DE, ka6i par6a t6hn DE t5wj 2ap6o ^+^ t5h@ AB 24ison parallhl4ogrammon parabebl4hsqw t6o DZ pl4ato@ poio5un t6hn DH: l4egw, 34oti 3h DH 2ek d4uo 2onom4atwn 2est6i tr4ith. -Kateskeu4asqw t6a a2ut6a to5i@ prodedeigm4enoi@. ka6i ^-^ 2epe6i 2ek d4uo m4eswn deut4era 2est6in 3h AB dihjrhm4enh kat6a t6o G, a3i AG, GB 24ara m4esai e2is6i dun4amei m4onon s4ummetroi m4eson peri4exousai: 34wste ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB m4eson 2est4in. ka4i 2estin 24ison t5wj DL: m4eson 24ara ka6i t6o DL. ka6i par4akeitai par6a 3rht6hn t6hn DE: 3rht6h 24ara 2est6i ka6i 3h MD ka6i 2as4ummetro@ t5hj DE m4hkei. di6a t6a a2ut6a d6h ka6i 3h MH 3rht4h 2esti ka6i 2as4ummetro@ t5hj ML, tout4esti t5hj DE, m4hkei: 3rht6h 24ara 2est6in 3ekat4era t5wn DM, MH ka6i 2as4ummetro@ t5hj DE m4hkei. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h AG t5hj GB m4hkei, 3w@ d6e 3h AG pr6o@ t6hn GB, o34utw@ t6o 2ap6o t5h@ AG pr6o@ t6o 3up6o t5wn AGB, 2as4ummetron 24ara ka6i t6o 2ap6o t5h@ AG t5wj 3up6o t5wn AGB. 34wste ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB t5wj d6i@ 3up6o t5wn AGB 2as4ummetr4on 2estin, tout4esti t6o DL t5wj MZ: 34wste ka6i 3h DM t5hj MH 2as4ummetr4o@ 2estin. ka4i e2isi 3rhta4i: 2ek d4uo 24ara 2onom4atwn 2est6in 3h DH. -Deikt4eon <22>, 34oti ka6i tr4ith. -3Omo4iw@ d6h to5i@ prot4eroi@ 2epilogio4umeqa, 34oti me4izwn ^+^ 2est6in 3h DM t5h@ MH, ka6i s4ummetro@ 3h DK t5hj KM. ka4i 2esti t6o 3up6o t5wn DKM 24ison t5wj 2ap6o t5h@ MN: 3h DM 24ara t5h@ MH me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. ka6i o2udet4era t5wn DM, MH s4ummetr4o@ 2esti t5hj DE m4hkei. -3H DH 24ara 2ek d4uo 2onom4atwn 2est6i tr4ith: 34oper 24edei de5icai. ##63##-------cg41 -T6o 2ap6o t5h@ me4izono@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn tet4arthn. -24Estw me4izwn 3h AB dihjrhm4enh kat6a t6o G, 34wste me4izona e25inai t6hn AG t5h@ GB, 3rht6h d6e 3h DE, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn DE parabebl4hsqw t6o DZ parallhl4ogrammon pl4ato@ poio5un t6hn DH: l4egw, 34oti 3h DH 2ek d4uo 2onom4atwn 2est6i tet4arth. -Kateskeu4asqw t6a a2ut6a to5i@ prodedeigm4enoi@. ka6i 2epe6i me4izwn 2est6in 3h AB dihjrhm4enh kat6a t6o G, a3i AG, GB dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d6e 3up' a2ut5wn m4eson. 2epe6i o25un 3rht4on 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB, 3rht6on 24ara 2est6i t6o DL: 3rht6h 24ara ka6i 3h DM ^+^ ka6i s4ummetro@ t5hj DE m4hkei. p4alin, 2epe6i m4eson 2est6i t6o d6i@ 3up6o t5wn AG, GB, tout4esti t6o MZ, ka6i par6a 3rht4hn 2esti t6hn ML, 3rht6h 24ara 2est6i ka6i 3h MH ka6i 2as4ummetro@ t5hj DE m4hkei: 2as4ummetro@ 24ara 2est6i ka6i 3h DM t5hj MH m4hkei. a3i DM, MH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h DH. -Deikt4eon <22>, 34oti ka6i tet4arth. -3Omo4iw@ d6h de4icomen to5i@ pr4oteron, 34oti me4izwn 2est6in 3h DM t5h@ MH, ka6i 34oti t6o 3up6o DKM 24ison 2est6i t5wj 2ap6o t5h@ MN. 2epe6i o25un 2as4ummetr4on 2esti t6o 2ap6o t5h@ AG t5wj 2ap6o t5h@ GB, 2as4ummetron 24ara 2est6i ka6i t6o DQ t5wj KL: 34wste 2as4ummetro@ ka6i 3h DK t5hj KM 2estin. 2e6an d6e 25wsi d4uo e2uqe5iai 24anisoi, t5wj d6e tet4artwj m4erei to5u 2ap6o t5h@ 2el4assono@ 24ison parallhl4ogrammon par6a t6hn me4izona parablhq5hj 2elle5ipon e24idei tetrag4wnwj ka6i e2i@ 2as4ummetra a2ut6hn diair5hj, 3h me4izwn t5h@ 2el4assono@ me5izon dun4hsetai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei: 3h DM 24ara t5h@ MH me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i e2isin a3i DM, MH 3rhta6i dun4amei m4onon s4ummetroi, ka6i 3h DM s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj DE. -3H DH 24ara 2ek d4uo 2onom4atwn 2est6i tet4arth: 34oper ^-^ 24edei de5icai. ^+^ ##64##-------cd41 -T6o 2ap6o t5h@ 3rht6on ka6i m4eson dunam4enh@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn p4empthn. -24Estw 3rht6on ka6i m4eson dunam4enh 3h AB dihjrhm4enh e2i@ t6a@ e2uqe4ia@ kat6a t6o G, 34wste me4izona e25inai t6hn AG, ka6i 2ekke4isqw 3rht6h 3h DE, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn DE parabebl4hsqw t6o DZ pl4ato@ poio5un t6hn DH: l4egw, 34oti 3h DH 2ek d4uo 2onom4atwn 2est6i p4empth. -Kateskeu4asqw t6a a2ut6a to5i@ pr6o to4utou. 2epe6i o25un 3rht6on ka6i m4eson dunam4enh 2est6in 3h AB dihjrhm4enh kat6a t6o G, a3i AG, GB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on. 2epe6i o25un m4eson 2est6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB, m4eson 24ara 2est6i t6o DL: 34wste 3rht4h 2estin 3h DM ka6i m4hkei 2as4ummetro@ t5hj DE. p4alin, 2epe6i 3rht4on 2esti t6o d6i@ 3up6o t5wn AGB, tout4esti t6o MZ, 3rht6h 24ara 3h MH ka6i s4ummetro@ t5hj DE. 2as4ummetro@ 24ara 3h DM t5hj MH: a3i DM, MH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h DH. -L4egw d4h, 34oti ka6i p4empth. -3Omo4iw@ g6ar deixq4hsetai, 34oti t6o 3up6o t5wn DKM 24ison ^+^ 2est6i t5wj 2ap6o t5h@ MN, ka6i 2as4ummetro@ 3h DK t5hj KM m4hkei: 3h DM 24ara t5h@ MH me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i e2isin a3i DM, MH <2<3rhta6i>2> dun4amei m4onon s4ummetroi, ka6i 3h 2el4asswn 3h MH s4ummetro@ t5hj DE m4hkei. -3H DH 24ara 2ek d4uo 2onom4atwn 2est6i p4empth: 34oper ^-^ 24edei de5icai. ##65##-------ce41 -T6o 2ap6o t5h@ d4uo m4esa dunam4enh@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn 34ekthn. -24Estw d4uo m4esa dunam4enh 3h AB dihjrhm4enh kat6a t6o G, 3rht6h d6e 24estw 3h DE. ka6i par6a t6hn DE t5wj 2ap6o t5h@ AB 24ison parabebl4hsqw t6o DZ pl4ato@ poio5un t6hn DH: l4egw, 34oti 3h DH 2ek d4uo 2onom4atwn 2est6in 34ekth. -Kateskeu4asqw g6ar t6a a2ut6a to5i@ pr4oteron. ka6i 2epe6i 3h AB d4uo m4esa dunam4enh 2est6i dihjrhm4enh kat6a t6o G, a3i AG, GB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson ka6i t6o 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t6o 2ek t5wn 2ap' a2ut5wn tetrag4wnwn sugke4imenon t5wj 3up' a2ut5wn: 34wste kat6a t6a prodedeigm4ena m4eson 2est6in 3ek4ateron t5wn ^+^ DL, MZ. ka6i par6a 3rht6hn t6hn DE par4akeitai: 3rht6h 24ara 2est6in 3ekat4era t5wn DM, MH ka6i 2as4ummetro@ t5hj DE m4hkei. ka6i 2epe6i 2as4ummetr4on 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB t5wj d6i@ 3up6o t5wn AG, GB, 2as4ummetron 24ara 2est6i t6o DL t5wj MZ. 2as4ummetro@ 24ara ka6i 3h DM t5hj MH: a3i DM, MH 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h DH. -L4egw d4h, 34oti ka6i 34ekth. -3Omo4iw@ d6h p4alin de4icomen, 34oti t6o 3up6o t5wn DKM 24ison 2est6i t5wj 2ap6o t5h@ MN, ka6i 34oti 3h DK t5hj KM m4hkei 2est6in 2as4ummetro@: ka6i di6a t6a a2ut6a d6h 3h DM t5h@ MH me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei. ka6i o2udet4era t5wn DM, MH s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj DE m4hkei. -3H DH 24ara 2ek d4uo 2onom4atwn 2est6in 34ekth: 34oper ^-^ 24edei de5icai. ##66##-------cst41 -3H t5hj 2ek d4uo 2onom4atwn m4hkei s4ummetro@ ka6i a2ut6h 2ek d4uo 2onom4atwn 2est6i ka6i t5hj t4acei 3h a2ut4h. -24Estw 2ek d4uo 2onom4atwn 3h AB, ka6i t5hj AB m4hkei s4ummetro@ 24estw 3h GD: l4egw, 34oti 3h GD 2ek d4uo 2onom4atwn 2est6i ka6i t5hj t4acei 3h a2ut6h t5hj AB. ^+^ -2Epe6i g6ar 2ek d4uo 2onom4atwn 2est6in 3h AB, dihjr4hsqw e2i@ t6a 2on4omata kat6a t6o E, ka6i 24estw me5izon 24onoma t6o AE: a3i AE, EB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. gegon4etw 3w@ 3h AB pr6o@ t6hn GD, o34utw@ 3h AE pr6o@ t6hn GZ: ka6i loip6h 24ara 3h EB pr6o@ loip6hn t6hn ZD 2estin, 3w@ 3h AB pr6o@ t6hn GD. s4ummetro@ d6e 3h AB t5hj GD m4hkei. s4ummetro@ 24ara 2est6i ka6i 3h m6en AE t5hj GZ, 3h d6e EB t5hj ZD. ka4i e2isi 3rhta6i a3i AE, EB: 3rhta6i 24ara e2is6i ka6i a3i GZ, ZD. ka6i <2<2epe4i>2> 2estin 3w@ 3h AE pr6o@ GZ, 3h EB pr6o@ ZD. 2enall6ac 24ara 2est6in 3w@ 3h AE pr6o@ EB, 3h GZ pr6o@ ZD. a3i d6e AE, EB dun4amei m4onon <22> s4ummetroi: ka6i a3i GZ, ZD 24ara dun4amei m4onon e2is6i s4ummetroi. ka4i e2isi 3rhta4i: 2ek d4uo 24ara 2onom4atwn 2est6in 3h GD. -L4egw d4h, 34oti t5hj t4acei 2est6in 3h a2ut6h t5hj AB. -3H g6ar AE t5h@ EB me5izon d4unatai 24htoi t5wj 2ap6o summ4etrou 3eaut5hj 26h t5wj 2ap6o 2asumm4etrou. e2i m6en o25un 3h AE t5h@ EB me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h GZ t5h@ ZD me5izon dun4hsetai t5wj 2ap6o summ4etrou 3eaut5hj. ka6i e2i m6en s4ummetr4o@ 2estin 3h AE t5hj 2ekkeim4enhj 3rht5hj, ka6i 3h GZ s4ummetro@ a2ut5hj 24estai, ka6i di6a to5uto 3ekat4era t5wn AB, GD 2ek d4uo 2onom4atwn 2est6i pr4wth, ^+^ tout4esti t5hj t4acei 3h a2ut4h. e2i d6e 3h EB s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj, ka6i 3h ZD s4ummetr4o@ 2estin a2ut5hj, ka6i di6a to5uto p4alin t5hj t4acei 3h a2ut6h 24estai t5hj AB: 3ekat4era g6ar a2ut5wn 24estai 2ek d4uo 2onom4atwn deut4era. e2i d6e o2udet4era t5wn AE, EB s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj, o2udet4era t5wn GZ, ZD s4ummetro@ a2ut5hj 24estai, ka4i 2estin 3ekat4era tr4ith. e2i d6e 3h AE t5h@ EB me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i 3h GZ t5h@ ZD me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka6i e2i m6en 3h AE s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj, ka6i 3h GZ s4ummetr4o@ 2estin a2ut5hj, ka4i 2estin 3ekat4era tet4arth. e2i d6e 3h EB, ka6i 3h ZD, ka6i 24estai 3ekat4era p4empth. e2i d6e o2udet4era t5wn AE, EB, ka6i t5wn GZ, ZD o2udet4era s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj, ka6i 24estai 3ekat4era 34ekth. -34Wste 3h t5hj 2ek d4uo 2onom4atwn m4hkei s4ummetro@ 2ek d4uo 2onom4atwn 2est6i ka6i t5hj t4acei 3h a2ut4h: 34oper 24edei ^-^ de5icai. ##67##-------cz41 -3H t5hj 2ek d4uo m4eswn m4hkei s4ummetro@ ka6i a2ut6h 2ek d4uo m4eswn 2est6i ka6i t5hj t4acei 3h a2ut4h. ^+^ -24Estw 2ek d4uo m4eswn 3h AB, ka6i t5hj AB s4ummetro@ 24estw m4hkei 3h GD: l4egw, 34oti 3h GD 2ek d4uo m4eswn 2est6i ka6i t5hj t4acei 3h a2ut6h t5hj AB. -2Epe6i g6ar 2ek d4uo m4eswn 2est6in 3h AB, dihjr4hsqw e2i@ t6a@ m4esa@ kat6a t6o E: a3i AE, EB 24ara m4esai e2is6i dun4amei m4onon s4ummetroi. ka6i gegon4etw 3w@ 3h AB pr6o@ GD, 3h AE pr6o@ GZ: ka6i loip6h 24ara 3h EB pr6o@ loip6hn t6hn ZD 2estin, 3w@ 3h AB pr6o@ GD. s4ummetro@ d6e 3h AB t5hj GD m4hkei: s4ummetro@ 24ara ka6i 3ekat4era t5wn AE, EB 3ekat4eraj t5wn GZ, ZD. m4esai d6e a3i AE, EB: m4esai 24ara ka6i a3i GZ, ZD. ka6i 2epe4i 2estin 3w@ 3h AE pr6o@ EB, 3h GZ pr6o@ ZD, a3i d6e AE, EB dun4amei m4onon s4ummetro4i e2isin, ka6i a3i GZ, ZD <2<24ara>2> dun4amei m4onon s4ummetro4i e2isin. 2ede4ixqhsan d6e ka6i m4esai: 3h GD 24ara 2ek d4uo m4eswn 2est4in. -L4egw d4h, 34oti ka6i t5hj t4acei 3h a2ut4h 2esti t5hj AB. -2Epe6i g4ar 2estin 3w@ 3h AE pr6o@ EB, 3h GZ pr6o@ ZD, ka6i 3w@ 24ara t6o 2ap6o t5h@ AE pr6o@ t6o 3up6o t5wn AEB, o34utw@ t6o 2ap6o t5h@ GZ pr6o@ t6o 3up6o t5wn GZD: 2enall6ac 3w@ t6o 2ap6o t5h@ AE pr6o@ t6o 2ap6o t5h@ GZ, o34utw@ t6o 3up6o t5wn AEB pr6o@ t6o 3up6o t5wn GZD. s4ummetron d6e t6o 2ap6o ^+^ t5h@ AE t5wj 2ap6o t5h@ GZ: s4ummetron 24ara ka6i t6o 3up6o t5wn AEB t5wj 3up6o t5wn GZD. e24ite o25un 3rht4on 2esti t6o 3up6o t5wn AEB, ka6i t6o 3up6o t5wn GZD 3rht4on 2estin <22>. e24ite m4eson, m4eson, ka4i 2estin 3ekat4era deut4era. -Ka6i di6a to5uto 24estai 3h GD t5hj AB t5hj t4acei 3h a2ut4h: 34oper 24edei de5icai. ##68##-------ch41 -3H t5hj me4izoni s4ummetro@ ka6i a2ut6h me4izwn 2est4in. -24Estw me4izwn 3h AB, ka6i t5hj AB s4ummetro@ 24estw 3h GD: l4egw 34oti 3h GD me4izwn 2est4in. -Dihjr4hsqw 3h AB kat6a t6o E: a3i AE, EB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d' 3up' a2ut5wn m4eson: ka6i gegon4etw t6a a2ut6a to5i@ pr4oteron ka6i 2epe4i 2estin 3w@ 3h AB pr6o@ t6hn GD, o34utw@ 34h te AE pr6o@ t6hn GZ ka6i 3h EB pr6o@ t6hn ZD, ka6i 3w@ 24ara 3h AE pr6o@ t6hn GZ, o34utw@ 3h EB pr6o@ t6hn ZD. s4ummetro@ d6e 3h AB t5hj GD. s4ummetro@ 24ara ka6i 3ekat4era t5wn AE, EB 3ekat4eraj t5wn GZ, ZD. ^+^ ka6i 2epe4i 2estin 3w@ 3h AE pr6o@ t6hn GZ, o34utw@ 3h EB pr6o@ t6hn ZD, ka6i 2enall6ac 3w@ 3h AE pr6o@ EB, o34utw@ 3h GZ pr6o@ ZD, ka6i sunq4enti 24ara 2est6in 3w@ 3h AB pr6o@ t6hn BE, o34utw@ 3h GD pr6o@ t6hn DZ: ka6i 3w@ 24ara t6o 2ap6o t5h@ AB pr6o@ t6o 2ap6o t5h@ BE, o34utw@ t6o 2ap6o t5h@ GD pr6o@ t6o 2ap6o t5h@ DZ. 3omo4iw@ d6h de4icomen, 34oti ka6i 3w@ t6o 2ap6o t5h@ AB pr6o@ t6o 2ap6o t5h@ AE, o34utw@ t6o 2ap6o t5h@ GD pr6o@ t6o 2ap6o t5h@ GZ. ka6i 3w@ 24ara t6o 2ap6o t5h@ AB pr6o@ t6a 2ap6o t5wn AE, EB, o34utw@ t6o 2ap6o t5h@ GD pr6o@ t6a 2ap6o t5wn GZ, ZD: ka6i 2enall6ac 24ara 2est6in 3w@ t6o 2ap6o t5h@ AB pr6o@ t6o 2ap6o t5h@ GD, o34utw@ t6a 2ap6o t5wn AE, EB pr6o@ t6a 2ap6o t5wn GZ, ZD. s4ummetron d6e t6o 2ap6o t5h@ AB t5wj 2ap6o t5h@ GD: s4ummetra 24ara ka6i t6a 2ap6o t5wn AE, EB to5i@ 2ap6o t5wn GZ, ZD. ka4i 2esti t6a 2ap6o t5wn AE, EB 34ama 3rht4on, ka6i t6a 2ap6o t5wn GZ, ZD 34ama 3rht4on 2estin. 3omo4iw@ d6e ka6i t6o d6i@ 3up6o t5wn AE, EB s4ummetr4on 2esti t5wj d6i@ 3up6o t5wn GZ, ZD. ka4i 2esti m4eson t6o d6i@ 3up6o t5wn AE, EB: m4eson 24ara ka6i t6o d6i@ 3up6o t5wn GZ, ZD. a3i GZ, ZD 24ara dun4amei 2as4ummetro4i e2isi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 34ama ^+^ 3rht4on, t6o d6e d6i@ 3up' a2ut5wn m4eson: 34olh 24ara 3h GD 24alog4o@ 2estin 3h kaloum4enh me4izwn. -3H 24ara t5hj me4izoni s4ummetro@ me4izwn 2est4in: 34oper ^-^ 24edei de5icai. ##69##-------cq41 -3H t5hj 3rht6on ka6i m4eson dunam4enhj s4ummetro@ <22> 3rht6on ka6i m4eson dunam4enh 2est4in. -24Estw 3rht6on ka6i m4eson dunam4enh 3h AB, ka6i t5hj AB s4ummetro@ 24estw 3h GD: deikt4eon, 34oti ka6i 3h GD 3rht6on ka6i m4eson dunam4enh 2est4in. -Dihjr4hsqw 3h AB e2i@ t6a@ e2uqe4ia@ kat6a t6o E: a3i AE, EB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on: ka6i t6a a2ut6a kateskeu4asqw to5i@ pr4oteron. 3omo4iw@ d6h de4icomen, 34oti ka6i a3i GZ, ZD dun4amei e2is6in 2as4ummetroi, ka6i s4ummetron t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn GZ, ZD, t6o d6e 3up6o AE, EB t5wj 3up6o GZ, ZD: 34wste ka6i t6o <22> sugke4imenon 2ek t5wn 2ap6o t5wn GZ, ZD tetrag4wnwn 2est6i m4eson, t6o d' 3up6o t5wn GZ, ZD 3rht4on. -3Rht6on 24ara ka6i m4eson dunam4enh 2est6in 3h GD: 34oper ^-^ 24edei de5icai. ##70##-------o41 -3H t5hj d4uo m4esa dunam4enhj s4ummetro@ d4uo m4esa dunam4enh 2est4in. ^+^ -24Estw d4uo m4esa dunam4enh 3h AB, ka6i t5hj AB s4ummetro@ 3h GD: deikt4eon, 34oti ka6i 3h GD d4uo m4esa dunam4enh 2est4in. -2Epe6i g6ar d4uo m4esa dunam4enh 2est6in 3h AB, dihjr4hsqw e2i@ t6a@ e2uqe4ia@ kat6a t6o E: a3i AE, EB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn <22> m4eson ka6i t6o 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t6o sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB tetrag4wnwn t5wj 3up6o t5wn AE, EB: ka6i kateskeu4asqw t6a a2ut6a to5i@ pr4oteron. 3omo4iw@ d6h de4icomen, 34oti ka6i a3i GZ, ZD dun4amei e2is6in 2as4ummetroi ka6i s4ummetron t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn GZ, ZD, t6o d6e 3up6o t5wn AE, EB t5wj 3up6o t5wn GZ, ZD: 34wste ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn GZ, ZD tetrag4wnwn m4eson 2est6i ka6i t6o 3up6o t5wn GZ, ZD m4eson ka6i 24eti 2as4ummetron t6o sugke4imenon 2ek t5wn 2ap6o t5wn GZ, ZD tetrag4wnwn t5wj 3up6o t5wn GZ, ZD. -3H 24ara GD d4uo m4esa dunam4enh 2est4in: 34oper 24edei ^-^ de5icai. ##71##-------oa41 -3Rhto5u ka6i m4esou suntiqem4enou t4essare@ 24alogoi g4ignontai 24htoi 2ek d4uo 2onom4atwn 26h 2ek d4uo m4eswn pr4wth 26h me4izwn 26h 3rht6on ka6i m4eson dunam4enh. -24Estw 3rht6on m6en t6o AB, m4eson d6e t6o GD: l4egw, 34oti 3h t6o AD xwr4ion dunam4enh 24htoi 2ek d4uo 2onom4atwn 2est6in 26h 2ek d4uo m4eswn pr4wth 26h me4izwn 26h 3rht6on ka6i m4eson dunam4enh. ^+^ -T6o g6ar AB to5u GD 24htoi me5iz4on 2estin 26h 24elasson. 24estw pr4oteron me5izon: ka6i 2ekke4isqw 3rht6h 3h EZ, ka6i parabebl4hsqw par6a t6hn EZ t5wj AB 24ison t6o EH pl4ato@ poio5un t6hn EQ: t5wj d6e DG 24ison par6a t6hn EZ parabebl4hsqw t6o QI pl4ato@ poio5un t6hn QK. ka6i 2epe6i 3rht4on 2esti t6o AB ka4i 2estin 24ison t5wj EH, 3rht6on 24ara ka6i t6o EH. ka6i par6a <2<3rht6hn>2> t6hn EZ parab4eblhtai pl4ato@ poio5un t6hn EQ: 3h EQ 24ara 3rht4h 2esti ka6i s4ummetro@ t5hj EZ m4hkei. p4alin, 2epe6i m4eson 2est6i t6o GD ka4i 2estin 24ison t5wj QI, m4eson 24ara 2est6i ka6i t6o QI. ka6i par6a 3rht6hn t6hn EZ par4akeitai pl4ato@ poio5un t6hn QK: 3rht6h 24ara 2est6in 3h QK ka6i 2as4ummetro@ t5hj EZ m4hkei. ka6i 2epe6i m4eson 2est6i t6o GD, 3rht6on d6e t6o AB, 2as4ummetron 24ara 2est6i t6o AB t5wj GD: 34wste ka6i t6o EH 2as4ummetr4on 2esti t5wj QI. 3w@ d6e t6o EH pr6o@ t6o QI, o34utw@ 2est6in 3h EQ pr6o@ t6hn QK: 2as4ummetro@ 24ara 2est6i ka6i 3h EQ t5hj QK m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i EQ, QK 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h EK dihjrhm4enh kat6a t6o Q. ka6i 2epe6i me5iz4on 2esti t6o AB to5u GD, 24ison d6e t6o m6en AB t5wj EH, ^+^ t6o d6e GD t5wj QI, me5izon 24ara ka6i t6o EH to5u QI: ka6i 3h EQ 24ara me4izwn 2est6i t5h@ QK. 24htoi o25un 3h EQ t5h@ QK me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei 26h t5wj 2ap6o 2asumm4etrou. dun4asqw pr4oteron t5wj 2ap6o summ4etrou 3eaut5hj. ka4i 2estin 3h me4izwn 3h QE s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj t5hj EZ: 3h 24ara EK 2ek d4uo 2onom4atwn 2est6i pr4wth. 3rht6h d6e 3h EZ: 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn pr4wth@, 3h t6o xwr4ion dunam4enh 2ek d4uo 2onom4atwn 2est4in. 3h 24ara t6o EI dunam4enh 2ek d4uo 2onom4atwn 2est4in: 34wste ka6i 3h t6o AD dunam4enh 2ek d4uo 2onom4atwn 2est4in. 2all6a d6h dun4asqw 3h EQ t5h@ QK me5izon t5wj 2ap6o 2asumm4etrou 3eaut5hj: ka4i 2estin 3h me4izwn 3h EQ s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj t5hj EZ m4hkei: 3h 24ara EK 2ek d4uo 2onom4atwn 2est6i tet4arth. 3rht6h d6e 3h EZ: 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn tet4arth@, 3h t6o xwr4ion dunam4enh 24alog4o@ 2estin 3h kaloum4enh me4izwn. 3h 24ara t6o EI xwr4ion dunam4enh me4izwn 2est4in: 34wste ka6i 3h t6o AD dunam4enh me4izwn 2est4in. -2All6a d6h 24estw 24elasson t6o AB to5u GD: ka6i t6o EH 24ara 24elass4on 2esti to5u QI: 34wste ka6i 3h EQ 2el4asswn 2est6i t5h@ QK. ^+^ 24htoi d6e 3h QK t5h@ EQ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj 26h t5wj 2ap6o 2asumm4etrou. dun4asqw pr4oteron t5wj 2ap6o summ4etrou 3eaut5hj m4hkei: ka4i 2estin 3h 2el4asswn 3h EQ s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj t5hj EZ m4hkei: 3h 24ara EK 2ek d4uo 2onom4atwn 2est6i deut4era. 3rht6h d6e 3h EZ: 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn deut4era@, 3h t6o xwr4ion dunam4enh 2ek d4uo m4eswn 2est6i pr4wth. 3h 24ara t6o EI xwr4ion dunam4enh 2ek d4uo m4eswn 2est6i pr4wth: 34wste ka6i 3h t6o AD dunam4enh 2ek d4uo m4eswn 2est6i pr4wth. 2all6a d6h 3h QK t5h@ QE me5izon dun4asqw t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i 2estin 3h 2el4asswn 3h EQ s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj t5hj EZ: 3h 24ara EK 2ek d4uo 2onom4atwn 2est6i p4empth. 3rht6h d6e 3h EZ: 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn p4empth@, 3h t6o xwr4ion dunam4enh 3rht6on ka6i m4eson dunam4enh 2est4in. 3h 24ara t6o EI xwr4ion dunam4enh 3rht6on ka6i m4eson dunam4enh 2est4in: 34wste ka6i 3h t6o AD xwr4ion dunam4enh 3rht6on ka6i m4eson dunam4enh 2est4in. -3Rhto5u 24ara ka6i m4esou suntiqem4enou t4essare@ 24alogoi g4ignontai 24htoi 2ek d4uo 2onom4atwn 26h 2ek d4uo m4eswn pr4wth 26h me4izwn 26h 3rht6on ka6i m4eson dunam4enh: 34oper 24edei ^-^ de5icai. ^+^ ##72##-------ob41 -D4uo m4eswn 2asumm4etrwn 2all4hloi@ suntiqem4enwn a3i loipa6i d4uo 24alogoi g4ignontai 24htoi 2ek d4uo m4eswn deut4era 26h <2<3h>2> d4uo m4esa dunam4enh. -Sugke4isqw g6ar d4uo m4esa 2as4ummetra 2all4hloi@ t6a AB, GD: l4egw, 34oti 3h t6o AD xwr4ion dunam4enh 24htoi 2ek d4uo m4eswn 2est6i deut4era 26h d4uo m4esa dunam4enh. -T6o g6ar AB to5u GD 24htoi me5iz4on 2estin 26h 24elasson. 24estw, e2i t4uxoi, pr4oteron me5izon t6o AB to5u GD: ka6i 2ekke4isqw 3rht6h 3h EZ, ka6i t5wj m6en AB 24ison par6a t6hn EZ parabebl4hsqw t6o EH pl4ato@ poio5un t6hn EQ, t5wj d6e GD 24ison t6o QI pl4aton poio5un t6hn QK. ka6i 2epe6i m4eson 2est6in 3ek4ateron t5wn AB, GD, m4eson 24ara ka6i 3ek4ateron t5wn EH, QI. ka6i par6a 3rht6hn t6hn ZE par4akeitai pl4ato@ poio5un t6a@ EQ, QK: 3ekat4era 24ara t5wn EQ, QK 3rht4h 2esti ka6i 2as4ummetro@ t5hj EZ m4hkei. ka6i 2epe6i 2as4ummetr4on 2esti t6o AB t5wj GD, ka4i 2estin 24ison t6o m6en AB t5wj EH, t6o d6e GD t5wj QI, 2as4ummetron 24ara 2est6i ka6i t6o EH t5wj QI. 3w@ d6e t6o EH pr6o@ t6o QI, o34utw@ 2est6in ^+^ 3h EQ pr6o@ QK: 2as4ummetro@ 24ara 2est6in 3h EQ t5hj QK m4hkei. a3i EQ, QK 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 24ara 2onom4atwn 2est6in 3h EK. 24htoi d6e 3h EQ t5h@ QK me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj 26h t5wj 2ap6o 2asumm4etrou. dun4asqw pr4oteron t5wj 2ap6o summ4etrou 3eaut5hj m4hkei: ka6i o2udet4era t5wn EQ, QK s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj EZ m4hkei: 3h EK 24ara 2ek d4uo 2onom4atwn 2est6i tr4ith. 3rht6h d6e 3h EZ: 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn tr4ith@, 3h t6o xwr4ion dunam4enh 2ek d4uo m4eswn 2est6i deut4era: 3h 24ara t6o EI, tout4esti t6o AD, dunam4enh 2ek d4uo m4eswn 2est6i deut4era. 2all6a d6h 3h EQ t5h@ QK me5izon dun4asqw t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei: ka6i 2as4ummetr4o@ 2estin 3ekat4era t5wn EQ, QK t5hj EZ m4hkei: 3h 24ara EK 2ek d4uo 2onom4atwn 2est6in 34ekth. 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i t5h@ 2ek d4uo 2onom4atwn 34ekth@, 3h t6o xwr4ion dunam4enh 3h d4uo m4esa dunam4enh 2est4in: 34wste ka6i 3h t6o AD xwr4ion dunam4enh 3h d4uo m4esa dunam4enh 2est4in. <2<3Omo4iw@ d6h de4icomen, 34oti k26an 24elatton 25hj t6o AB to5u GD, 3h t6o AD xwr4ion dunam4enh 26h 2ek d4uo m4eswn deut4era 2est6in 24htoi d4uo m4esa dunam4enh>2>. -D4uo 24ara m4eswn 2asumm4etrwn 2all4hloi@ suntiqem4enwn a3i loipa6i d4uo 24alogoi g4ignontai 24htoi 2ek d4uo m4eswn deut4era 26h d4uo m4esa dunam4enh. ^+^ -3H 2ek d4uo 2onom4atwn ka6i a3i met' a2ut6hn 24alogoi o24ute t5hj m4eshj o24ute 2all4hlai@ e2is6in a3i a2uta4i. t6o m6en g6ar 2ap6o m4esh@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 3rht6hn ka6i 2as4ummetron t5hj par' 36hn par4akeitai m4hkei. t6o d6e 2ap6o t5h@ 2ek d4uo 2onom4atwn par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn pr4wthn. t6o d6e 2ap6o t5h@ 2ek d4uo m4eswn pr4wth@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn deut4eran. t6o d6e 2ap6o t5h@ 2ek d4uo m4eswn deut4era@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn tr4ithn. t6o d6e 2ap6o t5h@ me4izono@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn tet4arthn. t6o d6e 2ap6o t5h@ 3rht6on ka6i m4eson dunam4enh@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn p4empthn. t6o d6e 2ap6o t5h@ d4uo m4esa dunam4enh@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn 34ekthn. t6a d' e2irhm4ena pl4ath diaf4erei to5u te pr4wtou ka6i 2all4hlwn, to5u m6en pr4wtou, 34oti 3rht4h 2estin, 2all4hlwn d4e, 34oti t5hj t4acei o2uk e2is6in a3i a2uta4i: 34wste ka6i a2uta6i a3i 24alogoi diaf4erousin 2all4hlwn. ##73##-------og41 -2E6an 2ap6o 3rht5h@ 3rht6h 2afaireq5hj dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, 3h loip6h 24alog4o@ 2estin: kale4isqw d6e 2apotom4h. ^+^ -2Ap6o g6ar 3rht5h@ t5h@ AB 3rht6h 2afhjr4hsqw 3h BG dun4amei m4onon s4ummetro@ o25usa t5hj 34olh: l4egw, 34oti 3h loip6h 3h AG 24alog4o@ 2estin 3h kaloum4enh 2apotom4h. -2Epe6i g6ar 2as4ummetr4o@ 2estin 3h AB t5hj BG m4hkei, ka4i 2estin 3w@ 3h AB pr6o@ t6hn BG, o34utw@ t6o 2ap6o t5h@ AB pr6o@ t6o 3up6o t5wn AB, BG, 2as4ummetron 24ara 2est6i t6o 2ap6o t5h@ AB t5wj 3up6o t5wn AB, BG. 2all6a t5wj m6en 2ap6o t5h@ AB s4ummetr4a 2esti t6a 2ap6o t5wn AB, BG tetr4agwna, t5wj d6e 3up6o t5wn AB, BG s4ummetr4on 2esti t6o d6i@ 3up6o t5wn AB, BG. ka6i 2epeid4hper t6a 2ap6o t5wn AB, BG 24isa 2est6i t5wj d6i@ 3up6o t5wn AB, BG met6a to5u 2ap6o GA, ka6i loip5wj 24ara t5wj 2ap6o t5h@ AG 2as4ummetr4a 2esti t6a 2ap6o t5wn AB, BG. 3rht6a d6e t6a 2ap6o t5wn AB, BG: 24alogo@ 24ara 2est6in 3h AG: kale4isqw d6e 2apotom4h. 34oper 24edei de5icai. ^+^ ##74##-------od41 -2E6an 2ap6o m4esh@ m4esh 2afaireq5hj dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ 3rht6on peri4exousa, 3h loip6h 24alog4o@ 2estin: kale4isqw d6e m4esh@ 2apotom6h pr4wth. -2Ap6o g6ar m4esh@ t5h@ AB m4esh 2afhjr4hsqw 3h BG dun4amei m4onon s4ummetro@ o25usa t5hj AB, met6a d6e t5h@ AB 3rht6on poio5usa t6o 3up6o t5wn AB, BG: l4egw, 34oti 3h loip6h 3h AG 24alog4o@ 2estin: kale4isqw d6e m4esh@ 2apotom6h pr4wth. -2Epe6i g6ar a3i AB, BG m4esai e2is4in, m4esa 2est6i ka6i t6a 2ap6o t5wn AB, BG. 3rht6on d6e t6o d6i@ 3up6o t5wn AB, BG: 2as4ummetra 24ara t6a 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG: ka6i loip5wj 24ara t5wj 2ap6o t5h@ AG 2as4ummetr4on 2esti t6o d6i@ 3up6o t5wn AB, BG, 2epe6i k26an t6o 34olon 3en6i a2ut5wn 2as4ummetron 25hj, ka6i t6a 2ec 2arx5h@ meg4eqh 2as4ummetra 24estai. 3rht6on d6e t6o d6i@ 3up6o t5wn AB, BG: 24alogon 24ara t6o 2ap6o t5h@ AG: 24alogo@ 24ara 2est6in 3h AG: kale4isqw d6e m4esh@ 2apotom6h pr4wth. ##75##-------oe41 -2E6an 2ap6o m4esh@ m4esh 2afaireq5hj dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ m4eson peri4exousa, 3h loip6h 24alog4o@ 2estin: kale4isqw d6e m4esh@ 2apotom6h deut4era. ^+^ -2Ap6o g6ar m4esh@ t5h@ AB m4esh 2afhjr4hsqw 3h GB dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj t5hj AB, met6a d6e t5h@ 34olh@ t5h@ AB m4eson peri4exousa t6o 3up6o t5wn AB, BG: l4egw, 34oti 3h loip6h 3h AG 24alog4o@ 2estin: kale4isqw d6e m4esh@ 2apotom6h deut4era. -2Ekke4isqw g6ar 3rht6h 3h DI, ka6i to5i@ m6en 2ap6o t5wn AB, BG 24ison par6a t6hn DI parabebl4hsqw t6o DE pl4ato@ poio5un t6hn DH, t5wj d6e d6i@ 3up6o t5wn AB, BG 24ison par6a t6hn DI parabebl4hsqw t6o DQ pl4ato@ poio5un t6hn DZ: loip6on 24ara t6o ZE 24ison 2est6i t5wj 2ap6o t5h@ AG. ka6i 2epe6i m4esa ka6i s4ummetr4a 2esti t6a 2ap6o t5wn AB, BG, m4eson 24ara ka6i t6o DE. ka6i par6a 3rht6hn t6hn DI par4akeitai pl4ato@ poio5un t6hn DH: 3rht6h 24ara 2est6in 3h DH ka6i 2as4ummetro@ t5hj DI m4hkei. p4alin, 2epe6i m4eson 2est6i t6o 3up6o t5wn AB, BG, ka6i t6o d6i@ 24ara 3up6o t5wn AB, BG m4eson 2est4in. ka4i 2estin 24ison t5wj DQ: ka6i t6o DQ 24ara m4eson 2est4in. ka6i par6a 3rht6hn t6hn DI parab4eblhtai pl4ato@ poio5un t6hn DZ: ^+^ 3rht6h 24ara 2est6in 3h DZ ka6i 2as4ummetro@ t5hj DI m4hkei. ka6i 2epe6i a3i AB, BG dun4amei m4onon s4ummetro4i e2isin, 2as4ummetro@ 24ara 2est6in 3h AB t5hj BG m4hkei: 2as4ummetron 24ara ka6i t6o 2ap6o t5h@ AB tetr4agwnon t5wj 3up6o t5wn AB, BG. 2all6a t5wj m6en 2ap6o t5h@ AB s4ummetr4a 2esti t6a 2ap6o t5wn AB, BG, t5wj d6e 3up6o t5wn AB, BG s4ummetr4on 2esti t6o d6i@ 3up6o t5wn AB, BG: 2as4ummetron 24ara 2est6i t6o d6i@ 3up6o t5wn AB, BG to5i@ 2ap6o t5wn AB, BG. 24ison d6e to5i@ m6en 2ap6o t5wn AB, BG t6o DE, t5wj d6e d6i@ 3up6o t5wn AB, BG t6o DQ: 2as4ummetron 24ara <2<2est6i>2> t6o DE t5wj DQ. 3w@ d6e t6o DE pr6o@ t6o DQ, o34utw@ 3h HD pr6o@ t6hn DZ: 2as4ummetro@ 24ara 2est6in 3h HD t5hj DZ. ka4i e2isin 2amf4oterai 3rhta4i: a3i 24ara HD, DZ 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h ZH 24ara 2apotom4h 2estin. 3rht6h d6e 3h DI: t6o d6e 3up6o 3rht5h@ ka6i 2al4ogou periex4omenon 24alog4on 2estin, ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin. ka6i d4unatai t6o ZE 3h AG: 3h AG 24ara 24alog4o@ 2estin: kale4isqw d6e m4esh@ 2apotom6h deut4era. 34oper 24edei de5icai. ^+^ ##76##-------ost41 -2E6an 2ap6o e2uqe4ia@ e2uqe5ia 2afaireq5hj dun4amei 2as4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ poio5usa t6a m6en 2ap' a2ut5wn 34ama 3rht4on, t6o d' 3up' a2ut5wn m4eson, 3h loip6h 24alog4o@ 2estin: kale4isqw d6e 2el4asswn. -2Ap6o g6ar e2uqe4ia@ t5h@ AB e2uqe5ia 2afhjr4hsqw 3h BG dun4amei 2as4ummetro@ o25usa t5hj 34olhj poio5usa t6a proke4imena. l4egw, 34oti 3h loip6h 3h AG 24alog4o@ 2estin 3h kaloum4enh 2el4asswn. -2Epe6i g6ar t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG tetrag4wnwn 3rht4on 2estin, t6o d6e d6i@ 3up6o t5wn AB, BG m4eson, 2as4ummetra 24ara 2est6i t6a 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG: ka6i 2anastr4eyanti loip5wj t5wj 2ap6o t5h@ AG 2as4ummetr4a 2esti t6a 2ap6o t5wn AB, BG. 3rht6a d6e t6a 2ap6o t5wn AB, BG. 24alogon 24ara t6o 2ap6o t5h@ AG: 24alogo@ 24ara 3h AG: kale4isqw d6e 2el4asswn. 34oper 24edei de5icai. ##77##-------oz41 -2E6an 2ap6o e2uqe4ia@ e2uqe5ia 2afaireq5hj dun4amei 2as4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ poio5usa t6o m6en sugke4imenon ^+^ 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d6e d6i@ 3up' a2ut5wn 3rht4on, 3h loip6h 24alog4o@ 2estin: kale4isqw d6e 3h met6a 3rhto5u m4eson t6o 34olon poio5usa. -2Ap6o g6ar e2uqe4ia@ t5h@ AB e2uqe5ia 2afhjr4hsqw 3h BG dun4amei 2as4ummetro@ o25usa t5hj AB poio5usa t6a proke4imena: l4egw, 34oti 3h loip6h 3h AG 24alog4o@ 2estin 3h pro* eirhm4enh. -2Epe6i g6ar t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG tetrag4wnwn m4eson 2est4in, t6o d6e d6i@ 3up6o t5wn AB, BG 3rht4on, 2as4ummetra 24ara 2est6i t6a 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG: ka6i loip6on 24ara t6o 2ap6o t5h@ AG 2as4ummetr4on 2esti t5wj d6i@ 3up6o t5wn AB, BG. ka4i 2esti t6o d6i@ 3up6o t5wn AB, BG 3rht4on: t6o 24ara 2ap6o t5h@ AG 24alog4on 2estin: 24alogo@ 24ara 2est6in 3h AG: kale4isqw d6e 3h met6a 3rhto5u m4eson t6o 34olon poio5usa. 34oper 24edei de5icai. ##78##-------oh41 -2E6an 2ap6o e2uqe4ia@ e2uqe5ia 2afaireq5hj dun4amei 2as4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ poio5usa t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson t4o te d6i@ 3up' ^+^ a2ut5wn m4eson ka6i 24eti t6a 2ap' a2ut5wn tetr4agwna 2as4ummetra t5wj d6i@ 3up' a2ut5wn, 3h loip6h 24alog4o@ 2estin: kale4isqw d6e 3h met6a m4esou m4eson t6o 34olon poio5usa. -2Ap6o g6ar e2uqe4ia@ t5h@ AB e2uqe5ia 2afhjr4hsqw 3h BG dun4amei 2as4ummetro@ o25usa t5hj AB poio5usa t6a proke4imena: l4egw, 34oti 3h loip6h 3h AG 24alog4o@ 2estin 3h kaloum4enh 3h met6a m4esou m4eson t6o 34olon poio5usa. -2Ekke4isqw g6ar 3rht6h 3h DI, ka6i to5i@ m6en 2ap6o t5wn AB, BG 24ison par6a t6hn DI parabebl4hsqw t6o DE pl4ato@ poio5un t6hn DH, t5wj d6e d6i@ 3up6o t5wn AB, BG 24ison 2afhjr4hsqw t6o DQ <22>. loip6on 24ara t6o ZE 24ison 2est6i t5wj 2ap6o t5h@ AG: 34wste 3h AG d4unatai t6o ZE. ka6i 2epe6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AB, BG tetrag4wnwn m4eson 2est6i ka4i 2estin 24ison t5wj DE, m4eson 24ara <2<2est6i>2> t6o DE. ka6i par6a 3rht6hn t6hn DI par4akeitai pl4ato@ poio5un t6hn DH: 3rht6h 24ara 2est6in 3h DH ka6i 2as4ummetro@ t5hj DI m4hkei. p4alin, 2epe6i t6o d6i@ 3up6o t5wn AB, BG m4eson 2est6i ka4i 2estin 24ison t5wj DQ, t6o 24ara DQ m4eson 2est4in. ka6i par6a 3rht6hn t6hn DI par4akeitai pl4ato@ poio5un t6hn DZ: 3rht6h 24ara 2est6i ka6i 3h DZ ka6i 2as4ummetro@ ^+^ t5hj DI m4hkei. ka6i 2epe6i 2as4ummetr4a 2esti t6a 2ap6o t5wn AB, BG t5wj d6i@ 3up6o t5wn AB, BG, 2as4ummetron 24ara ka6i t6o DE t5wj DQ. 3w@ d6e t6o DE pr6o@ t6o DQ, o34utw@ 2est6i ka6i 3h DH pr6o@ t6hn DZ: 2as4ummetro@ 24ara 3h DH t5hj DZ. ka4i e2isin 2amf4oterai 3rhta4i: a3i HD, DZ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. 2apotom6h 24ara 2est6in 3h ZH: 3rht6h d6e 3h ZQ. t6o d6e 3up6o 3rht5h@ ka6i 2apotom5h@ periex4omenon <2<2orqog4wnion>2> 24alog4on 2estin, ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin. ka6i d4unatai t6o ZE 3h AG: 3h AG 24ara 24alog4o@ 2estin: kale4isqw d6e 3h met6a m4esou m4eson t6o 34olon poio5usa. 34oper 24edei de5icai. ##79##-------oq41 -T5hj 2apotom5hj m4ia <22> prosarm4ozei e2uqe5ia 3rht6h dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj. -24Estw 2apotom6h 3h AB, prosarm4ozousa d6e a2ut5hj 3h BG: a3i AG, GB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: l4egw, 34oti t5hj AB 3et4era o2u prosarm4ozei 3rht6h dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj. -E2i g6ar dunat4on, prosarmoz4etw 3h BD: ka6i a3i AD, DB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. ka6i 2epe4i, 35wj 3uper4exei t6a 2ap6o t5wn AD, DB to5u d6i@ 3up6o ^+^ t5wn AD, DB, to4utwj 3uper4exei ka6i t6a 2ap6o t5wn AG, GB to5u d6i@ 3up6o t5wn AG, GB: t5wj g6ar a2ut5wj t5wj 2ap6o t5h@ AB 2amf4otera 3uper4exei: 2enall6ac 24ara, 35wj 3uper4exei t6a 2ap6o t5wn AD, DB t5wn 2ap6o t5wn AG, GB, to4utwj 3uper4exei <22> t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB. t6a d6e 2ap6o t5wn AD, DB t5wn 2ap6o t5wn AG, GB 3uper4exei 3rht5wj: 3rht6a g6ar 2amf4otera. ka6i t6o d6i@ 24ara 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB 3uper4exei 3rht5wj: 34oper 2est6in 2ad4unaton: m4esa g6ar 2amf4otera, m4eson d6e m4esou o2ux 3uper4exei 3rht5wj. t5hj 24ara AB 3et4era o2u prosarm4ozei 3rht6h dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj. -M4ia 24ara m4onh t5hj 2apotom5hj prosarm4ozei 3rht6h dun4amei m4onon s4ummetro@ o25usa t5hj 34olh: 34oper 24edei de5icai. ##80##-------p41 -T5hj m4esh@ 2apotom5hj pr4wthj m4ia m4onon prosarm4ozei e2uqe5ia m4esh dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ 3rht6on peri4exousa. -24Estw g6ar m4esh@ 2apotom6h pr4wth 3h AB, ka6i t5hj AB prosarmoz4etw 3h BG: a3i AG, GB 24ara m4esai e2is6i dun4amei ^+^ m4onon s4ummetroi 3rht6on peri4exousai t6o 3up6o t5wn AG, GB: l4egw, 34oti t5hj AB 3et4era o2u prosarm4ozei m4esh dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ 3rht6on peri4exousa. -E2i g6ar dunat4on, prosarmoz4etw ka6i 3h DB. a3i 24ara AD, DB m4esai e2is6i dun4amei m4onon s4ummetroi 3rht6on peri4exousai t6o 3up6o t5wn AD, DB. ka6i 2epe4i, 35wj 3uper4exei t6a 2ap6o t5wn AD, DB to5u d6i@ 3up6o t5wn AD, DB, to4utwj 3uper4exei ka6i t6a 2ap6o t5wn AG, GB to5u d6i@ 3up6o t5wn AG, GB: t5wj g6ar a2ut5wj <22> 3uper4exousi t5wj 2ap6o t5h@ AB: 2enall6ac 24ara, 35wj 3uper4exei t6a 2ap6o t5wn AD, DB t5wn 2ap6o t5wn AG, GB, to4utwj 3uper4exei ka6i t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB. t6o d6e d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB 3uper4exei 3rht5wj: 3rht6a g6ar 2amf4otera. ka6i t6a 2ap6o t5wn AD, DB 24ara t5wn 2ap6o t5wn AG, GB <22> 3uper4exei 3rht5wj: 34oper 2est6in 2ad4unaton: m4esa g4ar 2estin 2amf4otera, m4eson d6e m4esou o2ux 3uper4exei 3rht5wj. -T5hj 24ara m4esh@ 2apotom5hj pr4wthj m4ia m4onon prosarm4ozei e2uqe5ia m4esh dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ 3rht6on peri4exousa: 34oper 24edei de5icai. ##81##-------pa41 -T5hj m4esh@ 2apotom5hj deut4eraj m4ia m4onon prosarm4ozei e2uqe5ia m4esh dun4amei m4onon s4ummetro@ t5hj 34olhj, met6a d6e t5h@ 34olh@ m4eson peri4exousa. ^+^ -24Estw m4esh@ 2apotom6h deut4era 3h AB ka6i t5hj AB prosarm4ozousa 3h BG: a3i 24ara AG, GB m4esai e2is6i dun4amei m4onon s4ummetroi m4eson peri4exousai t6o 3up6o t5wn AG, GB: l4egw, 34oti t5hj AB 3et4era o2u prosarm4osei e2uqe5ia m4esh dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ m4eson peri4exousa. -E2i g6ar dunat4on, prosarmoz4etw 3h BD: ka6i a3i AD, DB 24ara m4esai e2is6i dun4amei m4onon s4ummetroi m4eson peri4exousai t6o 3up6o t5wn AD, DB. ka6i 2ekke4isqw 3rht6h 3h EZ, ka6i to5i@ m6en 2ap6o t5wn AG, GB 24ison par6a t6hn EZ parabebl4hsqw t6o EH pl4ato@ poio5un t6hn EM: t5wj d6e d6i@ 3up6o t5wn AG, GB 24ison 2afhjr4hsqw t6o QH pl4ato@ poio5un t6hn QM: loip6on 24ara t6o EL 24ison 2est6i t5wj 2ap6o t5h@ AB: 34wste 3h AB d4unatai t6o EL. p4alin d6h to5i@ 2ap6o t5wn AD, DB 24ison par6a t6hn EZ parabebl4hsqw t6o EI pl4ato@ poio5un t6hn EN: 24esti d6e ka6i t6o EL 24ison t5wj 2ap6o t5h@ AB tetrag4wnwj: loip6on 24ara t6o QI 24ison 2est6i t5wj d6i@ 3up6o t5wn AD, DB. ka6i 2epe6i m4esai e2is6in a3i AG, GB, m4esa 24ara 2est6i ka6i t6a 2ap6o t5wn AG, GB. ka4i 2estin 24isa t5wj EH: m4eson 24ara ka6i t6o EH. ka6i par6a 3rht6hn t6hn EZ par4akeitai pl4ato@ poio5un t6hn EM: 3rht6h 24ara 2est6in 3h EM ka6i 2as4ummetro@ t5hj EZ m4hkei. p4alin, ^+^ 2epe6i m4eson 2est6i t6o 3up6o t5wn AG, GB, ka6i t6o d6i@ 3up6o t5wn AG, GB m4eson 2est4in. ka4i 2estin 24ison t5wj QH: ka6i t6o QH 24ara m4eson 2est4in. ka6i par6a 3rht6hn t6hn EZ par4akeitai pl4ato@ poio5un t6hn QM: 3rht6h 24ara 2est6i ka6i 3h QM ka6i 2as4ummetro@ t5hj EZ m4hkei. ka6i 2epe6i a3i AG, GB dun4amei m4onon s4ummetro4i e2isin, 2as4ummetro@ 24ara 2est6in 3h AG t5hj GB m4hkei. 3w@ d6e 3h AG pr6o@ t6hn GB, o34utw@ 2est6i t6o 2ap6o t5h@ AG pr6o@ t6o 3up6o t5wn AG, GB: 2as4ummetron 24ara 2est6i t6o 2ap6o t5h@ AG t5wj 3up6o t5wn AG, GB. 2all6a t5wj m6en 2ap6o t5h@ AG s4ummetr4a 2esti t6a 2ap6o t5wn AG, GB, t5wj d6e 3up6o t5wn AG, GB s4ummetr4on 2esti t6o d6i@ 3up6o t5wn AG, GB: 2as4ummetra 24ara 2est6i t6a 2ap6o t5wn AG, GB t5wj d6i@ 3up6o t5wn AG, GB. ka4i 2esti to5i@ m6en 2ap6o t5wn AG, GB 24ison t6o EH, t5wj d6e d6i@ 3up6o t5wn AG, GB 24ison t6o HQ: 2as4ummetron 24ara 2est6i t6o EH t5wj QH. 3w@ d6e t6o EH pr6o@ t6o QH, o34utw@ 2est6in 3h EM pr6o@ t6hn QM: 2as4ummetro@ 24ara 2est6in 3h EM t5hj MQ m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i EM, MQ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h EQ, prosarm4ozousa d6e a2ut5hj 3h QM. 3omo4iw@ d6h de4icomen, 34oti ka6i 3h QN a2ut5hj prosarm4ozei: t5hj 24ara 2apotom5hj 24allh ka6i 24allh prosarm4ozei e2uqe5ia dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj: 34oper 2est6in 2ad4unaton. ^+^ -T5hj 24ara m4esh@ 2apotom5hj deut4eraj m4ia m4onon prosarm4ozei e2uqe5ia m4esh dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ m4eson peri4exousa: 34oper 24edei de5icai. ##82##-------pb41 -T5hj 2el4assoni m4ia m4onon prosarm4ozei e2uqe5ia dun4amei 2as4ummetro@ o25usa t5hj 34olhj poio5usa met6a t5h@ 34olh@ t6o m6en 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d6e d6i@ 3up' a2ut5wn m4eson. -24Estw 3h 2el4asswn 3h AB, ka6i t5hj AB prosarm4ozousa 24estw 3h BG: a3i 24ara AG, GB dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d6e d6i@ 3up' a2ut5wn m4eson: l4egw, 34oti t5hj AB 3et4era e2uqe5ia o2u prosarm4osei t6a a2ut6a poio5usa. -E2i g6ar dunat4on, prosarmoz4etw 3h BD: ka6i a3i AD, DB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6a proeirhm4ena. ka6i 2epe4i, 35wj 3uper4exei t6a 2ap6o t5wn AD, DB t5wn 2ap6o t5wn AG, GB, to4utwj 3uper4exei ka6i t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB, t6a d6e 2ap6o t5wn AD, ^+^ DB tetr4agwna t5wn 2ap6o t5wn AG, GB tetrag4wnwn 3uper4exei 3rht5wj: 3rht6a g4ar 2estin 2amf4otera: ka6i t6o d6i@ 3up6o t5wn AD, DB 24ara to5u d6i@ 3up6o t5wn AG, GB 3uper4exei 3rht5wj: 34oper 2est6in 2ad4unaton: m4esa g4ar 2estin 2amf4otera. -T5hj 24ara 2el4assoni m4ia m4onon prosarm4ozei e2uqe5ia dun4amei 2as4ummetro@ o25usa t5hj 34olhj ka6i poio5usa t6a m6en 2ap' a2ut5wn tetr4agwna 34ama 3rht4on, t6o d6e d6i@ 3up' a2ut5wn m4eson: 34oper 24edei de5icai. ##83##-------pg41 -T5hj met6a 3rhto5u m4eson t6o 34olon poio4ushj m4ia m4onon prosarm4ozei e2uqe5ia dun4amei 2as4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ poio5usa t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d6e d6i@ 3up' a2ut5wn 3rht4on. -24Estw 3h met6a 3rhto5u m4eson t6o 34olon poio5usa 3h AB, ka6i t5hj AB prosarmoz4etw 3h BG: a3i 24ara AG, GB dun4amei e2is6in 2as4ummetroi poio5usai t6a proke4imena: l4egw, 34oti t5hj AB 3et4era o2u prosarm4osei t6a a2ut6a poio5usa. -E2i g6ar dunat4on, prosarmoz4etw 3h BD: ka6i a3i AD, DB 24ara e2uqe5iai dun4amei e2is6in 2as4ummetroi poio5usai t6a proke4imena. ^+^ 2epe6i o25un, 35wj 3uper4exei t6a 2ap6o t5wn AD, DB t5wn 2ap6o t5wn AG, GB, to4utwj 3uper4exei ka6i t6o d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB 2akolo4uqw@ to5i@ pr6o a2uto5u, t6o d6e d6i@ 3up6o t5wn AD, DB to5u d6i@ 3up6o t5wn AG, GB 3uper4exei 3rht5wj: 3rht6a g4ar 2estin 2amf4otera: ka6i t6a 2ap6o t5wn AD, DB 24ara t5wn 2ap6o t5wn AG, GB 3uper4exei 3rht5wj: 34oper 2est6in 2ad4unaton: m4esa g4ar 2estin 2amf4otera. o2uk 24ara t5hj AB 3et4era prosarm4osei e2uqe5ia dun4amei 2as4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ poio5usa t6a proeirhm4ena: m4ia 24ara m4onon prosarm4osei: 34oper 24edei de5icai. ##84##-------pd41 -T5hj met6a m4esou m4eson t6o 34olon poio4ushj m4ia m4onh prosarm4ozei e2uqe5ia dun4amei 2as4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ poio5usa t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson t4o te d6i@ 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t5wj sugkeim4enwj 2ek t5wn 2ap' a2ut5wn. -24Estw 3h met6a m4esou m4eson t6o 34olon poio5usa 3h AB, prosarm4ozousa d6e a2ut5hj 3h BG: a3i 24ara AG, GB dun4amei e2is6in 2as4ummetroi poio5usai t6a proeirhm4ena. l4egw, 34oti t5hj ^+^ AB 3et4era o2u prosarm4osei poio5usa t6a proeirhm4ena. -E2i g6ar dunat4on, prosarmoz4etw 3h BD, 34wste ka6i t6a@ AD, DB dun4amei 2asumm4etrou@ e25inai poio4usa@ t4a te 2ap6o t5wn AD, DB tetr4agwna 34ama m4eson ka6i t6o d6i@ 3up6o t5wn AD, DB m4eson ka6i 24eti t6a 2ap6o t5wn AD, DB 2as4ummetra t5wj d6i@ 3up6o t5wn AD, DB: ka6i 2ekke4isqw 3rht6h 3h EZ, ka6i to5i@ m6en 2ap6o t5wn AG, GB 24ison par6a t6hn EZ parabebl4hsqw t6o EH pl4ato@ poio5un t6hn EM, t5wj d6e d6i@ 3up6o t5wn AG, GB 24ison par6a t6hn EZ parabebl4hsqw t6o QH pl4ato@ poio5un t6hn QM: loip6on 24ara t6o 2ap6o t5h@ AB 24ison 2est6i t5wj EL: 3h 24ara AB d4unatai t6o EL. p4alin to5i@ 2ap6o t5wn AD, DB 24ison par6a t6hn EZ parabebl4hsqw t6o EI pl4ato@ poio5un t6hn EN. 24esti d6e ka6i t6o 2ap6o t5h@ AB 24ison t5wj EL: loip6on 24ara t6o d6i@ 3up6o t5wn AD, DB 24ison <2<2est6i>2> t5wj QI. ka6i 2epe6i m4eson 2est6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AG, GB ka4i 2estin 24ison t5wj EH, m4eson 24ara 2est6i ka6i t6o EH. ka6i par6a 3rht6hn t6hn EZ par4akeitai pl4ato@ poio5un t6hn EM: 3rht6h 24ara 2est6in 3h EM ka6i 2as4ummetro@ t5hj EZ m4hkei. p4alin, 2epe6i m4eson 2est6i t6o d6i@ 3up6o t5wn AG, GB ka4i 2estin 24ison t5wj QH, m4eson 24ara ka6i t6o QH. ^+^ ka6i par6a 3rht6hn t6hn EZ par4akeitai pl4ato@ poio5un t6hn QM: 3rht6h 24ara 2est6in 3h QM ka6i 2as4ummetro@ t5hj EZ m4hkei. ka6i 2epe6i 2as4ummetr4a 2esti t6a 2ap6o t5wn AG, GB t5wj d6i@ 3up6o t5wn AG, GB, 2as4ummetr4on 2esti ka6i t6o EH t5wj QH: 2as4ummetro@ 24ara 2est6i ka6i 3h EM t5hj MQ m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i 24ara EM, MQ 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h EQ, prosarm4ozousa d6e a2ut5hj 3h QM. 3omo4iw@ d6h de4icomen, 34oti 3h EQ p4alin 2apotom4h 2estin, prosarm4ozousa d6e a2ut5hj 3h QN. t5hj 24ara 2apotom5hj 24allh ka6i 24allh prosarm4ozei 3rht6h dun4amei m4onon s4ummetro@ o25usa t5hj 34olhj: 34oper 2ede4ixqh 2ad4unaton. o2uk 24ara t5hj AB 3et4era prosarm4osei e2uqe5ia. -T5hj 24ara AB m4ia m4onon prosarm4ozei e2uqe5ia dun4amei 2as4ummetro@ o25usa t5hj 34olhj, met6a d6e t5h@ 34olh@ poio5usa t4a te 2ap' a2ut5wn tetr4agwna 34ama m4eson ka6i t6o d6i@ 3up' a2ut5wn m4eson ka6i 24eti t6a 2ap' a2ut5wn tetr4agwna 2as4ummetra t5wj d6i@ 3up' a2ut5wn: 34oper 24edei de5icai. ###DEF3###-----<00> ##1##-a41 3Upokeim4enh@ 3rht5h@ ka6i 2apotom5h@, 2e6an m6en 3h 34olh t5h@ prosarmozo4ush@ me5izon d4unhtai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei, ka6i 3h 34olh s4ummetro@ 25hj t5hj 2ekkeim4enhj 3rht5hj m4hkei, kale4isqw 2apotom6h pr4wth. ##2##-b41 2E6an d6e 3h prosarm4ozousa s4ummetro@ 25hj t5hj 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h 34olh t5h@ prosarmozo4ush@ ^+^ me5izon d4unhtai t5wj 2ap6o summ4etrou 3eaut5hj, kale4isqw 2apotom6h deut4era. ##3##-g41 2E6an d6e mhdet4era s4ummetro@ 25hj t5hj 2ekkeim4enhj 3rht5hj m4hkei, 3h d6e 34olh t5h@ prosarmozo4ush@ me5izon d4unhtai t5wj 2ap6o summ4etrou 3eaut5hj, kale4isqw 2apotom6h tr4ith. ##4##-d41 P4alin, 2e6an 3h 34olh t5h@ prosarmozo4ush@ me5izon d4unhtai t5wj 2ap6o 2asumm4etrou 3eaut5hj <22>, 2e6an m6en 3h 34olh s4ummetro@ 25hj t5hj 2ekkeim4enhj 3rht5hj m4hkei, kale4isqw 2apotom6h tet4arth. ##5##-e41 2E6an d6e 3h prosarm4ozousa, p4empth. ##6##-st41 2E6an d6e mhdet4era, 34ekth. ####***X#### ###PROP### ##85##-------pe41 -E3ure5in t6hn pr4wthn 2apotom4hn. -2Ekke4isqw 3rht6h 3h A, ka6i t5hj A m4hkei s4ummetro@ 24estw 3h BH: 3rht6h 24ara 2est6i ka6i 3h BH. ka6i 2ekke4isqwsan d4uo tetr4agwnoi 2ariqmo6i o3i DE, EZ, 35wn 3h 3uperox6h 3o ZD m6h 24estw tetr4agwno@: o2ud' 24ara 3o ED pr6o@ t6on DZ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. ka6i pepoi4hsqw 3w@ 3o ED pr6o@ t6on DZ, o34utw@ t6o 2ap6o ^+^ t5h@ BH tetr4agwnon pr6o@ t6o 2ap6o t5h@ HG tetr4agwnon: s4ummetron 24ara 2est6i t6o 2ap6o t5h@ BH t5wj 2ap6o t5h@ HG. 3rht6on d6e t6o 2ap6o t5h@ BH: 3rht6on 24ara ka6i t6o 2ap6o t5h@ HG: 3rht6h 24ara 2est6i ka6i 3h HG. ka6i 2epe6i 3o ED pr6o@ t6on DZ l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h BH t5hj HG m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i BH, HG 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h 24ara BG 2apotom4h 2estin. -L4egw d4h, 34oti ka6i pr4wth. -35Wi g6ar me5iz4on 2esti t6o 2ap6o t5h@ BH to5u 2ap6o t5h@ HG, 24estw t6o 2ap6o t5h@ Q. ka6i 2epe4i 2estin 3w@ 3o ED pr6o@ t6on ZD, o34utw@ t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG, ka6i 2anastr4eyanti 24ara 2est6in 3w@ 3o DE pr6o@ t6on EZ, o34utw@ t6o 2ap6o t5h@ HB pr6o@ t6o 2ap6o t5h@ Q. 3o d6e DE pr6o@ t6on EZ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 3ek4atero@ g6ar tetr4agwn4o@ 2estin: ka6i t6o 2ap6o t5h@ HB 24ara pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: s4ummetro@ 24ara 2est6in 3h BH t5hj Q m4hkei. ka6i d4unatai 3h BH t5h@ HG me5izon t5wj 2ap6o t5h@ Q: 3h BH 24ara t5h@ HG me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. ka4i 2estin 3h 34olh 3h BH s4ummetro@ ^+^ t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj A. 3h BG 24ara 2apotom4h 2esti pr4wth. -E34urhtai 24ara 3h pr4wth 2apotom6h 3h BG: 34oper 24edei e3ure5in. ##86##-------pst41 -E3ure5in t6hn deut4eran 2apotom4hn. -2Ekke4isqw 3rht6h 3h A ka6i t5hj A s4ummetro@ m4hkei 3h HG. 3rht6h 24ara 2est6in 3h HG. ka6i 2ekke4isqwsan d4uo tetr4agwnoi 2ariqmo6i o3i DE, EZ, 35wn 3h 3uperox6h 3o DZ m6h 24estw tetr4agwno@. ka6i pepoi4hsqw 3w@ 3o ZD pr6o@ t6on DE, o34utw@ t6o 2ap6o t5h@ GH tetr4agwnon pr6o@ t6o 2ap6o t5h@ HB tetr4agwnon. s4ummetron 24ara 2est6i t6o 2ap6o t5h@ GH tetr4agwnon t5wj 2ap6o t5h@ HB tetrag4wnwj. 3rht6on d6e t6o 2ap6o t5h@ HG. 3rht6on 24ara <2<2est6i>2> ka6i t6o 2ap6o t5h@ HB: 3rht6h 24ara 2est6in 3h BH. ka6i 2epe6i t6o 2ap6o t5h@ HG tetr4agwnon pr6o@ t6o 2ap6o t5h@ HB l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, 2as4ummetr4o@ 2estin 3h GH t5hj HB m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i GH, HB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h BG 24ara 2apotom4h 2estin. ^+^ -L4egw d4h, 34oti ka6i deut4era. -35Wi g6ar me5iz4on 2esti t6o 2ap6o t5h@ BH to5u 2ap6o t5h@ HG, 24estw t6o 2ap6o t5h@ Q. 2epe6i o25un 2estin 3w@ t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG, o34utw@ 3o ED 2ariqm6o@ pr6o@ t6on DZ 2ariqm4on, 2anastr4eyanti 24ara 2est6in 3w@ t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ Q, o34utw@ 3o DE pr6o@ t6on EZ. ka4i 2estin 3ek4atero@ t5wn DE, EZ tetr4agwno@: t6o 24ara 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: s4ummetro@ 24ara 2est6in 3h BH t5hj Q m4hkei. ka6i d4unatai 3h BH t5h@ HG me5izon t5wj 2ap6o t5h@ Q: 3h BH 24ara t5h@ HG me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. ka4i 2estin 3h prosarm4ozousa 3h GH t5hj 2ekkeim4enhj 3rht5hj s4ummetro@ t5hj A. 3h BG 24ara 2apotom4h 2esti deut4era. -E34urhtai 24ara deut4era 2apotom6h 3h BG: 34oper 24edei de5icai. ##87##-------pz41 -E3ure5in t6hn tr4ithn 2apotom4hn. -2Ekke4isqw 3rht6h 3h A, ka6i 2ekke4isqwsan tre5i@ 2ariqmo6i o3i E, BG, GD l4ogon m6h 24exonte@ pr6o@ 2all4hlou@, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, 3o d6e ^+^ GB pr6o@ t6on BD l4ogon 2ex4etw, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, ka6i pepoi4hsqw 3w@ m6en 3o E pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ ZH tetr4agwnon, 3w@ d6e 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH tetr4agwnon pr6o@ t6o 2ap6o t5h@ HQ. 2epe6i o25un 2estin 3w@ 3o E pr6o@ t6on BG, ^-^ o34utw@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ ZH tetr4agwnon, s4ummetron 24ara 2est6i t6o 2ap6o t5h@ A tetr4agwnon t5wj 2ap6o t5h@ ZH tetrag4wnwj. 3rht6on d6e t6o 2ap6o t5h@ A tetr4agwnon. 3rht6on 24ara ka6i t6o 2ap6o t5h@ ZH: 3rht6h 24ara 2est6in 3h ZH. ka6i 2epe6i 3o E pr6o@ t6on BG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ ZH <22> l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h A t5hj ZH m4hkei. p4alin, 2epe4i 2estin 3w@ 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH tetr4agwnon pr6o@ t6o 2ap6o t5h@ HQ, s4ummetron 24ara 2est6i t6o 2ap6o t5h@ ZH t5wj 2ap6o t5h@ HQ. 3rht6on d6e t6o 2ap6o t5h@ ZH: 3rht6on 24ara ka6i t6o 2ap6o t5h@ HQ: 3rht6h 24ara 2est6in 3h HQ. ka6i 2epe6i 3o BG pr6o@ t6on GD l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in ^+^ 3h ZH t5hj HQ m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i ZH, HQ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h ZQ. -L4egw d4h, 34oti ka6i tr4ith. -2Epe6i g4ar 2estin 3w@ m6en 3o E pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ A tetr4agwnon pr6o@ t6o 2ap6o t5h@ ZH, 3w@ d6e 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ QH, di' 24isou 24ara 2est6in 3w@ 3o E pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ QH. 3o d6e E pr6o@ t6on GD l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ HQ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 3h A t5hj HQ m4hkei. o2udet4era 24ara t5wn ZH, HQ s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj A m4hkei. 35wj o25un me5iz4on 2esti t6o 2ap6o t5h@ ZH to5u 2ap6o t5h@ HQ, 24estw t6o 2ap6o t5h@ K. 2epe6i o25un 2estin 3w@ 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, 2anastr4eyanti 24ara 2est6in 3w@ 3o BG pr6o@ t6on BD, o34utw@ t6o 2ap6o t5h@ ZH tetr4agwnon pr6o@ t6o 2ap6o t5h@ K. 3o d6e BG pr6o@ t6on BD l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i t6o 2ap6o t5h@ ZH 24ara pr6o@ t6o 2ap6o t5h@ K l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. s4ummetro@ 24ara 2est6in 3h ZH t5hj K m4hkei, ka6i d4unatai 3h ZH t5h@ HQ me5izon t5wj 2ap6o summ4etrou ^+^ 3eaut5hj. ka6i o2udet4era t5wn ZH, HQ s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj A m4hkei: 3h ZQ 24ara 2apotom4h 2esti tr4ith. -E34urhtai 24ara 3h tr4ith 2apotom6h 3h ZQ: 34oper 24edei ^-^ de5icai. ##88##-------ph41 -E3ure5in t6hn tet4arthn 2apotom4hn. -2Ekke4isqw 3rht6h 3h A ka6i t5hj A m4hkei s4ummetro@ 3h BH: 3rht6h 24ara 2est6i ka6i 3h BH. ka6i 2ekke4isqwsan d4uo 2ariqmo6i o3i DZ, ZE, 34wste t6on DE 34olon pr6o@ 3ek4ateron t5wn DZ, EZ l4ogon m6h 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on. ka6i pepoi4hsqw 3w@ 3o DE pr6o@ t6on EZ, o34utw@ t6o 2ap6o t5h@ BH tetr4agwnon pr6o@ t6o 2ap6o t5h@ HG. s4ummetron 24ara 2est6i t6o 2ap6o t5h@ BH t5wj 2ap6o t5h@ HG. 3rht6on d6e t6o 2ap6o t5h@ BH: 3rht6on 24ara ka6i t6o 2ap6o t5h@ HG: 3rht6h 24ara 2est6in 3h HG. ka6i 2epe6i 3o DE pr6o@ t6on EZ l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h BH t5hj HG m4hkei. ka4i ^+^ e2isin 2amf4oterai 3rhta4i: a3i BH, HG 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h BG. -<22>. -35Wi o25un me5iz4on 2esti t6o 2ap6o t5h@ BH to5u 2ap6o t5h@ HG, 24estw t6o 2ap6o t5h@ Q. 2epe6i o25un 2estin 3w@ 3o DE pr6o@ t6on EZ, o34utw@ t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG, ka6i 2anastr4eyanti 24ara 2est6in 3w@ 3o ED pr6o@ t6on DZ, o34utw@ t6o 2ap6o t5h@ HB pr6o@ t6o 2ap6o t5h@ Q. 3o d6e ED pr6o@ t6on DZ l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ HB pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h BH t5hj Q m4hkei. ka6i d4unatai 3h BH t5h@ HG me5izon t5wj 2ap6o t5h@ Q: 3h 24ara BH t5h@ HG me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i 2estin 34olh 3h BH s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj A. 3h 24ara BG 2apotom4h 2esti tet4arth. -E34urhtai 24ara 3h tet4arth 2apotom4h: 34oper 24edei de5icai ##89##-------pq41 -E3ure5in t6hn p4empthn 2apotom4hn. -2Ekke4isqw 3rht6h 3h A, ka6i t5hj A m4hkei s4ummetro@ 24estw 3h GH: 3rht6h 24ara <2<2est6in>2> 3h GH. ka6i 2ekke4isqwsan d4uo ^+^ 2ariqmo6i o3i DZ, ZE, 34wste t6on DE pr6o@ 3ek4ateron t5wn DZ, ZE l4ogon p4alin m6h 24exein, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i pepoi4hsqw 3w@ 3o ZE pr6o@ t6on ED, o34utw@ t6o 2ap6o t5h@ GH pr6o@ t6o 2ap6o t5h@ HB. 3rht6on 24ara ka6i t6o 2ap6o t5h@ HB: 3rht6h 24ara 2est6i ka6i 3h BH. ka6i 2epe4i 2estin 3w@ 3o DE pr6o@ t6on EZ, o34utw@ t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG, 3o d6e DE pr6o@ t6on EZ l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h BH t5hj HG m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i BH, HG 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h BG 24ara 2apotom4h 2estin. -L4egw d4h, 34oti ka6i p4empth. -35Wi g6ar me5iz4on 2esti t6o 2ap6o t5h@ BH to5u 2ap6o t5h@ HG, 24estw t6o 2ap6o t5h@ Q. 2epe6i o25un 2estin 3w@ t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ HG, o34utw@ 3o DE pr6o@ t6on EZ, 2anastr4eyanti 24ara 2est6in 3w@ 3o ED pr6o@ t6on DZ, o34utw@ t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ Q. 3o d6e ED pr6o@ t6on DZ l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ BH pr6o@ t6o 2ap6o t5h@ Q l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon ^+^ 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h BH t5hj Q m4hkei. ka6i d4unatai 3h BH t5h@ HG me5izon t5wj 2ap6o t5h@ Q: 3h HB 24ara t5h@ HG me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei. ka4i 2estin 3h prosarm4ozousa 3h GH s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj t5hj A m4hkei: 3h 24ara BG 2apotom4h 2esti p4empth. -E34urhtai 24ara 3h p4empth 2apotom6h 3h BG: 34oper 24edei de5icai. ##90##-------qq41 -E3ure5in t6hn 34ekthn 2apotom4hn. -2Ekke4isqw 3rht6h 3h A ka6i tre5i@ 2ariqmo6i o3i E, BG, GD l4ogon m6h 24exonte@ pr6o@ 2all4hlou@, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 24eti d6e ka6i 3o GB pr6o@ t6on BD l4ogon m6h 2ex4etw, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: ka6i pepoi4hsqw 3w@ m6en 3o E pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ ZH, 3w@ d6e 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ. -2Epe6i o25un 2estin 3w@ 3o E pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ ZH, s4ummetron 24ara t6o 2ap6o t5h@ A t5wj 2ap6o t5h@ ZH. 3rht6on d6e t6o 2ap6o t5h@ A: 3rht6on 24ara ka6i ^+^ t6o 2ap6o t5h@ ZH: 3rht6h 24ara 2est6i ka6i 3h ZH. ka6i 2epe6i 3o E pr6o@ t6on BG l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ ZH l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h A t5hj ZH m4hkei. p4alin, 2epe4i 2estin 3w@ 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, s4ummetron 24ara t6o 2ap6o t5h@ ZH t5wj 2ap6o t5h@ HQ. 3rht6on d6e t6o 2ap6o t5h@ ZH: 3rht6on 24ara ka6i t6o 2ap6o t5h@ HQ: 3rht6h 24ara ka6i 3h HQ. ka6i 2epe6i 3o BG pr6o@ t6on GD l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on, o2ud' 24ara t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h ZH t5hj HQ m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i ZH, HQ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h 24ara ZQ 2apotom4h 2estin. -L4egw d4h, 34oti ka6i 34ekth. -2Epe6i g4ar 2estin 3w@ m6en 3o E pr6o@ t6on BG, o34utw@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ ZH, 3w@ d6e 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, di' 24isou 24ara 2est6in 3w@ 3o E pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ HQ. 3o d6e E pr6o@ t6on GD l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ HQ l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h A t5hj HQ m4hkei: o2udet4era 24ara t5wn ^+^ ZH, HQ s4ummetr4o@ 2esti t5hj A 3rht5hj m4hkei. 35wj o25un me5iz4on 2esti t6o 2ap6o t5h@ ZH to5u 2ap6o t5h@ HQ, 24estw t6o 2ap6o t5h@ K. 2epe6i o25un 2estin 3w@ 3o BG pr6o@ t6on GD, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ HQ, 2anastr4eyanti 24ara 2est6in 3w@ 3o GB pr6o@ t6on BD, o34utw@ t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ K. 3o d6e GB pr6o@ t6on BD l4ogon o2uk 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: o2ud' 24ara t6o 2ap6o t5h@ ZH pr6o@ t6o 2ap6o t5h@ K l4ogon 24exei, 36on tetr4agwno@ 2ariqm6o@ pr6o@ tetr4agwnon 2ariqm4on: 2as4ummetro@ 24ara 2est6in 3h ZH t5hj K m4hkei. ka6i d4unatai 3h ZH t5h@ HQ me5izon t5wj 2ap6o t5h@ K: 3h ZH 24ara t5h@ HQ me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei. ka6i o2udet4era t5wn ZH, HQ s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj A. 3h 24ara ZQ 2apotom4h 2estin 34ekth. -E34urhtai 24ara 3h 34ekth 2apotom6h 3h ZQ: 34oper 24edei ^-^ de5icai. $-^P227^-^L9^ <3<####PBF&#### ###10AP### <00> ##90##-24Esti d6e ka6i suntom4wteron de5icai t6hn e34uresin t5wn e2irhm4enwn 36ec 2apotom5wn. ka6i d6h 24estw e3ure5in t6hn pr4wthn. 2ekke4isqw 3h 2ek d4uo 2onom4atwn pr4wth 3h AG, 35h@ me5izon 24onoma 3h AB, ka6i t5hj BG 24ish ke4isqw 3h BD. a3i AB, BG 24ara, tout4estin a3i AB, BD, 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h AB t5h@ BG, tout4esti t5h@ BD, me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h AB s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj m4hkei: 2apotom6h 24ara pr4wth 2est6in 3h AD. 3omo4iw@ d6h ka6i t6a@ loip6a@ 2apotom6a@ e3ur4hsomen 2ekq4emenoi t6a@ 2isar4iqmou@ 2ek d4uo 2onom4atwn: 34oper 24edei de5icai. ^+^>3> $-^P155^-^L16^ ####***X#### ###PROP### ##91##-------qqa41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ pr4wth@, 3h t6o xwr4ion dunam4enh 2apotom4h 2estin. -Periex4esqw g6ar xwr4ion t6o AB 3up6o 3rht5h@ t5h@ AG ka6i 2apotom5h@ pr4wth@ t5h@ AD: l4egw, 34oti 3h t6o AB xwr4ion dunam4enh 2apotom4h 2estin. ^+^ -2Epe6i g6ar 2apotom4h 2esti pr4wth 3h AD, 24estw a2ut5hj prosarm4ozousa 3h DH: a3i AH, HD 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. ka6i 34olh 3h AH s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj AG, ka6i 3h AH t5h@ HD me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei: 2e6an 24ara t5wj tet4artwj m4erei to5u 2ap6o t5h@ DH 24ison par6a t6hn AH parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ s4ummetra a2ut6hn diaire5i. tetm4hsqw 3h DH d4ixa kat6a t6o E, ka6i t5wj 2ap6o t5h@ EH 24ison par6a t6hn AH parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn AZ,ZH: s4ummetro@ 24ara 2est6in 3h AZ t5hj ZH. ka6i di6a t5wn E, Z, H shme4iwn t5hj AG par4allhloi 24hxqwsan a3i EQ, ZI, HK. -Ka6i 2epe6i s4ummetr4o@ 2estin 3h AZ t5hj ZH m4hkei, ka6i 3h AH 24ara 3ekat4eraj t5wn AZ, ZH s4ummetr4o@ 2esti m4hkei. 2all6a 3h AH s4ummetr4o@ 2esti t5hj AG: ka6i 3ekat4era 24ara t5wn AZ, ZH s4ummetr4o@ 2esti t5hj AG m4hkei. ka4i 2esti 3rht6h 3h AG: 3rht6h 24ara ka6i 3ekat4era t5wn AZ, ZH: 34wste ka6i 3ek4ateron t5wn AI, ZK 3rht4on 2estin. ka6i 2epe6i s4ummetr4o@ 2estin 3h DE t5hj EH m4hkei, ka6i 3h DH 24ara 3ekat4eraj t5wn ^+^ DE, EH s4ummetr4o@ 2esti m4hkei. 3rht6h d6e 3h DH ka6i 2as4ummetro@ t5hj AG m4hkei: 3rht6h 24ara ka6i 3ekat4era t5wn DE, EH ka6i 2as4ummetro@ t5hj AG m4hkei: 3ek4ateron 24ara t5wn DQ, EK m4eson 2est4in. -Ke4isqw d6h t5wj m6en AI 24ison tetr4agwnon t6o LM, t5wj d6e ZK 24ison tetr4agwnon 2afhjr4hsqw koin6hn gwn4ian 24exon a2ut5wj t6hn 3up6o LOM t6o NC: per6i t6hn a2ut6hn 24ara di4ametr4on 2esti t6a LM, NC tetr4agwna. 24estw a2ut5wn di4ametro@ 3h OR, ka6i katagegr4afqw t6o sx5hma. 2epe6i o25un 24ison 2est6i t6o 3up6o t5wn AZ, ZH periex4omenon 2orqog4wnion t5wj 2ap6o t5h@ EH tetrag4wnwj, 24estin 24ara 3w@ 3h AZ pr6o@ t6hn EH, o34utw@ 3h EH pr6o@ t6hn ZH. 2all' 3w@ m6en 3h AZ pr6o@ t6hn EH, o34utw@ t6o AI pr6o@ t6o EK, 3w@ d6e 3h EH pr6o@ t6hn ZH, o34utw@ 2est6i t6o EK pr6o@ t6o KZ: t5wn 24ara AI, KZ m4eson 2an4alog4on 2esti t6o EK. 24esti d6e ka6i t5wn LM, NC m4eson 2an4alogon t6o MN, 3w@ 2en to5i@ 24emprosqen 2ede4ixqh, ka4i 2esti t6o <22> AI t5wj LM tetrag4wnwj 24ison, t6o d6e KZ t5wj NC: ka6i t6o MN 24ara t5wj EK 24ison 2est4in. 2all6a t6o m6en EK t5wj DQ 2estin 24ison, t6o d6e MN t5wj LC: t6o 24ara DK 24ison 2est6i t5wj UFX gn4wmoni ka6i t5wj NC. 24esti d6e ka6i t6o AK 24ison to5i@ LM, NC tetrag4wnoi@: loip6on 24ara t6o AB 24ison 2est6i t5wj ST. t6o d6e ST t6o 2ap6o t5h@ LN 2esti tetr4agwnon: ^+^ t6o 24ara 2ap6o t5h@ LN tetr4agwnon 24ison 2est6i t5wj AB: 3h LN 24ara d4unatai t6o AB. -L4egw d4h, 34oti 3h LN 2apotom4h 2estin. -2Epe6i g6ar 3rht4on 2estin 3ek4ateron t5wn AI, ZK, ka4i 2estin 24ison to5i@ LM, NC, ka6i 3ek4ateron 24ara t5wn LM, NC 3rht4on 2estin, tout4esti t6o 2ap6o 3ekat4era@ t5wn LO, ON: ka6i 3ekat4era 24ara t5wn LO, ON 3rht4h 2estin. p4alin, 2epe6i m4eson 2est6i t6o DQ ka4i 2estin 24ison t5wj LC, m4eson 24ara 2est6i ka6i t6o LC. 2epe6i o25un t6o m6en LC m4eson 2est4in, t6o d6e NC 3rht4on, 2as4ummetron 24ara 2est6i t6o LC t5wj NC: 3w@ d6e t6o LC pr6o@ t6o NC, o34utw@ 2est6in 3h LO pr6o@ t6hn ON: 2as4ummetro@ 24ara 2est6in 3h LO t5hj ON m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i LO, ON 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h LN. ka6i d4unatai t6o AB xwr4ion: 3h 24ara t6o AB xwr4ion dunam4enh 2apotom4h 2estin. -2E6an 24ara xwr4ion peri4exhtai 3up6o 3rht5h@, ka6i t6a 3ec5h@. ##92##-------qqb41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ deut4era@, 3h t6o xwr4ion dunam4enh m4esh@ 2apotom4h 2esti pr4wth. -Xwr4ion g6ar t6o AB periex4esqw 3up6o 3rht5h@ t5h@ AG ka6i 2apotom5h@ deut4era@ t5h@ AD: l4egw, 34oti 3h t6o AB xwr4ion dunam4enh m4esh@ 2apotom4h 2esti pr4wth. ^+^ -24Estw g6ar t5hj AD prosarm4ozousa 3h DH: a3i 24ara AH, HD 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h prosarm4ozousa 3h DH s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj AG, 3h d6e 34olh 3h AH t5h@ prosarmozo4ush@ t5h@ HD me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. 2epe6i o25un 3h AH t5h@ HD me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, 2e6an 24ara t5wj tet4artwj m4erei to5u 2ap6o t5h@ HD 24ison par6a t6hn AH parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ s4ummetra a2ut6hn diaire5i. tetm4hsqw o25un 3h DH d4ixa kat6a t6o E: ka6i t5wj 2ap6o t5h@ EH 24ison par6a t6hn AH parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn AZ, ZH: s4ummetro@ 24ara 2est6in 3h AZ t5hj ZH m4hkei. ka6i 3h AH 24ara 3ekat4eraj t5wn AZ, ZH s4ummetr4o@ 2esti m4hkei. 3rht6h d6e 3h AH ka6i 2as4ummetro@ t5hj AG m4hkei: ka6i 3ekat4era 24ara t5wn AZ, ZH 3rht4h 2esti ka6i 2as4ummetro@ t5hj AG m4hkei: 3ek4ateron 24ara t5wn AI, ZK m4eson 2est4in. p4alin, 2epe6i s4ummetr4o@ 2estin 3h DE t5hj EH, ka6i 3h DH 24ara 3ekat4eraj t5wn DE, EH s4ummetr4o@ 2estin. 2all' 3h DH s4ummetr4o@ ^+^ 2esti t5hj AG m4hkei. <2<3rht6h 24ara ka6i 3ekat4era t5wn DE, EH ka6i s4ummetro@ t5hj AG m4hkei.>2> 3ek4ateron 24ara t5wn DQ, EK 3rht4on 2estin. -Sunest4atw o25un t5wj m6en AI 24ison tetr4agwnon t6o LM, t5wj d6e ZK 24ison 2afhjr4hsqw t6o NC per6i t6hn a2ut6hn gwn4ian 26on t5wj LM t6hn 3up6o t5wn LOM: per6i t6hn a2ut6hn 24ara 2est6i di4ametron t6a LM, NC tetr4agwna. 24estw a2ut5wn di4ametro@ 3h OR, ka6i katagegr4afqw t6o sx5hma. 2epe6i o25un t6a AI, ZK m4esa 2est6i ka4i 2estin 24isa to5i@ 2ap6o t5wn LO, ON, ka6i t6a 2ap6o t5wn LO, ON <2<24ara>2> m4esa 2est4in: ka6i a3i LO, ON 24ara m4esai e2is6i dun4amei m4onon s4ummetroi. ka6i 2epe6i t6o 3up6o t5wn AZ, ZH 24ison 2est6i t5wj 2ap6o t5h@ EH, 24estin 24ara 3w@ 3h AZ pr6o@ t6hn EH, o34utw@ 3h EH pr6o@ t6hn ZH: 2all' 3w@ m6en 3h AZ pr6o@ t6hn EH, o34utw@ t6o AI pr6o@ t6o EK: 3w@ d6e 3h EH pr6o@ t6hn ZH, o34utw@ <2<2est6i>2> t6o EK pr6o@ t6o ZK: t5wn 24ara AI, ZK m4eson 2an4alog4on 2esti t6o EK. 24esti d6e ka6i t5wn LM, NC tetrag4wnwn m4eson 2an4alogon t6o MN: ka4i 2estin 24ison t6o m6en AI t5wj LM, t6o d6e ZK t5wj NC: ka6i t6o MN 24ara 24ison 2est6i t5wj EK. 2all6a t5wj m6en EK 24ison <2<2est6i>2> t6o DQ, t5wj d6e MN 24ison t6o LC: 34olon 24ara t6o DK 24ison 2est6i t5wj UFX gn4wmoni ka6i t5wj NC. 2epe6i o25un 34olon ^+^ t6o AK 24ison 2est6i to5i@ LM, NC, 35wn t6o DK 24ison 2est6i t5wj UFX gn4wmoni ka6i t5wj NC, loip6on 24ara t6o AB 24ison 2est6i t5wj TS. t6o d6e TS 2esti t6o 2ap6o t5h@ LN: t6o 2ap6o t5h@ LN 24ara 24ison 2est6i t5wj AB xwr4iwj: 3h LN 24ara d4unatai t6o AB xwr4ion. -L4egw <22>, 34oti 3h LN m4esh@ 2apotom4h 2esti pr4wth. -2Epe6i g6ar 3rht4on 2esti t6o EK ka4i 2estin 24ison t5wj LC, 3rht6on 24ara 2est6i t6o LC, tout4esti t6o 3up6o t5wn LO, ON. m4eson d6e 2ede4ixqh t6o NC: 2as4ummetron 24ara 2est6i t6o LC t5wj NC: 3w@ d6e t6o LC pr6o@ t6o NC, o34utw@ 2est6in 3h LO pr6o@ ON: a3i LO, ON 24ara 2as4ummetro4i e2isi m4hkei. a3i 24ara LO, ON m4esai e2is6i dun4amei m4onon s4ummetroi 3rht6on peri4exousai: 3h LN 24ara m4esh@ 2apotom4h 2esti pr4wth: ka6i d4unatai t6o AB xwr4ion. -3H 24ara t6o AB xwr4ion dunam4enh m4esh@ 2apotom4h 2esti pr4wth: 34oper 24edei de5icai. ##93##-------qqg41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ tr4ith@, 3h t6o xwr4ion dunam4enh m4esh@ 2apotom4h 2esti deut4era. ^+^ -Xwr4ion g6ar t6o AB periex4esqw 3up6o 3rht5h@ t5h@ AG ka6i 2apotom5h@ tr4ith@ t5h@ AD: l4egw, 34oti 3h t6o AB xwr4ion dunam4enh m4esh@ 2apotom4h 2esti deut4era. -24Estw g6ar t5hj AD prosarm4ozousa 3h DH: a3i AH, HD 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i o2udet4era t5wn AH, HD s4ummetr4o@ 2esti m4hkei t5hj 2ekkeim4enhj 3rht5hj t5hj AG, 3h d6e 34olh 3h AH t5h@ prosarmozo4ush@ t5h@ DH me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. 2epe6i o25un 3h AH t5h@ HD me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, 2e6an 24ara t5wj tet4artwj m4erei to5u 2ap6o t5h@ DH 24ison par6a t6hn AH parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ s4ummetra a2ut6hn diele5i. tetm4hsqw o25un 3h DH d4ixa kat6a t6o E, ka6i t5wj 2ap6o t5h@ EH 24ison par6a t6hn AH parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn AZ, ZH. ka6i 24hxqwsan di6a t5wn E, Z, H shme4iwn t5hj AG par4allhloi a3i EQ, ZI, HK: s4ummetroi 24ara e2is6in a3i AZ, ZH: s4ummetron 24ara ka6i t6o AI t5wj ZK. ka6i 2epe6i a3i AZ, ZH s4ummetro4i e2isi m4hkei, ka6i 3h AH 24ara 3ekat4eraj t5wn AZ, ZH s4ummetr4o@ 2esti m4hkei. 3rht6h d6e 3h AH ka6i 2as4ummetro@ t5hj AG m4hkei: 34wste ka6i a3i AZ, ZH. ^+^. 3ek4ateron 24ara t5wn AI, ZK m4eson 2est4in. p4alin, 2epe6i s4ummetr4o@ 2estin 3h DE t5hj EH m4hkei, ka6i 3h DH 24ara 3ekat4eraj t5wn DE, EH s4ummetr4o@ 2esti m4hkei. 3rht6h d6e 3h HD ka6i 2as4ummetro@ t5hj AG m4hkei: 3rht6h 24ara ka6i 3ekat4era t5wn DE, EH ka6i 2as4ummetro@ t5hj AG m4hkei: 3ek4ateron 24ara t5wn DQ, EK m4eson 2est4in. ka6i 2epe6i a3i AH, HD dun4amei m4onon s4ummetro4i e2isin, 2as4ummetro@ 24ara 2est6i m4hkei 3h AH t5hj HD. 2all' 3h m6en AH t5hj AZ s4ummetr4o@ 2esti m4hkei, 3h d6e DH t5hj EH: 2as4ummetro@ 24ara 2est6in 3h AZ t5hj EH m4hkei. 3w@ d6e 3h AZ pr6o@ t6hn EH, o34utw@ 2est6i t6o AI pr6o@ t6o EK: 2as4ummetron 24ara 2est6i t6o AI t5wj EK. -Sunest4atw o25un t5wj m6en AI 24ison tetr4agwnon t6o LM, t5wj d6e ZK 24ison 2afhjr4hsqw t6o NC per6i t6hn a2ut6hn gwn4ian 26on t5wj LM: per6i t6hn a2ut6hn 24ara di4ametr4on 2esti t6a LM, NC. 24estw a2ut5wn di4ametro@ 3h OR, ka6i katagegr4afqw t6o sx5hma. 2epe6i o25un t6o 3up6o t5wn AZ, ZH 24ison 2est6i t5wj 2ap6o t5h@ EH, 24estin 24ara 3w@ 3h AZ pr6o@ t6hn EH, o34utw@ 3h EH pr6o@ t6hn ZH. 2all' 3w@ m6en 3h AZ pr6o@ t6hn EH, o34utw@ 2est6i t6o AI pr6o@ t6o EK: 3w@ d6e 3h EH pr6o@ t6hn ZH, ^+^ o34utw@ 2est6i t6o EK pr6o@ t6o ZK: ka6i 3w@ 24ara t6o AI pr6o@ t6o EK, o34utw@ t6o EK pr6o@ t6o ZK: t5wn 24ara AI, ZK m4eson 2an4alog4on 2esti t6o EK. 24esti d6e ka6i t5wn LM, NC tetrag4wnwn m4eson 2an4alogon t6o MN: ka4i 2estin 24ison t6o m6en AI t5wj LM, t6o d6e ZK t5wj NC: ka6i t6o EK 24ara 24ison 2est6i t5wj MN. 2all6a t6o m6en MN 24ison 2est6i t5wj LC, t6o d6e EK 24ison <2<2est6i>2> t5wj DQ: ka6i 34olon 24ara t6o DK 24ison 2est6i t5wj UFX gn4wmoni ka6i t5wj NC. 24esti d6e ka6i t6o AK 24ison to5i@ LM, NC: loip6on 24ara t6o AB 24ison 2est6i t5wj ST, tout4esti t5wj 2ap6o t5h@ LN tetrag4wnwj: 3h LN 24ara d4unatai t6o AB xwr4ion. -L4egw, 34oti 3h LN m4esh@ 2apotom4h 2esti deut4era. -2Epe6i g6ar m4esa 2ede4ixqh t6a AI, ZK ka4i 2estin 24isa to5i@ 2ap6o t5wn LO, ON, m4eson 24ara ka6i 3ek4ateron t5wn 2ap6o t5wn LO, ON: m4esh 24ara 3ekat4era t5wn LO, ON. ka6i 2epe6i s4ummetr4on 2esti t6o AI t5wj ZK, s4ummetron 24ara ka6i t6o 2ap6o t5h@ LO t5wj 2ap6o t5h@ ON. p4alin, 2epe6i 2as4ummetron 2ede4ixqh t6o AI t5wj EK, 2as4ummetron 24ara 2est6i ka6i t6o LM t5wj MN, tout4esti t6o 2ap6o t5h@ LO t5wj 3up6o t5wn LO, ON: 34wste ka6i 3h LO 2as4ummetr4o@ 2esti t5hj ON: a3i LO, ON 24ara m4esai e2is6i dun4amei m4onon s4ummetroi. -L4egw d4h, 34oti ka6i m4eson peri4exousin. -2Epe6i g6ar m4eson 2ede4ixqh t6o EK ka4i 2estin 24ison t5wj 3up6o t5wn LO, ON, m4eson 24ara 2est6i ka6i t6o 3up6o t5wn LO, ON: 34wste a3i LO, ON m4esai e2is6i dun4amei m4onon s4ummetroi ^+^ m4eson peri4exousai. 3h LN 24ara m4esh@ 2apotom4h 2esti deut4era: ka6i d4unatai t6o AB xwr4ion. -3H 24ara t6o AB xwr4ion dunam4enh m4esh@ 2apotom4h 2esti deut4era: 34oper 24edei de5icai. ##94##-------qqd41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ tet4arth@, 3h t6o xwr4ion dunam4enh 2el4asswn 2est4in. -Xwr4ion g6ar t6o AB periex4esqw 3up6o 3rht5h@ t5h@ AG ka6i 2apotom5h@ tet4arth@ t5h@ AD: l4egw, 34oti 3h t6o AB xwr4ion dunam4enh 2el4asswn 2est4in. -24Estw g6ar t5hj AD prosarm4ozousa 3h DH: a3i 24ara AH, HD 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h AH s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj AG m4hkei, 3h d6e 34olh 3h AH t5h@ prosarmozo4ush@ t5h@ DH me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei. 2epe6i o25un 3h AH t5h@ HD me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei, 2e6an 24ara t5wj tet4artwj m4erei to5u 2ap6o t5h@ DH 24ison par6a t6hn AH parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ 2as4ummetra a2ut6hn ^+^ diele5i. tetm4hsqw o25un 3h DH d4ixa kat6a t6o E, ka6i t5wj 2ap6o t5h@ EH 24ison par6a t6hn AH parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn AZ, ZH: 2as4ummetro@ 24ara 2est6i m4hkei 3h AZ t5hj ZH. 24hxqwsan o25un di6a t5wn E, Z, H par4allhloi ta5i@ AG, BD a3i EQ, ZI, HK. 2epe6i o25un 3rht4h 2estin 3h AH ka6i s4ummetro@ t5hj AG m4hkei, 3rht6on 24ara 2est6in 34olon t6o AK. p4alin, 2epe6i 2as4ummetr4o@ 2estin 3h DH t5hj AG m4hkei, ka4i e2isin 2amf4oterai 3rhta4i, m4eson 24ara 2est6i t6o DK. p4alin, 2epe6i 2as4ummetr4o@ 2estin 3h AZ t5hj ZH m4hkei, 2as4ummetron 24ara ka6i t6o AI t5wj ZK. sunest4atw o25un t5wj m6en AI 24ison tetr4agwnon t6o LM, t5wj d6e ZK 24ison 2afhjr4hsqw per6i t6hn a2ut6hn gwn4ian t6hn 3up6o t5wn LOM t6o NC. per6i t6hn a2ut6hn 24ara di4ametr4on 2esti t6a LM, NC tetr4agwna. 24estw a2ut5wn di4ametro@ 3h OR, ka6i katagegr4afqw t6o sx5hma. 2epe6i o25un t6o 3up6o t5wn AZ, ZH 24ison 2est6i t5wj 2ap6o t5h@ EH, 2an4alogon 24ara 2est6in 3w@ 3h AZ pr6o@ t6hn EH, o34utw@ 3h EH pr6o@ t6hn ZH. 2all' 3w@ m6en 3h AZ pr6o@ t6hn EH, o34utw@ 2est6i t6o AI pr6o@ t6o EK, 3w@ d6e 3h EH pr6o@ t6hn ZH, o34utw@ 2est6i t6o EK pr6o@ t6o ZK: t5wn 24ara AI, ZK m4eson 2an4alog4on 2esti t6o EK. 24esti d6e ka6i t5wn LM, NC tetrag4wnwn m4eson 2an4alogon t6o MN, ka4i 2estin 24ison t6o m6en AI t5wj LM, t6o d6e ZK t5wj ^+^ NC: ka6i t6o EK 24ara 24ison 2est6i t5wj MN. 2all6a t5wj m6en EK 24ison 2est6i t6o DQ, t5wj d6e MN 24ison 2est6i t6o LC: 34olon 24ara t6o DK 24ison 2est6i t5wj UFX gn4wmoni ka6i t5wj NC. 2epe6i o25un 34olon t6o AK 24ison 2est6i to5i@ LM, NC tetrag4wnoi@, 35wn t6o DK 24ison 2est6i t5wj UFX gn4wmoni ka6i t5wj NC tetrag4wnwj, loip6on 24ara t6o AB 24ison 2est6i t5wj ST, tout4esti t5wj 2ap6o t5h@ LN tetrag4wnwj: 3h LN 24ara d4unatai t6o AB xwr4ion. -L4egw, 34oti 3h LN 24alog4o@ 2estin 3h kaloum4enh 2el4asswn. -2Epe6i g6ar 3rht4on 2esti t6o AK ka4i 2estin 24ison to5i@ 2ap6o t5wn LO, ON tetrag4wnoi@, t6o 24ara sugke4imenon 2ek t5wn 2ap6o t5wn LO, ON 3rht4on 2estin. p4alin, 2epe6i t6o DK m4eson 2est4in, ka4i 2estin 24ison t6o DK t5wj d6i@ 3up6o t5wn LO, ON, t6o 24ara d6i@ 3up6o t5wn LO, ON m4eson 2est4in. ka6i 2epe6i 2as4ummetron 2ede4ixqh t6o AI t5wj ZK, 2as4ummetron 24ara ka6i t6o 2ap6o t5h@ LO tetr4agwnon t5wj 2ap6o t5h@ ON tetrag4wnwj. a3i LO, ON 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d6e d6i@ 3up' a2ut5wn m4eson. 3h LN 24ara 24alog4o@ 2estin 3h kaloum4enh 2el4asswn: ka6i d4unatai t6o AB xwr4ion. -3H 24ara t6o AB xwr4ion dunam4enh 2el4asswn 2est4in: 34oper 24edei de5icai. ^+^ ##95##-------qqe41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ p4empth@, 3h t6o xwr4ion dunam4enh <2<3h>2> met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. -Xwr4ion g6ar t6o AB periex4esqw 3up6o 3rht5h@ t5h@ AG ka6i 2apotom5h@ p4empth@ t5h@ AD: l4egw, 34oti 3h t6o AB xwr4ion dunam4enh <2<3h>2> met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. -24Estw g6ar t5hj AD prosarm4ozousa 3h DH: a3i 24ara AH, HD 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h prosarm4ozousa 3h HD s4ummetr4o@ 2esti m4hkei t5hj 2ekkeim4enhj 3rht5hj t5hj AG, 3h d6e 34olh 3h AH t5h@ prosarmozo4ush@ t5h@ DH me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. 2e6an 24ara t5wj tet4artwj m4erei to5u 2ap6o t5h@ DH 24ison par6a t6hn AH parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ 2as4ummetra a2ut6hn diele5i. tetm4hsqw o25un 3h DH d4ixa kat6a t6o E shme5ion, ka6i t5wj 2ap6o t5h@ EH 24ison par6a t6hn AH parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj ka6i 24estw t6o 3up6o t5wn AZ, ZH: 2as4ummetro@ 24ara 2est6in 3h AZ t5hj ZH m4hkei. ka6i 2epe6i 2as4ummetr4o@ 2estin 3h AH t5hj GA m4hkei, ka4i e2isin ^+^ 2amf4oterai 3rhta4i, m4eson 24ara 2est6i t6o AK. p4alin, 2epe6i 3rht4h 2estin 3h DH ka6i s4ummetro@ t5hj AG m4hkei, 3rht4on 2esti t6o DK. sunest4atw o25un t5wj m6en AI 24ison tetr4agwnon t6o LM, t5wj d6e ZK 24ison tetr4agwnon 2afhjr4hsqw t6o NC per6i t6hn a2ut6hn gwn4ian t6hn 3up6o LOM: per6i t6hn a2ut6hn 24ara di4ametr4on 2esti t6a LM, NC tetr4agwna. 24estw a2ut5wn di4ametro@ 3h OR, ka6i katagegr4afqw t6o sx5hma. 3omo4iw@ d6h de4icomen, 34oti 3h LN d4unatai t6o AB xwr4ion. -L4egw, 34oti 3h LN 3h met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. -2Epe6i g6ar m4eson 2ede4ixqh t6o AK ka4i 2estin 24ison to5i@ 2ap6o t5wn LO, ON, t6a 24ara sugke4imenon 2ek t5wn 2ap6o t5wn LO, ON m4eson 2est4in. p4alin, 2epe6i 3rht4on 2esti t6o DK ka4i 2estin 24ison t5wj d6i@ 3up6o t5wn LO, ON, ka6i a2ut6o 3rht4on 2estin. ka6i 2epe6i 2as4ummetr4on 2esti t6o AI t5wj ZK, 2as4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ LO t5wj 2ap6o t5h@ ON: a3i LO, ON 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d6e d6i@ 3up' a2ut5wn 3rht4on. 3h loip6h 24ara 3h LN 24alog4o@ 2estin 3h kaloum4enh met6a 3rhto5u m4eson t6o 34olon poio5usa: ka6i d4unatai t6o AB xwr4ion. -3H t6o AB 24ara xwr4ion dunam4enh met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin: 34oper 24edei de5icai. ^+^ ##96##-------qqst41 -2E6an xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ 34ekth@, 3h t6o xwr4ion dunam4enh met6a m4esou m4eson t6o 34olon poio5us4a 2estin. -Xwr4ion g6ar t6o AB periex4esqw 3up6o 3rht5h@ t5h@ AG ka6i 2apotom5h@ 34ekth@ t5h@ AD: l4egw, 34oti 3h t6o AB xwr4ion dunam4enh <2<3h>2> met6a m4esou m4eson t6o 34olon poio5us4a 2estin. -24Estw g6ar t5hj AD prosarm4ozousa 3h DH: a3i 24ara AH, HD 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i o2udet4era a2ut5wn s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj AG m4hkei, 3h d6e 34olh 3h AH t5h@ prosarmozo4ush@ t5h@ DH me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei. 2epe6i o25un 3h AH t5h@ HD me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj m4hkei, 2e6an 24ara t5wj tet4artwj m4erei to5u 2ap6o t5h@ DH 24ison par6a t6hn AH parablhq5hj 2elle5ipon e24idei tetrag4wnwj, e2i@ 2as4ummetra a2ut6hn diele5i. tetm4hsqw o25un 3h DH d4ixa kat6a t6o E <22>, ka6i t5wj 2ap6o t5h@ EH 24ison par6a t6hn AH parabebl4hsqw 2elle5ipon e24idei tetrag4wnwj, ka6i 24estw t6o 3up6o t5wn AZ, ZH: 2as4ummetro@ 24ara 2est6in 3h ^+^ AZ t5hj ZH m4hkei. 3w@ d6e 3h AZ pr6o@ t6hn ZH, o34utw@ 2est6i t6o AI pr6o@ t6o ZK: 2as4ummetron 24ara 2est6i t6o AI t5wj ZK. ka6i 2epe6i a3i AH, AG 3rhta4i e2isi dun4amei m4onon s4ummetroi, m4eson 2est6i t6o AK. p4alin, 2epe6i a3i AG, DH 3rhta4i e2isi ka6i 2as4ummetroi m4hkei, m4eson 2est6i ka6i t6o DK. 2epe6i o25un a3i AH, HD dun4amei m4onon s4ummetro4i e2isin, 2as4ummetro@ 24ara 2est6in 3h AH t5hj HD m4hkei. 3w@ d6e 3h AH pr6o@ t6hn HD, o34utw@ 2est6i t6o AK pr6o@ t6o KD: 2as4ummetron 24ara 2est6i t6o AK t5wj KD. sunest4atw o25un t5wj m6en AI 24ison tetr4agwnon t6o LM, t5wj d6e ZK 24ison 2afhjr4hsqw per6i t6hn a2ut6hn gwn4ian t6o NC: per6i t6hn a2ut6hn 24ara di4ametr4on 2esti t6a LM, NC tetr4agwna. 24estw a2ut5wn di4ametro@ 3h OR, ka6i katagegr4afqw t6o sx5hma. 3omo4iw@ d6h to5i@ 2ep4anw de4icomen, 34oti 3h LN d4unatai t6o AB xwr4ion. -L4egw, 34oti 3h LN <2<3h>2> met6a m4esou m4eson t6o 34olon ^-^ poio5us4a 2estin. -2Epe6i g6ar m4eson 2ede4ixqh t6o AK ka4i 2estin 24ison to5i@ 2ap6o t5wn LO, ON, t6o 24ara sugke4imenon 2ek t5wn 2ap6o t5wn LO, ON m4eson 2est4in. p4alin, 2epe6i m4eson 2ede4ixqh t6o DK ka4i 2estin 24ison t5wj d6i@ 3up6o t5wn LO, ON, ka6i t6o d6i@ 3up6o t5wn LO, ON m4eson 2est4in. ka6i 2epe6i 2as4ummetron 2ede4ixqh t6o AK t5wj DK, 2as4ummetra <2<24ara>2> 2est6i ka6i t6a 2ap6o t5wn LO, ON tetr4agwna t5wj d6i@ 3up6o t5wn LO, ON. ^+^ ka6i 2epe6i 2as4ummetr4on 2esti t6o AI t5wj ZK, 2as4ummetron 24ara ka6i t6o 2ap6o t5h@ LO t5wj 2ap6o t5h@ ON: a3i LO, ON 24ara dun4amei e2is6in 2as4ummetroi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson ka6i t6o d6i@ 3up' a2ut5wn m4eson 24eti te t6a 2ap' a2ut5wn tetr4agwna 2as4ummetra t5wj d6i@ 3up' a2ut5wn. 3h 24ara LN 24alog4o@ 2estin 3h kaloum4enh met6a m4esou m4eson t6o 34olon poio5usa: ka6i d4unatai t6o AB xwr4ion. -3H 24ara t6o xwr4ion dunam4enh met6a m4esou m4eson t6o 34olon poio5us4a 2estin: 34oper 24edei de5icai. ##97##-------qqz41 -T6o 2ap6o 2apotom5h@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn pr4wthn. -24Estw 2apotom6h 3h AB, 3rht6h d6e 3h GD, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: l4egw, 34oti 3h GZ 2apotom4h 2esti pr4wth. -24Estw g6ar t5hj AB prosarm4ozousa 3h BH: a3i 24ara AH, HB 3rhta4i e2isi dun4amei m4onon s4ummetroi. ka6i t5wj m6en 2ap6o t5h@ AH 24ison par6a t6hn GD parabebl4hsqw t6o GQ, t5wj d6e 2ap6o t5h@ BH t6o KL. 34olon 24ara t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB: 35wn t6o GE 24ison 2est6i t5wj 2ap6o t5h@ AB: loip6on 24ara t6o ZL 24ison 2est6i t5wj d6i@ 3up6o ^+^ t5wn AH, HB. tetm4hsqw 3h ZM d4ixa kat6a t6o N shme5ion, ka6i 24hxqw di6a to5u N t5hj GD par4allhlo@ 3h NC: 3ek4ateron 24ara t5wn ZC, LN 24ison 2est6i t5wj 3up6o t5wn AH, HB. ka6i 2epe6i t6a 2ap6o t5wn AH, HB 3rht4a 2estin, ka4i 2esti to5i@ 2ap6o t5wn AH, HB 24ison t6o DM, 3rht6on 24ara 2est6i t6o DM. ka6i par6a 3rht6hn t6hn GD parab4eblhtai pl4ato@ poio5un t6hn GM: 3rht6h 24ara 2est6in 3h GM ka6i s4ummetro@ t5hj GD m4hkei. p4alin, 2epe6i m4eson 2est6i t6o d6i@ 3up6o t5wn AH, HB, ka6i t5wj d6i@ 3up6o t5wn AH, HB 24ison t6o ZL, m4eson 24ara t6o ZL. ka6i par6a 3rht6hn t6hn GD par4akeitai pl4ato@ poio5un t6hn ZM: 3rht6h 24ara 2est6in 3h ZM ka6i 2as4ummetro@ t5hj GD m4hkei. ka6i 2epe6i t6a m6en 2ap6o t5wn AH, HB 3rht4a 2estin, t6o d6e d6i@ 3up6o t5wn AH, HB m4eson, 2as4ummetra 24ara 2est6i t6a 2ap6o t5wn AH, HB t5wj d6i@ 3up6o t5wn AH, HB. ka6i to5i@ m6en 2ap6o t5wn AH, HB 24ison 2est6i t6o GL, t5wj d6e d6i@ 3up6o t5wn AH, HB t6o ZL: 2as4ummetron 24ara 2est6i t6o DM t5wj ZL. 3w@ d6e t6o DM pr6o@ t6o ZL, o34utw@ 2est6in 3h GM pr6o@ t6hn ZM. 2as4ummetro@ 24ara 2est6in 3h GM t5hj ZM m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i 24ara GM, MZ 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h GZ 24ara 2apotom4h 2estin. -L4egw d4h, 34oti ka6i pr4wth. -2Epe6i g6ar t5wn 2ap6o t5wn AH, HB m4eson 2an4alog4on 2esti t6o 3up6o t5wn AH, HB, ka4i 2esti t5wj m6en 2ap6o t5h@ AH 24ison ^+^ t6o GQ, t5wj d6e 2ap6o t5h@ BH 24ison t6o KL, t5wj d6e 3up6o t5wn AH, HB t6o NL, ka6i t5wn GQ, KL 24ara m4eson 2an4alog4on 2esti t6o NL: 24estin 24ara 3w@ t6o GQ pr6o@ t6o NL, o34utw@ t6o NL pr6o@ t6o KL. 2all' 3w@ m6en t6o GQ pr6o@ t6o NL, o34utw@ 2est6in 3h GK pr6o@ t6hn NM: 3w@ d6e t6o NL pr6o@ t6o KL, o34utw@ 2est6in 3h NM pr6o@ t6hn KM: t6o 24ara 3up6o t5wn GK, KM 24ison 2est6i t5wj 2ap6o t5h@ NM, tout4esti t5wj tet4artwj m4erei to5u 2ap6o t5h@ ZM. ka6i 2epe6i s4ummetr4on 2esti t6o 2ap6o t5h@ AH t5wj 2ap6o t5h@ HB, s4ummetr4on <2<2esti>2> ka6i t6o GQ t5wj KL. 3w@ d6e t6o GQ pr6o@ t6o KL, o34utw@ 3h GK pr6o@ t6hn KM: s4ummetro@ 24ara 2est6in 3h GK t5hj KM. 2epe6i o25un d4uo e2uqe5iai 24aniso4i e2isin a3i GM, MZ, ka6i t5wj tet4artwj m4erei to5u 2ap6o t5h@ ZM 24ison par6a t6hn GM parab4eblhtai 2elle5ipon e24idei tetrag4wnwj t6o 3up6o t5wn GK, KM, ka4i 2esti s4ummetro@ 3h GK t5hj KM, 3h 24ara GM t5h@ MZ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. ka4i 2estin 3h GM s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj t5hj GD m4hkei: 3h 24ara GZ 2apotom4h 2esti pr4wth. -T6o 24ara 2ap6o 2apotom5h@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn pr4wthn: 34oper 24edei de5icai. ^+^ ##98##-------qqh41 -T6o 2ap6o m4esh@ 2apotom5h@ pr4wth@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn deut4eran. -24Estw m4esh@ 2apotom6h pr4wth 3h AB, 3rht6h d6e 3h GD, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: l4egw, 34oti 3h GZ 2apotom4h 2esti deut4era. -24Estw g6ar t5hj AB prosarm4ozousa 3h BH: a3i 24ara AH, HB m4esai e2is6i dun4amei m4onon s4ummetroi 3rht6on peri4exousai. ka6i t5wj m6en 2ap6o t5h@ AH 24ison par6a t6hn GD parabebl4hsqw t6o GQ pl4ato@ poio5un t6hn GK, t5wj d6e 2ap6o t5h@ HB 24ison t6o KL pl4ato@ poio5un t6hn KM: 34olon 24ara t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB: m4eson 24ara ka6i t6o GL. ka6i par6a 3rht6hn t6hn GD par4akeitai pl4ato@ poio5un t6hn GM: 3rht6h 24ara 2est6in 3h GM ka6i 2as4ummetro@ t5hj GD m4hkei. ka6i 2epe6i t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB, 35wn t6o 2ap6o t5h@ AB 24ison 2est6i t5wj GE, loip6on 24ara t6o d6i@ 3up6o t5wn AH, HB 24ison 2est6i t5wj ZL. 3rht6on d4e <2<2esti>2> t6o d6i@ 3up6o t5wn AH, HB: 3rht6on 24ara t6o ZL. ka6i par6a 3rht6hn t6hn ZE par4akeitai pl4ato@ poio5un t6hn ZM: 3rht6h 24ara 2est6i ka6i 3h ZM ka6i s4ummetro@ t5hj GD m4hkei. 2epe6i o25un t6a m6en 2ap6o t5wn AH, HB, tout4esti t6o GL, ^+^ m4eson 2est4in, t6o d6e d6i@ 3up6o t5wn AH, HB, tout4esti t6o ZL, 3rht4on, 2as4ummetron 24ara 2est6i t6o GL t5wj ZL. 3w@ d6e t6o GL pr6o@ t6o ZL, o34utw@ 2est6in 3h GM pr6o@ t6hn ZM: 2as4ummetro@ 24ara 3h GM t5hj ZM m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i 24ara GM, MZ 3rhta4i e2isi dun4amei m4onon s4ummetroi: 3h GZ 24ara 2apotom4h 2estin. -L4egw d4h, 34oti ka6i deut4era. -Tetm4hsqw g6ar 3h ZM d4ixa kat6a t6o N, ka6i 24hxqw di6a to5u N t5hj GD par4allhlo@ 3h NC: 3ek4ateron 24ara t5wn ZC, NL 24ison 2est6i t5wj 3up6o t5wn AH, HB. ka6i 2epe6i t5wn 2ap6o t5wn AH, HB tetrag4wnwn m4eson 2an4alog4on 2esti t6o 3up6o t5wn AH, HB, ka4i 2estin 24ison t6o m6en 2ap6o t5h@ AH t5wj GQ, t6o d6e 3up6o t5wn AH, HB t5wj NL, t6o d6e 2ap6o t5h@ BH t5wj KL, ka6i t5wn GQ, KL 24ara m4eson 2an4alog4on 2esti t6o NL: 24estin 24ara 3w@ t6o GQ pr6o@ t6o NL, o34utw@ t6o NL pr6o@ t6o KL. 2all' 3w@ m6en t6o GQ pr6o@ t6o NL, o34utw@ 2est6in 3h GK pr6o@ t6hn NM, 3w@ d6e t6o NL pr6o@ t6o KL, o34utw@ 2est6in 3h NM pr6o@ t6hn MK: 3w@ 24ara 3h GK pr6o@ t6hn NM, o34utw@ 2est6in 3h NM pr6o@ t6hn KM: t6o 24ara 3up6o t5wn GK, KM 24ison 2est6i t5wj 2ap6o t5h@ NM, tout4esti t5wj tet4artwj m4erei to5u 2ap6o t5h@ ZM. <22> ^+^ <22> 2epe6i o25un d4uo e2uqe5iai 24aniso4i e2isin a3i GM, MZ, ka6i t5wj tet4artwj m4erei to5u 2ap6o t5h@ MZ 24ison par6a t6hn me4izona t6hn GM parab4eblhtai 2elle5ipon e24idei tetrag4wnwj t6o 3up6o t5wn GK, KM ka6i e2i@ s4ummetra a2ut6hn diaire5i, 3h 24ara GM t5h@ MZ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj m4hkei. ka4i 2estin 3h prosarm4ozousa 3h ZM s4ummetro@ m4hkei t5hj 2ekkeim4enhj 3rht5hj t5hj GD: 3h 24ara GZ 2apotom4h 2esti deut4era. -T6o 24ara 2ap6o m4esh@ 2apotom5h@ pr4wth@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn deut4eran: 34oper 24edei de5icai. ##99##-------qqq41 -T6o 2ap6o m4esh@ 2apotom5h@ deut4era@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn tr4ithn. -24Estw m4esh@ 2apotom6h deut4era 3h AB, 3rht6h d6e 3h GD, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: l4egw, 34oti 3h GZ 2apotom4h 2esti tr4ith. -24Estw g6ar t5hj AB prosarm4ozousa 3h BH: a3i 24ara AH, HB m4esai e2is6i dun4amei m4onon s4ummetroi m4eson peri4exousai. ka6i ^+^ t5wj m6en 2ap6o t5h@ AH 24ison par6a t6hn GD parabebl4hsqw t6o GQ pl4ato@ poio5un t6hn GK, t5wj d6e 2ap6o t5h@ BH 24ison par6a t6hn KQ parabebl4hsqw t6o KL pl4ato@ poio5un t6hn KM: 34olon 24ara t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB <22>: m4eson 24ara ka6i t6o GL. ka6i par6a 3rht6hn t6hn GD parab4eblhtai pl4ato@ poio5un t6hn GM: 3rht6h 24ara 2est6in 3h GM ka6i 2as4ummetro@ t5hj GD m4hkei. ka6i 2epe6i 34olon t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB, 35wn t6o GE 24ison 2est6i t5wj 2ap6o t5h@ AB, loip6on 24ara t6o LZ 24ison 2est6i t5wj d6i@ 3up6o t5wn AH, HB. tetm4hsqw o25un 3h ZM d4ixa kat6a t6o N shme5ion, ka6i t5hj GD par4allhlo@ 24hxqw 3h NC: 3ek4ateron 24ara t5wn ZC, NL 24ison 2est6i t5wj 3up6o t5wn AH, HB. m4eson d6e t6o 3up6o t5wn AH, HB: m4eson 24ara 2est6i ka6i t6o ZL. ka6i par6a 3rht6hn t6hn EZ par4akeitai pl4ato@ poio5un t6hn ZM: 3rht6h 24ara ka6i 3h ZM ka6i 2as4ummetro@ t5hj GD m4hkei. ka6i 2epe6i a3i AH, HB dun4amei m4onon e2is6i s4ummetroi, 2as4ummetro@ 24ara <2<2est6i>2> m4hkei 3h AH t5hj HB: 2as4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ AH t5wj 3up6o t5wn AH, HB. 2all6a t5wj m6en 2ap6o t5h@ AH s4ummetr4a 2esti t6a 2ap6o t5wn AH, HB, t5wj d6e 3up6o t5wn AH, HB t6o d6i@ 3up6o t5wn AH, HB: 2as4ummetra 24ara 2est6i t6a 2ap6o t5wn AH, HB t5wj d6i@ 3up6o t5wn AH, HB. 2all6a to5i@ m6en 2ap6o t5wn AH, HB 24ison 2est6i t6o GL, t5wj d6e d6i@ 3up6o t5wn AH, HB 24ison 2est6i t6o ZL: 2as4ummetron 24ara 2est6i t6o GL t5wj ZL. ^+^ 3w@ d6e t6o GL pr6o@ t6o ZL, o34utw@ 2est6in 3h GM pr6o@ t6hn ZM: 2as4ummetro@ 24ara 2est6in 3h GM t5hj ZM m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i 24ara GM, MZ 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h GZ. -L4egw d4h, 34oti ka6i tr4ith. -2Epe6i g6ar s4ummetr4on 2esti t6o 2ap6o t5h@ AH t5wj 2ap6o t5h@ HB, s4ummetron 24ara ka6i t6o GQ t5wj KL: 34wste ka6i 3h GK t5hj KM. ka6i 2epe6i t5wn 2ap6o t5wn AH, HB m4eson 2an4alog4on 2esti t6o 3up6o t5wn AH, HB, ka4i 2esti t5wj m6en 2ap6o t5h@ AH 24ison t6o GQ, t5wj d6e 2ap6o t5h@ HB 24ison t6o KL, t5wj d6e 3up6o t5wn AH, HB 24ison t6o NL, ka6i t5wn GQ, KL 24ara m4eson 2an4alog4on 2esti t6o NL: 24estin 24ara 3w@ t6o GQ pr6o@ t6o NL, o34utw@ t6o NL pr6o@ t6o KL. 2all' 3w@ m6en t6o GQ pr6o@ t6o NL, o34utw@ 2est6in 3h GK pr6o@ t6hn NM, 3w@ d6e t6o NL pr6o@ t6o KL, o34utw@ 2est6in 3h NM pr6o@ t6hn KM: 3w@ 24ara 3h GK pr6o@ t6hn MN, o34utw@ 2est6in 3h MN pr6o@ t6hn KM: t6o 24ara 3up6o t5wn GK, KM 24ison 2est6i t5wj <2<2ap6o t5h@ MN, tout4esti t5wj>2> tet4artwj m4erei to5u 2ap6o t5h@ ZM. 2epe6i o25un d4uo e2uqe5iai 24aniso4i e2isin a3i GM, MZ, ka6i t5wj tet4artwj m4erei to5u 2ap6o t5h@ ZM 24ison par6a t6hn GM parab4eblhtai 2elle5ipon e24idei tetrag4wnwj ka6i e2i@ s4ummetra a2ut6hn diaire5i, 3h GM 24ara t5h@ MZ me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj. ka6i o2udet4era t5wn GM, MZ s4ummetr4o@ 2esti m4hkei t5hj 2ekkeim4enhj 3rht5hj t5hj GD: 3h 24ara GZ 2apotom4h 2esti tr4ith. ^+^ -T6o 24ara 2ap6o m4esh@ 2apotom5h@ deut4era@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn tr4ithn: 34oper 24edei de5icai. ##100##-------r41 -T6o 2ap6o 2el4assono@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn tet4arthn. -24Estw 2el4asswn 3h AB, 3rht6h d6e 3h GD, ka6i t5wj 2ap6o t5h@ AB 24ison par6a 3rht6hn t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: l4egw, 34oti 3h GZ 2apotom4h 2esti tet4arth. -24Estw g6ar t5hj AB prosarm4ozousa 3h BH: a3i 24ara AH, HB dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AH, HB tetrag4wnwn 3rht4on, t6o d6e d6i@ 3up6o t5wn AH, HB m4eson. ka6i t5wj m6en 2ap6o t5h@ AH 24ison par6a t6hn GD parabebl4hsqw t6o GQ pl4ato@ poio5un t6hn GK, t5wj d6e 2ap6o t5h@ BH 24ison t6o KL pl4ato@ poio5un t6hn KM: 34olon 24ara t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB. ka4i 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn AH, HB 3rht4on: 3rht6on 24ara 2est6i ka6i t6o GL. ka6i par6a 3rht6hn t6hn GD par4akeitai pl4ato@ poio5un t6hn GM: 3rht6h 24ara ka6i 3h GM ka6i s4ummetro@ t5hj GD m4hkei. ka6i 2epe6i 34olon t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB, 35wn t6o GE 24ison 2est6i t5wj 2ap6o t5h@ AB, loip6on 24ara t6o ZL 24ison ^+^ 2est6i t5wj d6i@ 3up6o t5wn AH, HB. tetm4hsqw o25un 3h ZM d4ixa kat6a t6o N shme5ion, ka6i 24hxqw di6a to5u N 3opot4eraj t5wn GD, ML par4allhlo@ 3h NC: 3ek4ateron 24ara t5wn ZC, NL 24ison 2est6i t5wj 3up6o t5wn AH, HB. ka6i 2epe6i t6o d6i@ 3up6o t5wn AH, HB m4eson 2est6i ka4i 2estin 24ison t5wj ZL, ka6i t6o ZL 24ara m4eson 2est4in. ka6i par6a 3rht6hn t6hn ZE par4akeitai pl4ato@ poio5un t6hn ZM: 3rht6h 24ara 2est6in 3h ZM ka6i 2as4ummetro@ t5hj GD m4hkei. ka6i 2epe6i t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AH, HB 3rht4on 2estin, t6o d6e d6i@ 3up6o t5wn AH, HB m4eson, 2as4ummetra <2<24ara>2> 2est6i t6a 2ap6o t5wn AH, HB t5wj d6i@ 3up6o t5wn AH, HB. 24ison d4e <2<2esti>2> t6o GL to5i@ 2ap6o t5wn AH, HB, t5wj d6e d6i@ 3up6o t5wn AH, HB 24ison t6o ZL: 2as4ummetron 24ara <2<2est6i>2> t6o GL t5wj ZL. 3w@ d6e t6o GL pr6o@ t6o ZL, o34utw@ 2est6in 3h GM pr6o@ t6hn MZ: 2as4ummetro@ 24ara 2est6in 3h GM t5hj MZ m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i 24ara GM, MZ 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h GZ. -L4egw <22>, 34oti ka6i tet4arth. -2Epe6i g6ar a3i AH, HB dun4amei e2is6in 2as4ummetroi, 2as4ummetron 24ara ka6i t6o 2ap6o t5h@ AH t5wj 2ap6o t5h@ HB. ka4i 2esti t5wj m6en 2ap6o t5h@ AH 24ison t6o GQ, t5wj d6e 2ap6o t5h@ HB 24ison t6o KL: 2as4ummetron 24ara 2est6i t6o GQ t5wj KL. 3w@ d6e t6o GQ pr6o@ t6o KL, o34utw@ 2est6in 3h GK pr6o@ t6hn KM: 2as4ummetro@ 24ara 2est6in 3h GK t5hj KM m4hkei. ka6i ^+^ 2epe6i t5wn 2ap6o t5wn AH, HB m4eson 2an4alog4on 2esti t6o 3up6o t5wn AH, HB, ka4i 2estin 24ison t6o m6en 2ap6o t5h@ AH t5wj GQ, t6o d6e 2ap6o t5h@ HB t5wj KL, t6o d6e 3up6o t5wn AH, HB t5wj NL, t5wn 24ara GQ, KL m4eson 2an4alog4on 2esti t6o NL: 24estin 24ara 3w@ t6o GQ pr6o@ t6o NL, o34utw@ t6o NL pr6o@ t6o KL. 2all' 3w@ m6en t6o GQ pr6o@ t6o NL, o34utw@ 2est6in 3h GK pr6o@ t6hn NM, 3w@ d6e t6o NL pr6o@ t6o KL, o34utw@ 2est6in 3h NM pr6o@ t6hn KM: 3w@ 24ara 3h GK pr6o@ t6hn MN, o34utw@ 2est6in 3h MN pr6o@ t6hn KM: t6o 24ara 3up6o t5wn GK, KM 24ison 2est6i t5wj 2ap6o t5h@ MN, tout4esti t5wj tet4artwj m4erei to5u 2ap6o t5h@ ZM. 2epe6i o25un d4uo e2uqe5iai 24aniso4i e2isin a3i GM, MZ, ka6i t5wj tet4artwj m4erei to5u 2ap6o t5h@ MZ 24ison par6a t6hn GM parab4eblhtai 2elle5ipon e24idei tetrag4wnwj t6o 3up6o t5wn GK, KM ka6i e2i@ 2as4ummetra a2ut6hn diaire5i, 3h 24ara GM t5h@ MZ me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i 2estin 34olh 3h GM s4ummetro@ m4hkei t5hj 2ekkeim4enhj 3rht5hj t5hj GD: 3h 24ara GZ 2apotom4h 2esti te* t4arth. -T6o 24ara 2ap6o 2el4assono@ ka6i t6a 3ec5h@. ##101##-------ra41 -T6o 2ap6o t5h@ met6a 3rhto5u m4eson t6o 34olon poio4ush@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn p4empthn. ^+^ -24Estw 3h met6a 3rhto5u m4eson t6o 34olon poio5usa 3h AB, 3rht6h d6e 3h GD, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: l4egw, 34oti 3h GZ 2apotom4h 2esti p4empth. -24Estw g6ar t5hj AB prosarm4ozousa 3h BH: a3i 24ara AH, HB e2uqe5iai dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson, t6o d6e d6i@ 3up' a2ut5wn 3rht4on. ka6i t5wj m6en 2ap6o t5h@ AH 24ison par6a t6hn GD parabebl4hsqw t6o GQ, t5wj d6e 2ap6o t5h@ HB 24ison t6o KL: 34olon 24ara t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB. t6o d6e sugke4imenon 2ek t5wn 2ap6o t5wn AH, HB 34ama m4eson 2est4in: m4eson 24ara 2est6i t6o GL. ka6i par6a 3rht6hn t6hn GD par4akeitai pl4ato@ poio5un t6hn GM: 3rht6h 24ara 2est6in 3h GM ka6i 2as4ummetro@ t5hj GD. ka6i 2epe6i 34olon t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB, 35wn t6o GE 24ison 2est6i t5wj 2ap6o t5h@ AB, loip6on 24ara t6o ZL 24ison 2est6i t5wj d6i@ 3up6o t5wn AH, HB. tetm4hsqw o25un 3h ZM d4ixa kat6a t6o N, ka6i 24hxqw di6a to5u N 3opot4eraj t5wn GD, ML par4allhlo@ 3h NC: 3ek4ateron 24ara t5wn ZC, NL 24ison 2est6i t5wj 3up6o t5wn AH, HB. ka6i 2epe6i t6o d6i@ 3up6o t5wn AH, HB 3rht4on 2esti ka4i <2<2estin>2> 24ison t5wj ZL, 3rht6on 24ara 2est6i t6o ZL. ka6i par6a 3rht6hn t6hn EZ par4akeitai pl4ato@ ^+^ poio5un t6hn ZM: 3rht6h 24ara 2est6in 3h ZM ka6i s4ummetro@ t5hj GD m4hkei. ka6i 2epe6i t6o m6en GL m4eson 2est4in, t6o d6e ZL 3rht4on, 2as4ummetron 24ara 2est6i t6o GL t5wj ZL. 3w@ d6e t6o GL pr6o@ t6o ZL, o34utw@ 3h GM pr6o@ t6hn MZ: 2as4ummetro@ 24ara 2est6in 3h GM t5hj MZ m4hkei. ka4i e2isin 2amf4oterai 3rhta4i: a3i 24ara GM, MZ 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h GZ. -L4egw d4h, 34oti ka6i p4empth. -3Omo4iw@ g6ar de4icomen, 34oti t6o 3up6o t5wn GKM 24ison 2est6i ^-^ t5wj 2ap6o t5h@ NM, tout4esti t5wj tet4artwj m4erei to5u 2ap6o t5h@ ZM. ka6i 2epe6i 2as4ummetr4on 2esti t6o 2ap6o t5h@ AH t5wj 2ap6o t5h@ HB, 24ison d6e t6o m6en 2ap6o t5h@ AH t5wj GQ, t6o d6e 2ap6o t5h@ HB t5wj KL, 2as4ummetron 24ara t6o GQ t5wj KL. 3w@ d6e t6o GQ pr6o@ t6o KL, o34utw@ 3h GK pr6o@ t6hn KM: 2as4ummetro@ 24ara 3h GK t5hj KM m4hkei. 2epe6i o25un d4uo e2uqe5iai 24aniso4i e2isin a3i GM, MZ, ka6i t5wj tet4artwj m4erei to5u 2ap6o t5h@ ZM 24ison par6a t6hn GM parab4eblhtai 2elle5ipon e24idei tetrag4wnwj ka6i e2i@ 2as4ummetra a2ut6hn diaire5i, 3h 24ara GM t5h@ MZ me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka4i 2estin 3h prosarm4ozousa 3h ZM s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj t5hj GD: 3h 24ara GZ 2apotom4h 2esti p4empth: 34oper ^-^ 24edei de5icai. ^+^ ##102##-------rb41 -T6o 2ap6o t5h@ met6a m4esou m4eson t6o 34olon poio4ush@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn 34ekthn. -24Estw 3h met6a m4esou m4eson t6o 34olon poio5usa 3h AB, 3rht6h d6e 3h GD, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: l4egw, 34oti 3h GZ 2apotom4h 2estin 34ekth. -24Estw g6ar t5hj AB prosarm4ozousa 3h BH: a3i 24ara AH, HB dun4amei e2is6in 2as4ummetroi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson ka6i t6o d6i@ 3up6o t5wn AH, HB m4eson ka6i 2as4ummetron t6a 2ap6o t5wn AH, HB t5wj d6i@ 3up6o t5wn AH, HB. parabebl4hsqw o25un par6a t6hn GD t5wj m6en 2ap6o t5h@ AH 24ison t6o GQ pl4ato@ poio5un t6hn GK, t5wj d6e 2ap6o t5h@ BH t6o KL: 34olon 24ara t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB: m4eson 24ara <2<2est6i>2> ka6i t6o GL. ka6i par6a 3rht6hn t6hn GD par4akeitai pl4ato@ poio5un t6hn GM: 3rht6h 24ara 2est6in 3h GM ka6i 2as4ummetro@ t5hj GD m4hkei. 2epe6i o25un t6o GL 24ison 2est6i to5i@ 2ap6o t5wn AH, HB, 35wn t6o GE 24ison t5wj 2ap6o t5h@ AB, loip6on 24ara t6o ZL 24ison 2est6i d6i@ 3up6o t5wn AH, HB. ka4i 2esti t6o d6i@ 3up6o t5wn AH, HB m4eson: ka6i t6o ZL 24ara m4eson 2est4in. ka6i par6a 3rht6hn t6hn ZE par4akeitai pl4ato@ poio5un t6hn ^+^ ZM: 3rht6h 24ara 2est6in 3h ZM ka6i 2as4ummetro@ t5hj GD m4hkei. ka6i 2epe6i t6a 2ap6o t5wn AH, HB 2as4ummetr4a 2esti t5wj d6i@ 3up6o t5wn AH, HB, ka4i 2esti to5i@ m6en 2ap6o t5wn AH, HB 24ison t6o GL, t5wj d6e d6i@ 3up6o t5wn AH, HB 24ison t6o ZL, 2as4ummetron 24ara <2<2est6i>2> t6o GL t5wj ZL. 3w@ d6e t6o GL pr6o@ t6o ZL, o34utw@ 2est6in 3h GM pr6o@ t6hn MZ: 2as4ummetro@ 24ara 2est6in 3h GM t5hj MZ m4hkei. ka4i e2isin 2amf4oterai 3rhta4i. a3i GM, MZ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h GZ. -L4egw d4h, 34oti ka6i 34ekth. -2Epe6i g6ar t6o ZL 24ison 2est6i t5wj d6i@ 3up6o t5wn AH, HB, tetm4hsqw d4ixa 3h ZM kat6a t6o N, ka6i 24hxqw di6a to5u N t5hj GD par4allhlo@ 3h NC: 3ek4ateron 24ara t5wn ZC, NL 24ison 2est6i t5wj 3up6o t5wn AH, HB. ka6i 2epe6i a3i AH, HB dun4amei e2is6in 2as4ummetroi, 2as4ummetron 24ara 2est6i t6o 2ap6o t5h@ AH t5wj 2ap6o t5h@ HB. 2all6a t5wj m6en 2ap6o t5h@ AH 24ison 2est6i t6o GQ, t5wj d6e 2ap6o t5h@ HB 24ison 2est6i t6o KL: 2as4ummetron 24ara 2est6i t6o GQ t5wj KL. 3w@ d6e t6o GQ pr6o@ t6o KL, o34utw@ 2est6in 3h GK pr6o@ t6hn KM: 2as4ummetro@ 24ara 2est6in 3h GK t5hj KM. ka6i 2epe6i t5wn 2ap6o t5wn AH, HB m4eson 2an4alog4on 2esti t6o 3up6o t5wn AH, HB, ka4i 2esti t5wj m6en 2ap6o t5h@ AH 24ison t6o GQ, t5wj d6e 2ap6o t5h@ HB 24ison t6o KL, t5wj d6e 3up6o t5wn AH, HB 24ison t6o NL, ka6i t5wn 24ara GQ, KL m4eson 2an4alog4on 2esti t6o NL: 24estin 24ara ^+^ 3w@ t6o GQ pr6o@ t6o NL, o34utw@ t6o NL pr6o@ t6o KL. ka6i di6a t6a a2ut6a 3h GM t5h@ MZ me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka6i o2udet4era a2ut5wn s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj t5hj GD: 3h GZ 24ara 2apotom4h 2estin 34ekth: 34oper 24edei de5icai. ##103##-------rg41 -3H t5hj 2apotom5hj m4hkei s4ummetro@ 2apotom4h 2esti ^-^ ka6i t5hj t4acei 3h a2ut4h. -24Estw 2apotom6h 3h AB, ka6i t5hj AB m4hkei s4ummetro@ 24estw 3h GD: l4egw, 34oti ka6i 3h GD 2apotom4h 2esti ka6i t5hj t4acei 3h a2ut6h t5hj AB. -2Epe6i g6ar 2apotom4h 2estin 3h AB, 24estw a2ut5hj prosarm4ozousa 3h BE: a3i AE, EB 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. ka6i t5wj t5h@ AB pr6o@ t6hn GD l4ogwj 3o a2ut6o@ gegon4etw 3o t5h@ BE pr6o@ t6hn DZ: ka6i 3w@ 36en 24ara pr6o@ 34en, p4anta <2<2est6i>2> pr6o@ p4anta: 24estin 24ara ka6i ^+^ 3w@ 34olh 3h AE pr6o@ 34olhn t6hn GZ, o34utw@ 3h AB pr6o@ t6hn GD. s4ummetro@ d6e 3h AB t5hj GD m4hkei. s4ummetro@ 24ara ka6i 3h AE m6en t5hj GZ, 3h d6e BE t5hj DZ. ka6i a3i AE, EB 3rhta4i e2isi dun4amei m4onon s4ummetroi: ka6i a3i GZ, ZD 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. <2<2apotom6h 24ara 2est6in 3h GD. -L4egw d4h, 34oti ka6i t5hj t4acei 3h a2ut6h t5hj AB.>2> -2Epe6i o25un 2estin 3w@ 3h AE pr6o@ t6hn GZ, o34utw@ 3h BE pr6o@ t6hn DZ, 2enall6ac 24ara 2est6in 3w@ 3h AE pr6o@ t6hn EB, o34utw@ 3h GZ pr6o@ t6hn ZD. 24htoi d6h 3h AE t5h@ EB me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj 26h t5wj 2ap6o 2asumm4etrou. e2i m6en o25un 3h AE t5h@ EB me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h GZ t5h@ ZD me5izon dun4hsetai t5wj 2ap6o summ4etrou 3eaut5hj. ka6i e2i m6en s4ummetr4o@ 2estin 3h AE t5hj 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h GZ, e2i d6e 3h BE, ka6i 3h DZ, e2i d6e o2udet4era t5wn AE, EB, ka6i o2udet4era t5wn GZ, ZD. e2i d6e 3h AE <22> me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i 3h GZ t5h@ ZD me5izon dun4hsetai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka6i e2i m6en s4ummetr4o@ 2estin 3h AE t5hj ^+^ 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h GZ, e2i d6e 3h BE, ka6i 3h DZ, e2i d6e o2udet4era t5wn AE, EB, o2udet4era t5wn GZ, ZD. -2Apotom6h 24ara 2est6in 3h GD ka6i t5hj t4acei 3h a2ut6h t5hj AB: 34oper 24edei de5icai. ##104##-------rd41 -3H t5hj m4esh@ 2apotom5hj s4ummetro@ m4esh@ 2apotom4h 2esti ka6i t5hj t4acei 3h a2ut4h. -24Estw m4esh@ 2apotom6h 3h AB, ka6i t5hj AB m4hkei s4ummetro@ 24estw 3h GD: l4egw, 34oti ka6i 3h GD m4esh@ 2apotom4h 2esti ka6i t5hj t4acei 3h a2ut6h t5hj AB. -2Epe6i g6ar m4esh@ 2apotom4h 2estin 3h AB, 24estw a2ut5hj prosarm4ozousa 3h EB. a3i AE, EB 24ara m4esai e2is6i dun4amei m4onon s4ummetroi. ka6i gegon4etw 3w@ 3h AB pr6o@ t6hn GD, o34utw@ 3h BE pr6o@ t6hn DZ: s4ummetro@ 24ara <2<2est6i>2> ka6i 3h AE t5hj GZ, 3h d6e BE t5hj DZ. a3i d6e AE, EB m4esai e2is6i dun4amei m4onon s4ummetroi: ka6i a3i GZ, ZD 24ara m4esai e2is6i dun4amei m4onon s4ummetroi: m4esh@ 24ara 2apotom4h 2estin 3h GD. ^+^ -L4egw d4h, 34oti ka6i t5hj t4acei 2est6in 3h a2ut6h t5hj AB. -2Epe6i <22> 2estin 3w@ 3h AE pr6o@ t6hn EB, o34utw@ 3h GZ pr6o@ t6hn ZD <2<2all' 3w@ m6en 3h AE pr6o@ t6hn EB, o34utw@ t6o 2ap6o t5h@ AE pr6o@ t6o 3up6o t5wn AE, EB, 3w@ d6e 3h GZ pr6o@ t6hn ZD, o34utw@ t6o 2ap6o t5h@ GZ pr6o@ t6o 3up6o t5wn GZ, ZD>2>, 24estin 24ara ka6i 3w@ t6o 2ap6o t5h@ AE pr6o@ t6o 3up6o t5wn AE, EB, o34utw@ t6o 2ap6o t5h@ GZ pr6o@ t6o 3up6o t5wn GZ, ZD <22>. s4ummetron d6e t6o 2ap6o t5h@ AE t5wj 2ap6o t5h@ GZ: s4ummetron 24ara 2est6i ka6i t6o 3up6o t5wn AE, EB t5wj 3up6o t5wn GZ, ZD. e24ite o25un 3rht4on 2esti t6o 3up6o t5wn AE, EB, 3rht6on 24estai ka6i t6o 3up6o t5wn GZ, ZD, e24ite m4eson <2<2est6i>2> t6o 3up6o t5wn AE, EB, m4eson <2<2est6i>2> ka6i t6o 3up6o t5wn GZ, ZD. -M4esh@ 24ara 2apotom4h 2estin 3h GD ka6i t5hj t4acei 3h a2ut6h t5hj AB: 34oper 24edei de5icai. ##105##-------re41 -3H t5hj 2el4assoni s4ummetro@ 2el4asswn 2est4in. -24Estw g6ar 2el4asswn 3h AB ka6i t5hj AB s4ummetro@ 3h GD: l4egw, 34oti ka6i 3h GD 2el4asswn 2est4in. ^+^ -Gegon4etw g6ar t6a a2ut4a: ka6i 2epe6i a3i AE, EB dun4amei e2is6in 2as4ummetroi, ka6i a3i GZ, ZD 24ara dun4amei e2is6in 2as4ummetroi. 2epe6i o25un 2estin 3w@ 3h AE pr6o@ t6hn EB, o34utw@ 3h GZ pr6o@ t6hn ZD, 24estin 24ara ka6i 3w@ t6o 2ap6o t5h@ AE pr6o@ t6o 2ap6o t5h@ EB, o34utw@ t6o 2ap6o t5h@ GZ pr6o@ t6o 2ap6o t5h@ ZD. sunq4enti 24ara 2est6in 3w@ t6a 2ap6o t5wn AE, EB pr6o@ t6o 2ap6o t5h@ EB, o34utw@ t6a 2ap6o t5wn GZ, ZD pr6o@ t6o 2ap6o t5h@ ZD <22>: s4ummetron d4e 2esti t6o 2ap6o t5h@ BE t5wj 2ap6o t5h@ DZ: s4ummetron 24ara ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB tetrag4wnwn t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn GZ, ZD tetrag4wnwn. 3rht6on d4e 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB tetrag4wnwn: 3rht6on 24ara 2est6i ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn GZ, ZD tetrag4wnwn. p4alin, 2epe4i 2estin 3w@ t6o 2ap6o t5h@ AE pr6o@ t6o 3up6o t5wn AE, EB, o34utw@ t6o 2ap6o t5h@ GZ pr6o@ t6o 3up6o t5wn GZ, ZD, s4ummetron d6e t6o 2ap6o t5h@ AE tetr4agwnon t5wj 2ap6o t5h@ GZ tetrag4wnwj, s4ummetron 24ara 2est6i ka6i t6o 3up6o t5wn AE, EB t5wj 3up6o t5wn GZ, ZD. m4eson d6e t6o 3up6o t5wn AE, EB: m4eson 24ara ka6i t6o ^+^ 3up6o t5wn GZ, ZD: a3i GZ, ZD 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn 3rht4on, t6o d' 3up' a2ut5wn m4eson. -2El4asswn 24ara 2est6in 3h GD: 34oper 24edei de5icai. ##106##-------rst41 -3H t5hj met6a 3rhto5u m4eson t6o 34olon poio4ushj s4ummetro@ met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. -24Estw met6a 3rhto5u m4eson t6o 34olon poio5usa 3h AB ka6i t5hj AB s4ummetro@ 3h GD: l4egw, 34oti ka6i 3h GD met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. -24Estw g6ar t5hj AB prosarm4ozousa 3h BE: a3i AE, EB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on. ka6i t6a a2ut6a kateskeu4asqw. 3omo4iw@ d6h de4icomen to5i@ pr4oteron, 34oti a3i GZ, ZD 2en t5wj a2ut5wj l4ogwj e2is6i ta5i@ AE, EB, ka6i s4ummetr4on 2esti t6o sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB tetrag4wnwn t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn GZ, ZD tetrag4wnwn, t6o d6e 3up6o t5wn AE, EB t5wj 3up6o t5wn GZ, ZD: 34wste ka6i a3i GZ, ZD dun4amei e2is6in ^+^ 2as4ummetroi poio5usai t6o m6en sugke4imenon 2ek t5wn 2ap6o t5wn GZ, ZD tetrag4wnwn m4eson, t6o d' 3up' a2ut5wn 3rht4on. -3H GD 24ara met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin: 34oper 24edei de5icai. ##107##-------rz41 -3H t5hj met6a m4esou m4eson t6o 34olon poio4ushj s4ummetro@ ka6i a2ut6h met6a m4esou m4eson t6o 34olon poio5us4a 2estin. -24Estw met6a m4esou m4eson t6o 34olon poio5usa 3h AB, ka6i t5hj AB 24estw s4ummetro@ 3h GD: l4egw, 34oti ka6i 3h GD met6a m4esou m4eson t6o 34olon poio5us4a 2estin. -24Estw g6ar t5hj AB prosarm4ozousa 3h BE, ka6i t6a a2ut6a kateskeu4asqw: a3i AE, EB 24ara dun4amei e2is6in 2as4ummetroi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson ka6i t6o 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t6o sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn t5wj 3up' a2ut5wn. ka4i e2isin, 3w@ 2ede4ixqh, a3i AE, EB s4ummetroi ta5i@ GZ, ZD, ka6i t6o sugke4imenon 2ek t5wn 2ap6o t5wn AE, EB tetrag4wnwn t5wj sugkeim4enwj 2ek t5wn 2ap6o t5wn GZ, ZD, t6o d6e 3up6o t5wn AE, EB t5wj 3up6o t5wn GZ, ZD: ka6i a3i GZ, ZD 24ara dun4amei e2is6in 2as4ummetroi poio5usai t4o te sugke4imenon 2ek t5wn 2ap' a2ut5wn tetrag4wnwn m4eson ka6i t6o 3up' a2ut5wn m4eson ka6i 24eti 2as4ummetron t6o sugke4imenon ^+^ 2ek t5wn 2ap' a2ut5wn <22> t5wj 3up' a2ut5wn. -3H GD 24ara met6a m4esou m4eson t6o 34olon poio5us4a 2estin: 34oper 24edei de5icai. ##108##-------rh41 -2Ap6o 3rhto5u m4esou 2afairoum4enou 3h t6o loip6on xwr4ion dunam4enh m4ia d4uo 2al4ogwn g4inetai 24htoi 2apotom6h 26h 2el4asswn. -2Ap6o g6ar 3rhto5u to5u BG m4eson 2afhjr4hsqw t6o BD: l4egw, 34oti 3h t6o loip6on dunam4enh t6o EG m4ia d4uo 2al4ogwn g4inetai 24htoi 2apotom6h 26h 2el4asswn. -2Ekke4isqw g6ar 3rht6h 3h ZH, ka6i t5wj m6en BG 24ison par6a t6hn ZH parabebl4hsqw 2orqog4wnion parallhl4ogrammon t6o HQ, t5wj d6e DB 24ison 2afhjr4hsqw t6o HK: loip6on 24ara t6o EG 24ison 2est6i t5wj LQ. 2epe6i o25un 3rht6on m4en 2esti t6o BG, m4eson d6e t6o BD, 24ison d6e t6o m6en BG t5wj HQ, t6o d6e BD ^+^ t5wj HK, 3rht6on m6en 24ara 2est6i t6o HQ, m4eson d6e t6o HK. ka6i par6a 3rht6hn t6hn ZH par4akeitai: 3rht6h m6en 24ara 3h ZQ ka6i s4ummetro@ t5hj ZH m4hkei, 3rht6h d6e 3h ZK ka6i 2as4ummetro@ t5hj ZH m4hkei: 2as4ummetro@ 24ara 2est6in 3h ZQ t5hj ZK m4hkei. a3i ZQ, ZK 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h KQ, prosarm4ozousa d6e a2ut5hj 3h KZ. 24htoi d6h 3h QZ t5h@ ZK me5izon d4unatai t5wj 2ap6o summ4etrou 26h o24u. -Dun4asqw pr4oteron t5wj 2ap6o summ4etrou. ka4i 2estin 34olh 3h QZ s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj ZH: 2apotom6h 24ara pr4wth 2est6in 3h KQ. t6o d' 3up6o 3rht5h@ ka6i 2apotom5h@ pr4wth@ periex4omenon 3h dunam4enh 2apotom4h 2estin. 3h 24ara t6o LQ, tout4esti t6o EG, dunam4enh 2apotom4h 2estin. -E2i d6e 3h QZ t5h@ ZK me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka4i 2estin 34olh 3h ZQ s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj ZH, 2apotom6h tet4arth 2est6in 3h KQ. t6o d' 3up6o 3rht5h@ ka6i 2apotom5h@ tet4arth@ periex4omenon 3h dunam4enh 2el4asswn 2est4in: 34oper 24edei de5icai. ^+^ ##109##-------rq41 -2Ap6o m4esou 3rhto5u 2afairoum4enou 24allai d4uo 24alogoi g4inontai 24htoi m4esh@ 2apotom6h pr4wth 26h met6a 3rhto5u m4eson t6o 34olon poio5usa. -2Ap6o g6ar m4esou to5u BG 3rht6on 2afhjr4hsqw t6o BD. l4egw, 34oti 3h t6o loip6on t6o EG dunam4enh m4ia d4uo 2al4ogwn g4inetai 24htoi m4esh@ 2apotom6h pr4wth 26h met6a 3rhto5u m4eson t6o 34olon poio5usa. -2Ekke4isqw g6ar 3rht6h 3h ZH, ka6i parabebl4hsqw 3omo4iw@ t6a xwr4ia. 24esti d6h 2akolo4uqw@ 3rht6h m6en 3h ZQ ka6i 2as4ummetro@ t5hj ZH m4hkei, 3rht6h d6e 3h KZ ka6i s4ummetro@ t5hj ZH m4hkei: a3i ZQ, ZK 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h KQ, prosarm4ozousa d6e ta4uthj 3h ZK. 24htoi d6h 3h QZ t5h@ ZK me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj 26h t5wj 2ap6o 2asumm4etrou. -E2i m6en o25un 3h QZ t5h@ ZK me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka4i 2estin 3h prosarm4ozousa 3h ZK s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj ZH, 2apotom6h deut4era 2est6in 3h KQ. 3rht6h d6e 3h ZH: 34wste 3h ^+^ t6o LQ, tout4esti t6o EG, dunam4enh m4esh@ 2apotom6h pr4wth 2est4in. -E2i d6e 3h QZ t5h@ ZK me5izon d4unatai t5wj 2ap6o 2asumm4etrou, ka4i 2estin 3h prosarm4ozousa 3h ZK s4ummetro@ t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj ZH, 2apotom6h p4empth 2est6in 3h KQ: 34wste 3h t6o EG dunam4enh met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin: 34oper 24edei de5icai. ##110##-------ri41 -2Ap6o m4esou m4esou 2afairoum4enou 2asumm4etrou t5wj 34olwj a3i loipa6i d4uo 24alogoi g4inontai 24htoi m4esh@ 2apotom6h deut4era 26h met6a m4esou m4eson t6o 34olon poio5usa. -2Afhjr4hsqw g6ar 3w@ 2ep6i t5wn prokeim4enwn katagraf5wn 2ap6o m4esou to5u BG m4eson t6o BD 2as4ummetron t5wj 34olwj: l4egw, 34oti 3h t6o EG dunam4enh m4ia 2est6i d4uo 2al4ogwn 24htoi m4esh@ 2apotom6h deut4era 26h met6a m4esou m4eson t6o 34olon poio5usa. -2Epe6i g6ar m4eson 2est6in 3ek4ateron t5wn BG, BD, ka6i 2as4ummetron t6o GB t5wj BD, 24estai 2akolo4uqw@ 3rht6h 3ekat4era t5wn ZQ, ZK ka6i 2as4ummetro@ t5hj ZH m4hkei. ka6i 2epe6i 2as4ummetr4on 2esti t6o BG t5wj BD, tout4esti t6o HQ t5wj HK, 2as4ummetro@ ka6i 3h QZ t5hj ZK: a3i ZQ, ZK ^+^ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h KQ <22>. -E2i m6en d6h 3h ZQ t5h@ ZK me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i o2uqet4era t5wn ZQ, ZK s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj ZH, 2apotom6h tr4ith 2est6in 3h KQ. 3rht6h d6e 3h KL, t6o d' 3up6o 3rht5h@ ka6i 2apotom5h@ tr4ith@ periex4omenon 2orqog4wnion 24alog4on 2estin, ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin, kale5itai d6e m4esh@ 2apotom6h deut4era: 34wste 3h t6o LQ, tout4esti t6o EG, dunam4enh m4esh@ 2apotom4h 2esti deut4era. -E2i d6e 3h ZQ t5h@ ZK me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj <22>, ka6i o2uqet4era t5wn QZ, ZK s4ummetr4o@ 2esti t5hj ZH m4hkei, 2apotom6h 34ekth 2est6in 3h KQ. t6o d' 3up6o 3rht5h@ ka6i 2apotom5h@ 34ekth@ 3h dunam4enh 2est6i met6a m4esou m4eson t6o 34olon poio5usa. 3h t6o LQ 24ara, tout4esti t6o EG, dunam4enh met6a m4esou m4eson t6o 34olon poio5us4a 2estin: 34oper 24edei de5icai. ^+^ ##111##-------ria41 -3H 2apotom6h o2uk 24estin 3h a2ut6h t5hj 2ek d4uo 2onom4atwn. -24Estw 2apotom6h 3h AB: l4egw, 34oti 3h AB o2uk 24estin 3h a2ut6h t5hj 2ek d4uo 2onom4atwn. -E2i g6ar dunat4on, 24estw: ka6i 2ekke4isqw 3rht6h 3h DG, ka6i t5wj 2ap6o t5h@ AB 24ison par6a t6hn GD parabebl4hsqw 2orqog4wnion t6o GE pl4ato@ poio5un t6hn DE. 2epe6i o25un 2apotom4h 2estin 3h AB, 2apotom6h pr4wth 2est6in 3h DE. 24estw a2ut5hj prosarm4ozousa 3h EZ: a3i DZ, ZE 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h DZ t5h@ ZE me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h DZ s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj DG. p4alin, 2epe6i 2ek d4uo 2onom4atwn 2est6in 3h AB, 2ek d4uo 24ara 2onom4atwn pr4wth 2est6in 3h DE. dihjr4hsqw e2i@ t6a 2on4omata kat6a t6o H, ka6i 24estw me5izon 24onoma t6o DH: a3i DH, HE 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi, ka6i 3h DH t5h@ HE me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i t6o me5izon 3h DH s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj m4hkei t5hj DG. ka6i 3h DZ 24ara t5hj ^+^ DH s4ummetr4o@ 2esti m4hkei: ka6i loip6h 24ara 3h HZ s4ummetr4o@ 2esti t5hj DZ m4hkei. <2<2epe6i o25un s4ummetr4o@ 2estin 3h DZ t5hj HZ, 3rht6h d4e 2estin 3h DZ, 3rht6h 24ara 2est6i ka6i 3h HZ. 2epe6i o25un s4ummetr4o@ 2estin 3h DZ t5hj HZ m4hkei>2> 2as4ummetro@ d6e 3h DZ t5hj EZ m4hkei: 2as4ummetro@ 24ara 2est6i ka6i 3h ZH t5hj EZ m4hkei. a3i HZ, ZE 24ara 3rhta4i <22> dun4amei m4onon s4ummetroi: 2apotom6h 24ara 2est6in 3h EH. 2all6a ka6i 3rht4h: 34oper 2est6in 2ad4unaton. -3H 24ara 2apotom6h o2uk 24estin 3h a2ut6h t5hj 2ek d4uo 2onom4atwn: 34oper 24edei de5icai. ##111^1^Por^2##-----<22> -3H 2apotom6h ka6i a3i met' a2ut6hn 24alogoi o24ute t5hj m4eshj o24ute 2all4hlai@ e2is6in a3i a2uta4i. -T6o m6en g6ar 2ap6o m4esh@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 3rht6hn ka6i 2as4ummetron t5hj, par' 36hn par4akeitai, m4hkei, t6o d6e 2ap6o 2apotom5h@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn pr4wthn, t6o d6e 2ap6o m4esh@ 2apotom5h@ pr4wth@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn deut4eran, t6o d6e 2ap6o m4esh@ 2apotom5h@ deut4era@ par6a 3rht6hn paraball4omenon pl4ato@ ^+^ poie5i 2apotom6hn tr4ithn, t6o d6e 2ap6o 2el4assono@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn tet4arthn, t6o d6e 2ap6o t5h@ met6a 3rhto5u m4eson t6o 34olon poio4ush@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn p4empthn, t6o d6e 2ap6o t5h@ met6a m4esou m4eson t6o 34olon poio4ush@ par6a 3rht6hn paraball4omenon pl4ato@ poie5i 2apotom6hn 34ekthn. 2epe6i o25un t6a e2irhm4ena pl4ath diaf4erei to5u te pr4wtou ka6i 2all4hlwn, to5u m6en pr4wtou, 34oti 3rht4h 2estin, 2all4hlwn d4e, 2epe6i t5hj t4acei o2uk e2is6in a3i a2uta4i, d5hlon, 3w@ ka6i a2uta6i a3i 24alogoi diaf4erousin 2all4hlwn. ka6i 2epe6i d4edeiktai 3h 2apotom6h o2uk o25usa 3h a2ut6h t5hj 2ek d4uo 2onom4atwn, poio5usi d6e pl4ath par6a 3rht6hn paraball4omenai a3i met6a t6hn 2apotom6hn 2apotom6a@ 2akolo4uqw@ 3ek4asth t5hj t4acei t5hj kaq' a3ut4hn, a3i d6e met6a t6hn 2ek d4uo 2onom4atwn t6a@ 2ek d4uo 2onom4atwn ka6i a2uta6i t5hj t4acei 2akolo4uqw@, 34eterai 24ara e2is6in a3i met6a t6hn 2apotom6hn ka6i 34eterai a3i met6a t6hn 2ek d4uo 2onom4atwn, 3w@ e25inai t5hj t4acei p4asa@ 2al4ogou@ ig41, -M4eshn, -2Ek d4uo 2onom4atwn, -2Ek d4uo m4eswn pr4wthn, -2Ek d4uo m4eswn deut4eran, -Me4izona, -3Rht6on ka6i m4eson dunam4enhn, -D4uo m4esa dunam4enhn, -2Apotom4hn, -M4esh@ 2apotom6hn pr4wthn, ^+^ -M4esh@ 2apotom6hn deut4eran, -2El4assona, -Met6a 3rhto5u m4eson t6o 34olon poio5usan, -Met6a m4esou m4eson t6o 34olon poio5usan. ##112##-------rib41 -T6o 2ap6o 3rht5h@ par6a t6hn 2ek d4uo 2onom4atwn paraball4omenon pl4ato@ poie5i 2apotom4hn, 35h@ t6a 2on4omata s4ummetr4a 2esti to5i@ t5h@ 2ek d4uo 2onom4atwn 2on4omasi ka6i 24eti 2en t5wj a2ut5wj l4ogwj, ka6i 24eti 3h ginom4enh 2apotom6h t6hn a2ut6hn 34ecei t4acin t5hj 2ek d4uo 2onom4atwn. -24Estw 3rht6h m6en 3h A, 2ek d4uo 2onom4atwn d6e 3h BG, 35h@ me5izon 24onoma 24estw 3h DG, ka6i t5wj 2ap6o t5h@ A 24ison 24estw t6o 3up6o t5wn BG, EZ: l4egw, 34oti 3h EZ 2apotom4h 2estin, 35h@ t6a 2on4omata s4ummetr4a 2esti to5i@ GD, DB, ka6i 2en t5wj a2ut5wj l4ogwj, ka6i 24eti 3h EZ t6hn a2ut6hn 34ecei t4acin t5hj BG. -24Estw g6ar p4alin t5wj 2ap6o t5h@ A 24ison t6o 3up6o t5wn BD, H. 2epe6i o25un t6o 3up6o t5wn BG, EZ 24ison 2est6i t5wj 3up6o t5wn BD, H, 24estin 24ara 3w@ 3h GB pr6o@ t6hn BD, o34utw@ 3h H ^+^ pr6o@ t6hn EZ. me4izwn d6e 3h BG t5h@ BD: me4izwn 24ara 2est6i ka6i 3h H t5h@ EZ. 24estw t5hj H 24ish 3h EQ: 24estin 24ara 3w@ 3h GB pr6o@ t6hn BD, o34utw@ 3h QE pr6o@ t6hn EZ: diel4onti 24ara 2est6in 3w@ 3h GD pr6o@ t6hn BD, o34utw@ 3h QZ pr6o@ t6hn ZE. gegon4etw 3w@ 3h QZ pr6o@ t6hn ZE, o34utw@ 3h ZK pr6o@ t6hn KE: ka6i 34olh 24ara 3h QK pr6o@ 34olhn t6hn KZ 2estin, 3w@ 3h ZK pr6o@ KE: 3w@ g6ar 36en t5wn 3hgoum4enwn pr6o@ 36en t5wn 3epom4enwn, o34utw@ 34apanta t6a 3hgo4umena pr6o@ 34apanta t6a 3ep4omena. 3w@ d6e 3h ZK pr6o@ KE, o34utw@ 2est6in 3h GD pr6o@ t6hn DB: ka6i 3w@ 24ara 3h QK pr6o@ KZ, o34utw@ 3h GD pr6o@ t6hn DB. s4ummetron d6e t6o 2ap6o t5h@ GD t5wj 2ap6o t5h@ DB: s4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ QK t5wj 2ap6o t5h@ KZ. ka4i 2estin 3w@ t6o 2ap6o t5h@ QK pr6o@ t6o 2ap6o t5h@ KZ, o34utw@ 3h QK pr6o@ t6hn KE, 2epe6i a3i tre5i@ a3i QK, KZ, KE 2an4alog4on e2isin. s4ummetro@ 24ara 3h QK t5hj KE m4hkei: 34wste ka6i 3h QE t5hj EK s4ummetr4o@ 2esti m4hkei. ka6i 2epe6i t6o 2ap6o t5h@ A 24ison 2est6i t5wj 3up6o t5wn EQ, BD, ^+^ 3rht6on d6e 2esti t6o 2ap6o t5h@ A, 3rht6on 24ara 2est6i t6o 3up6o t5wn EQ, BD. ka6i par6a 3rht6hn t6hn BD par4akeitai: 3rht6h 24ara 2est6in 3h EQ ka6i s4ummetro@ t5hj BD m4hkei: 34wste ka6i 3h s4ummetro@ a2ut5hj 3h EK 3rht4h 2esti ka6i s4ummetro@ t5hj BD m4hkei. 2epe6i o25un 2estin 3w@ 3h GD pr6o@ DB, o34utw@ 3h ZK pr6o@ KE, a3i d6e GD, DB dun4amei m4onon e2is6i s4ummetroi, ka6i a3i ZK, KE dun4amei m4onon e2is6i s4ummetroi. 3rht6h d4e 2estin 3h KE: 3rht6h 24ara 2est6i ka6i 3h ZK. a3i ZK, KE 24ara 3rhta6i dun4amei m4onon e2is6i s4ummetroi: 2apotom6h 24ara 2est6in 3h EZ. -24Htoi d6e 3h GD t5h@ DB me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj 26h t5wj 2ap6o 2asumm4etrou. -E2i m6en o25un 3h GD t5h@ DB me5izon d4unatai t5wj 2ap6o summ4etrou <2<3eaut5hj>2>, ka6i 3h ZK t5h@ KE me5izon dun4hsetai t5wj 2ap6o summ4etrou 3eaut5hj. ka6i e2i m6en s4ummetr4o@ 2estin 3h GD t5hj 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h ZK: e2i d6e 3h BD, ka6i 3h KE: e2i d6e o2udet4era t5wn GD, DB, ka6i o2udet4era t5wn ZK, KE. -E2i d6e 3h GD t5h@ DB me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i 3h ZK t5h@ KE me5izon dun4hsetai t5wj ^+^ 2ap6o 2asumm4etrou 3eaut5hj. ka6i e2i m6en 3h GD s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h ZK: e2i d6e 3h BD, ka6i 3h KE: e2i d6e o2udet4era t5wn GD, DB, ka6i o2udet4era t5wn ZK, KE: 34wste 2apotom4h 2estin 3h ZE, 35h@ t6a 2on4omata t6a ZK, KE s4ummetr4a 2esti to5i@ t5h@ 2ek d4uo 2onom4atwn 2on4omasi to5i@ GD, DB ka6i 2en t5wj a2ut5wj l4ogwj, ka6i t6hn a2ut6hn t4acin 24exei t5hj BG: 34oper 24edei de5icai. ##113##-------rig41 -T6o 2ap6o 3rht5h@ par6a 2apotom6hn paraball4omenon pl4ato@ poie5i t6hn 2ek d4uo 2onom4atwn, 35h@ t6a 2on4omata s4ummetr4a 2esti to5i@ t5h@ 2apotom5h@ 2on4omasi ka6i 2en t5wj a2ut5wj l4ogwj, 24eti d6e 3h ginom4enh 2ek d4uo 2onom4atwn t6hn a2ut6hn t4acin 24exei t5hj 2apotom5hj. -24Estw 3rht6h m6en 3h A, 2apotom6h d6e 3h BD, ka6i t5wj 2ap6o t5h@ A 24ison 24estw t6o 3up6o t5wn BD, KQ, 34wste t6o 2ap6o t5h@ A 3rht5h@ par6a t6hn BD 2apotom6hn paraball4omenon pl4ato@ poie5i t6hn KQ: l4egw, 34oti 2ek d4uo 2onom4atwn 2est6in 3h KQ, 35h@ t6a 2on4omata s4ummetr4a 2esti to5i@ t5h@ BD 2on4omasi ka6i 2en t5wj a2ut5wj l4ogwj, ka6i 24eti 3h KQ t6hn a2ut6hn 24exei t4acin t5hj BD. -24Estw g6ar t5hj BD prosarm4ozousa 3h DG: a3i BG, GD 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi. ka6i t5wj 2ap6o ^+^ t5h@ A 24ison 24estw ka6i t6o 3up6o t5wn BG, H. 3rht6on d6e t6o 2ap6o t5h@ A: 3rht6on 24ara ka6i t6o 3up6o t5wn BG, H. ka6i par6a 3rht6hn t6hn BG parab4eblhtai: 3rht6h 24ara 2est6in 3h H ka6i s4ummetro@ t5hj BG m4hkei. 2epe6i o25un t6o 3up6o t5wn BG, H 24ison 2est6i t5wj 3up6o t5wn BD, KQ, 2an4alogon 24ara 2est6in 3w@ 3h GB pr6o@ BD, o34utw@ 3h KQ pr6o@ H. me4izwn d6e 3h BG t5h@ BD: me4izwn 24ara ka6i 3h KQ t5h@ H. ke4isqw t5hj H 24ish 3h KE: s4ummetro@ 24ara 2est6in 3h KE t5hj BG m4hkei. ka6i 2epe4i 2estin 3w@ 3h GB pr6o@ BD, o34utw@ 3h QK pr6o@ KE, 2anastr4eyanti 24ara 2est6in 3w@ 3h BG pr6o@ t6hn GD, o34utw@ 3h KQ pr6o@ QE. gegon4etw 3w@ 3h KQ pr6o@ QE, o34utw@ 3h QZ pr6o@ ZE: ka6i loip6h 24ara 3h KZ pr6o@ ZQ 2estin, 3w@ 3h KQ pr6o@ QE, tout4estin <2<3w@>2> 3h BG pr6o@ GD. a3i d6e BG, GD dun4amei m4onon <22> s4ummetroi: ka6i a3i KZ, ZQ 24ara dun4amei m4onon e2is6i s4ummetroi. ka6i 2epe4i 2estin 3w@ 3h KQ pr6o@ QE, 3h KZ pr6o@ ZQ, 2all' 3w@ 3h KQ pr6o@ QE, 3h QZ pr6o@ ZE, ka6i 3w@ 24ara 3h KZ pr6o@ ZQ, 3h QZ pr6o@ ZE: 34wste ka6i 3w@ 3h pr4wth pr6o@ t6hn tr4ithn, t6o 2ap6o t5h@ pr4wth@ pr6o@ t6o 2ap6o t5h@ deut4era@: ka6i 3w@ 24ara 3h KZ pr6o@ ZE, o34utw@ t6o 2ap6o t5h@ KZ pr6o@ t6o 2ap6o t5h@ ZQ. s4ummetron d4e 2esti t6o 2ap6o t5h@ KZ t5wj 2ap6o t5h@ ZQ: a3i ^+^ g6ar KZ, ZQ dun4amei e2is6i s4ummetroi: s4ummetro@ 24ara 2est6i ka6i 3h KZ t5hj ZE m4hkei: 34wste 3h KZ ka6i t5hj KE s4ummetr4o@ <2<2esti>2> m4hkei. 3rht6h d4e 2estin 3h KE ka6i s4ummetro@ t5hj BG m4hkei: 3rht6h 24ara ka6i 3h KZ ka6i s4ummetro@ t5hj BG m4hkei. ka6i 2epe4i 2estin 3w@ 3h BG pr6o@ GD, o34utw@ 3h KZ pr6o@ ZQ, 2enall6ac 3w@ 3h BG pr6o@ KZ, o34utw@ 3h DG pr6o@ ZQ. s4ummetro@ d6e 3h BG t5hj KZ: s4ummetro@ 24ara ka6i 3h ZQ t5hj GD m4hkei. a3i BG, GD d6e 3rhta4i e2isi dun4amei m4onon s4ummetroi: ka6i a3i KZ, ZQ 24ara 3rhta4i e2isi dun4amei m4onon s4ummetroi: 2ek d4uo 2onom4atwn 2est6in 24ara 3h KQ. -E2i m6en o25un 3h BG t5h@ GD me5izon d4unatai t5wj 2ap6o summ4etrou 3eaut5hj, ka6i 3h KZ t5h@ ZQ me5izon dun4hsetai t5wj 2ap6o summ4etrou 3eaut5hj. ka6i e2i m6en s4ummetr4o@ 2estin 3h BG t5hj 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h KZ, e2i d6e 3h GD s4ummetr4o@ 2esti t5hj 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h ZQ, e2i d6e o2udet4era t5wn BG, GD, o2udet4era t5wn KZ, ZQ. -E2i d6e 3h BG t5h@ GD me5izon d4unatai t5wj 2ap6o 2asumm4etrou 3eaut5hj, ka6i 3h KZ t5h@ ZQ me5izon dun4hsetai t5wj 2ap6o 2asumm4etrou 3eaut5hj. ka6i e2i m6en s4ummetr4o@ 2estin 3h BG ^+^ t5hj 2ekkeim4enhj 3rht5hj m4hkei, ka6i 3h KZ, e2i d6e 3h GD, ka6i 3h ZQ, e2i d6e o2udet4era t5wn BG, GD, o2udet4era t5wn KZ, ZQ. -2Ek d4uo 24ara 2onom4atwn 2est6in 3h KQ, 35h@ t6a 2on4omata t6a KZ, ZQ s4ummetr4a <2<2esti>2> to5i@ t5h@ 2apotom5h@ 2on4omasi to5i@ BG, GD ka6i 2en t5wj a2ut5wj l4ogwj, ka6i 24eti 3h KQ t5hj BG t6hn a2ut6hn 34ecei t4acin: 34oper 24edei de5icai. ##114##-------rid41 -2E6an xwr4ion peri4exhtai 3up6o 2apotom5h@ ka6i t5h@ 2ek d4uo 2onom4atwn, 35h@ t6a 2on4omata s4ummetr4a t4e 2esti to5i@ t5h@ 2apotom5h@ 2on4omasi ka6i 2en t5wj a2ut5wj l4ogwj, 3h t6o xwr4ion dunam4enh 3rht4h 2estin. -Periex4esqw g6ar xwr4ion t6o 3up6o t5wn AB, GD 3up6o 2apotom5h@ t5h@ AB ka6i t5h@ 2ek d4uo 2onom4atwn t5h@ GD, 35h@ me5izon 24onoma 24estw t6o GE, ka6i 24estw t6a 2on4omata t5h@ 2ek d4uo 2onom4atwn t6a GE, ED s4ummetr4a te to5i@ t5h@ 2apotom5h@ 2on4omasi to5i@ AZ, ZB ka6i 2en t5wj a2ut5wj l4ogwj, ka6i 24estw 3h t6o 3up6o t5wn AB, GD dunam4enh 3h H: l4egw, 34oti 3rht4h 2estin 3h H. -2Ekke4isqw g6ar 3rht6h 3h Q, ka6i t5wj 2ap6o t5h@ Q 24ison par6a t6hn GD parabebl4hsqw pl4ato@ poio5un t6hn KL: 2apotom6h 24ara 2est6in 3h KL, 35h@ t6a 2on4omata 24estw t6a KM, ML s4ummetra to5i@ t5h@ 2ek d4uo 2onom4atwn 2on4omasi ^+^ to5i@ GE, ED ka6i 2en t5wj a2ut5wj l4ogwj. 2all6a ka6i a3i GE, ED s4ummetro4i t4e e2isi ta5i@ AZ, ZB ka6i 2en t5wj a2ut5wj l4ogwj: 24estin 24ara 3w@ 3h AZ pr6o@ t6hn ZB, o34utw@ 3h KM pr6o@ ML. 2enall6ac 24ara 2est6in 3w@ 3h AZ pr6o@ t6hn KM, o34utw@ 3h BZ pr6o@ t6hn LM: ka6i loip6h 24ara 3h AB pr6o@ loip6hn t6hn KL 2estin 3w@ 3h AZ pr6o@ KM. s4ummetro@ d6e 3h AZ t5hj KM: s4ummetro@ 24ara 2est6i ka6i 3h AB t5hj KL. ka4i 2estin 3w@ 3h AB pr6o@ KL, o34utw@ t6o 3up6o t5wn GD, AB pr6o@ t6o 3up6o t5wn GD, KL: s4ummetron 24ara 2est6i ka6i t6o 3up6o t5wn GD, AB t5wj 3up6o t5wn GD, KL. 24ison d6e t6o 3up6o t5wn GD, KL t5wj 2ap6o t5h@ Q: s4ummetron 24ara 2est6i t6o 3up6o t5wn GD, AB t5wj 2ap6o t5h@ Q. t5wj d6e 3up6o t5wn GD, AB 24ison 2est6i t6o 2ap6o t5h@ H: s4ummetron 24ara 2est6i t6o 2ap6o t5h@ H t5wj 2ap6o t5h@ Q. 3rht6on d6e t6o 2ap6o t5h@ Q: 3rht6on 24ara 2est6i ka6i t6o 2ap6o t5h@ H: 3rht6h 24ara 2est6in 3h H. ka6i d4unatai t6o 3up6o t5wn GD, AB. -2E6an 24ara xwr4ion peri4exhtai 3up6o 2apotom5h@ ka6i t5h@ 2ek d4uo 2onom4atwn, 35h@ t6a 2on4omata s4ummetr4a 2esti to5i@ t5h@ 2apotom5h@ 2on4omasi ka6i 2en t5wj a2ut5wj l4ogwj, 3h t6o xwr4ion dunam4enh 3rht4h 2estin. ##114^1^Por^2##-----P4orisma -Ka6i g4egonen 3hm5in ka6i di6a to4utou faner4on, 34oti dunat4on 2esti 3rht6on xwr4ion 3up6o 2al4ogwn e2uqei5wn peri4exesqai. 34oper 24edei de5icai. ^+^ ##115##-------rie41 -2Ap6o m4esh@ 24apeiroi 24alogoi g4inontai, ka6i o2udem4ia o2udemi5aj t5wn pr4oteron 3h a2ut4h. -24Estw m4esh 3h A: L4egw, 34oti 2ap6o t5h@ A 24apeiroi 24alogoi g4inontai, ka6i o2udem4ia o2udemi5aj t5wn pr4oteron 3h a2ut4h. -2Ekke4isqw 3rht6h 3h B, ka6i t5wj 3up6o t5wn B, A 24ison 24estw t6o 2ap6o t5h@ G: 24alogo@ 24ara 2est6in 3h G: t6o g6ar 3up6o 2al4ogou ka6i 3rht5h@ 24alog4on 2estin. ka6i o2udemi5aj t5wn pr4oteron 3h a2ut4h: t6o g6ar 2ap' o2udemi5a@ t5wn pr4oteron par6a 3rht6hn paraball4omenon pl4ato@ poie5i m4eshn. p4alin d6h t5wj 3up6o t5wn B, G 24ison 24estw t6o 2ap6o t5h@ D: 24alogon 24ara 2est6i t6o 2ap6o t5h@ D. 24alogo@ 24ara 2est6in 3h D: ka6i o2udemi5aj t5wn pr4oteron 3h a2ut4h: t6o g6ar 2ap' o2udemi5a@ t5wn pr4oteron par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn G. 3omo4iw@ d6h t5h@ toia4uth@ t4acew@ 2ep' 24apeiron probaino4ush@ faner4on, 34oti 2ap6o t5h@ m4esh@ 24apeiroi 24alogoi g4inontai, ka6i o2udem4ia o2udemi5aj t5wn pr4oteron 3h a2ut4h: <2<34oper 24edei ^-^ de5icai>2>. $-^P228^-^L1^ <3<####PBF&####-----<00> ###10AP###--<00> ##115a##-----24Allw@ -24Estw m4esh 3h AG: l4egw, 34oti 2ap6o t5h@ AG ^-^ 24apeiroi 24alogoi g4ignontai, ka6i o2udem4ia o2udemi5aj t5wn pr4oteron 3h a2ut4h. -24Hxqw t5hj AG pr6o@ 2orq6a@ 3h AB, ka6i 24estw 3rht6h 3h AB, ka6i sumpeplhr4wsqw t6o BG: 24alogon 24ara 2est6i t6o BG, ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin. dun4asqw a2ut6o 3h GD: 24alogo@ 24ara 2est6in 3h GD. ka6i o2udemi5aj t5wn pr4oteron 3h a2ut4h: t6o g6ar 2ap' o2udemi5a@ t5wn pr4oteron par6a 3rht6hn paraball4omenon pl4ato@ poie5i m4eshn. p4alin sumpeplhr4wsqw t6o ED: 24alogon 24ara 2est6i t6o ED, ka6i 3h dunam4enh a2ut6o 24alog4o@ 2estin. dun4asqw a2ut6o 3h DZ: 24alogo@ 24ara 2est6in 3h DZ. ka6i o2udemi5aj t5wn pr4oteron 3h a2ut4h: t6o g6ar 2ap' o2udemi5a@ t5wn pr4oteron par6a 3rht6hn paraball4omenon pl4ato@ poie5i t6hn GD. -2Ap6o m4esh@ 24ara 24apeiroi 24alogoi g4inontai, ka6i o2udem4ia o2udemi5aj t5wn pr4oteron 3h a2ut4h 2estin: 34oper 24edei de5icai. ^+^ ####*PFV#### ###10AP### ##105a## -3H t5hj 2el4assoni s4ummetro@ 2el4asswn 2est4in. -24Estw 2el4asswn 3h A, ka6i t5hj A s4ummetro@ <2<24estw>2> 3h B: l4egw, 34oti 3h B 2el4asswn 2est4in. -Ke4isqw 3rht6h 3h GD ka6i t5wj 2ap6o t5h@ A 24ison par6a t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: 2apotom6h 24ara 2est6i tet4arth 3h GZ. t5wj d6e 2ap6o t5h@ B 24ison par6a t6hn ZE parabebl4hsqw t6o ZH pl4ato@ poio5un t6hn ZQ. 2epe6i o25un s4ummetr4o@ 2estin 3h A t5hj B, s4ummetron 24ara 2est6i ka6i t6o 2ap6o t5h@ A t5wj 2ap6o t5h@ B. 2all6a t5wj m6en 2ap6o t5h@ A 24ison 2est6i t6o GE, t5wj d6e 2ap6o t5h@ B 24ison 2est6i t6o ZH: s4ummetron 24ara 2est6i t6o GE t5wj ZH. 3w@ d6e t6o GE pr6o@ t6o ZH, o34utw@ 2est6in 3h GZ pr6o@ t6hn ZQ: s4ummetro@ 24ara 2est6in 3h GZ t5hj ZQ m4hkei. 2apotom6h d4e 2esti tet4arth 3h GZ: 2apotom6h 24ara 2est6i ka6i 3h ZQ tet4arth: t6o HZ 24ara peri4exetai 3up6o 3rht5h@ t5h@ ZE ka6i 2apotom5h@ tet4arth@ t5h@ ^+^ ZQ. 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ tet4arth@, 3h t6o xwr4ion dunam4enh 2el4asswn 2est4in. d4unatai d6e t6o ZH 3h B: 2el4asswn 24ara 2est6in 3h B. 34o 24edei de5icai. ##106a## -3H t5hj met6a 3rhto5u m4eson t6o 34olon poio4ushj s4ummetro@ met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. -24Estw met6a 3rhto5u m4eson t6o 34olon poio5usa 3h A, s4ummetro@ d6e a2ut5hj 3h B: l4egw, 34oti 3h B met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. -2Ekke4isqw 3rht6h 3h GD, ka6i t5wj m6en 2ap6o t5h@ A 24ison par6a t6hn GD parabebl4hsqw t6o GE pl4ato@ poio5un t6hn GZ: 2apotom6h 24ara 2est6i p4empth 3h GZ. t5wj d6e 2ap6o t5h@ B 24ison par6a t6hn ZE parabebl4hsqw t6o ZH pl4ato@ poio5un t6hn ZQ. 2epe6i o25un s4ummetr4o@ 2estin 3h A t5hj B, s4ummetr4on 2esti ka6i t6o 2ap6o t5h@ A t5wj ^+^ 2ap6o t5h@ B. 2all6a t5wj m6en 2ap6o t5h@ A 24ison t6o GE, t5wj d6e 2ap6o t5h@ B 24ison t6o ZH: s4ummetron 24ara 2est6i t6o GE t5wj ZH: s4ummetro@ 24ara ka6i 3h GZ t5hj ZQ m4hkei. 2apotom6h d6e p4empth 3h GZ: 2apotom6h 24ara 2est6i p4empth ka6i 3h ZQ. 3rht6h d6e 3h ZE: 2e6an d6e xwr4ion peri4exhtai 3up6o 3rht5h@ ka6i 2apotom5h@ p4empth@, 3h t6o xwr4ion dunam4enh met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin. d4unatai d6e t6o ZH 3h B: 3h B 24ara 3h met6a 3rhto5u m4eson t6o 34olon poio5us4a 2estin: 34oper 24edei de5icai. ##115b## -Proke4isqw 3hm5in de5icai, 34oti 2ep6i t5wn tetrag4wnwn sxhm4atwn 2as4ummetr4o@ 2estin 3h di4ametro@ t5hj pleur5aj m4hkei. -24Estw tetr4agwnon t6o ABGD, di4ametro@ d6e a2uto5u 3h AG: l4egw, 34oti 3h GA 2as4ummetr4o@ 2esti t5hj AB m4hkei. -E2i g6ar dunat4on, 24estw s4ummetro@: l4egw, 34oti sumb4hsetai t6on a2ut6on 2ariqm6on 24artion e25inai ka6i periss4on. faner6on m6en o25un, 34oti t6o 2ap6o t5h@ AG dipl4asion to5u ^+^ 2ap6o t5h@ AB. ka6i 2epe6i s4ummetr4o@ 2estin 3h GA t5hj AB, 3h GA 24ara pr6o@ t6hn AB l4ogon 24exei, 36on 2ariqm6o@ pr6o@ 2ariqm4on. 2ex4etw, 36on 3o EZ pr6o@ H, ka6i 24estwsan o3i EZ, H 2el4axistoi t5wn t6on a2ut6on l4ogon 2ex4ontwn a2uto5i@: o2uk 24ara mon6a@ 2est6in 3o EZ. e2i g6ar 24estai mon6a@ 3o EZ, 24exei d6e l4ogon pr6o@ t6on H, 36on 24exei 3h AG pr6o@ t6hn AB, ka6i me4izwn 3h AG t5h@ AB, me4izwn 24ara ka6i 3h EZ to5u H 2ariqmo5u: 34oper 24atopon. o2uk 24ara mon4a@ 2estin 3o EZ: 2ariqm6o@ 24ara ka6i 2epe4i 2estin 3w@ 3h GA pr6o@ t6hn AB, o34utw@ 3o EZ pr6o@ t6on H, ka6i 3w@ 24ara t6o 2ap6o t5h@ GA pr6o@ t6o 2ap6o t5h@ AB, o34utw@ 3o 2ap6o to5u EZ pr6o@ t6on 2ap6o to5u H. dipl4asion d6e t6o 2ap6o t5h@ GA to5u 2ap6o t5h@ AB: diplas4iwn 24ara ka6i 3o 2ap6o to5u EZ to5u 2ap6o to5u H: 24artio@ 24ara 2est6in 3o 2ap6o to5u EZ: 34wste ka6i a2ut6o@ 3o EZ 24arti4o@ 2estin. e2i g6ar 25hn periss4o@, ka6i 3o 2ap' a2uto5u tetr4agwno@ periss6o@ 25hn, 2epeid4hper, 2e6an perisso6i 2ariqmo6i 3oposoio5un sunteq5wsin, t6o d6e pl5hqo@ a2ut5wn periss6on 25hj, 3o 34olo@ periss4o@ 2estin: 3o EZ ^+^ 24ara 24arti4o@ 2estin. tetm4hsqw d4ixa kat6a t6o Q. ka6i 2epe6i o3i EZ, H 2el4axisto4i e2isi t5wn t6on a2ut6on l4ogon 2ex4ontwn <22>, pr5wtoi pr6o@ 2all4hlou@ e2is4in. ka6i 3o EZ 24artio@: periss6o@ 24ara 2est6in 3o H. e2i g6ar 25hn 24artio@, to6u@ EZ, H du6a@ 2em4etrei: p5a@ g6ar 24artio@ 24exei m4ero@ 34hmisu: pr4wtou@ 24onta@ pr6o@ 2all4hlou@: 34oper 2est6in 2ad4unaton. o2uk 24ara 24arti4o@ 2estin 3o H: periss6o@ 24ara. ka6i 2epe6i dipl4asio@ 3o EZ to5u EQ, tetrapl4asio@ 24ara 3o 2ap6o EZ to5u 2ap6o EQ. dipl4asio@ d6e 3o 2ap6o to5u EZ to5u 2ap6o to5u H: dipl4asio@ 24ara 3o 2ap6o to5u H to5u 2ap6o EQ: 24artio@ 24ara 2est6in 3o 2ap6o to5u H. 24artio@ 24ara di6a t6a e2irhm4ena 3o H: 2all6a ka6i periss4o@: 34oper 2est6in 2ad4unaton. o2uk 24ara s4ummetr4o@ 3h GA t5hj AB m4hkei: 34oper 24edei de5icai. ####PBF&#### ###10AP### ##115c## -----24Allw@ <22> -24Estw 2ant6i m6en diam4etrou 3h A, 2ant6i d6e t5h@ pleur5a@ 3h B. l4egw, 34oti 2as4ummetr4o@ 2estin 3h A t5hj B m4hkei. ^-^ e2i g6ar dunat4on, 24estw <22> p4alin 3w@ 3h A pr6o@ t6hn B, o34utw@ 3o EZ 2ariqm6o@ pr6o@ t6on H, ka6i 24estwsan 2el4axistoi t5wn t6on a2ut6on l4ogon 2ex4ontwn ^+^ a2uto5i@ o3i EZ, H: o3i EZ, H 24ara pr5wtoi pr6o@ 2all4hlou@ e2is4in. l4egw pr5wton, 34oti 3o H o2uk 24esti mon4a@. e2i g6ar dunat4on, 24estw mon4a@. ka6i 2epe4i 2estin 3w@ 3h A pr6o@ t6hn B, o34utw@ 3o EZ pr6o@ t6on H, ka6i 3w@ 24ara t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ B, o34utw@ 3o 2ap6o to5u EZ pr6o@ t6on 2ap6o to5u H. dipl4asion d6e t6o 2ap6o t5h@ A to5u 2ap6o t5h@ B: dipl4asio@ 24ara ka6i 3o 2ap6o to5u EZ to5u 2ap6o to5u H. ka4i 2esti mon6a@ 3o H: du6a@ 24ara 3o 2ap6o EZ tetr4agwno@: 34oper 2est6in 2ad4unaton. o2uk 24ara mon4a@ 2estin 3o H: 2ariqm6o@ 24ara. ka6i 2epe4i 2estin 3w@ t6o 2ap6o t5h@ A pr6o@ t6o 2ap6o t5h@ B, o34utw@ 3o 2ap6o EZ pr6o@ t6on 2ap6o to5u H, ka6i 2an4apalin 3w@ t6o 2ap6o t5h@ B pr6o@ t6o 2ap6o t5h@ A, o34utw@ 3o 2ap6o to5u H pr6o@ t6on 2ap6o to5u EZ, metre5i d6e t6o 2ap6o t5h@ B t6o 2ap6o t5h@ A, metre5i 24ara ka6i 3o 2ap6o to5u H tetr4agwno@ t6on 2ap6o to5u EZ: 34wste ka6i 3h pleur6a a2ut6h 3o H t6on EZ metre5i. metre5i d6e ka6i 3eaut6on 3o H: 3o H 24ara to6u@ EZ, H metre5i pr4wtou@ 24onta@ pr6o@ 2all4hlou@: 34oper 2est6in 2ad4unaton. o2uk 24ara s4ummetr4o@ 2estin 3h A t5hj B m4hkei: 2as4ummetro@ 24ara 2est4in: 34oper ^-^ 24edei de5icai. ^+^ ####PBF&#### ###10AP### ##SCHOL##-----Sx4olion -E3urhm4enwn d6h t5wn m4hkei 2asumm4etrwn e2uqei5wn, 3w@ t5wn A, B, e3ur4isketai ka6i 24alla ple5ista meg4eqh 2ek d4uo diast4asewn, l4egw d6h 2ep4ipeda, 2as4ummetra 2all4hloi@. 2e6an g6ar t5wn A, B e2uqei5wn m4eshn 2an4alogon l4abwmen t6hn G, 24estai 3w@ 3h A pr6o@ t6hn B, o34utw@ t6o 2ap6o t5h@ A 2ep4ipedon pr6o@ t6o 2ap6o t5h@ G t6o 34omoion ka6i 3omo4iw@ 2anagraf4omenon, e24ite tetr4agwna e24ih t6a 2anagraf4omena e24ite 34etera e2uq4ugramma 34omoia e24ite k4ukloi per6i diam4etrou@ t6a@ A, G, 2epe4iper o3i k4ukloi pr6o@ 2all4hlou@ e2is6in 3w@ t6a 2ap6o t5wn diam4etrwn tetr4agwna. e34urhntai 24ara ka6i 2ep4ipeda xwr4ia 2as4ummetra 2all4hloi@: 34oper 24edei de5icai. -Dedeigm4enwn d6h ka6i t5wn 2ek d4uo diast4asewn diaf4orwn 2asumm4etrwn xwr4iwn de4icomen to5i@ 2ap6o t5h@ t5wn stere5wn qewr4ia@, 3w@ 24esti ka6i stere6a s4ummetr4a te ka6i 2as4ummetra 2all4hloi@. 2e6an g6ar 2ep6i t5wn 2ap6o t5wn A, B tetrag4wnwn 26h t5wn 24iswn a2uto5i@ e2uqugr4ammwn 2anast4hswmen 2iso7uy5h ^+^ stere6a parallhlep4ipeda 26h puram4ida@ 26h pr4ismata, 24estai t6a 2anastaq4enta pr6o@ 24allhla 3w@ a3i b4asei@. ka6i e2i m6en s4ummetro4i e2isin a3i b4asei@, s4ummetra 24estai ka6i t6a stere4a, e2i d6e 2as4ummetroi, 2as4ummetra. 34oper 24edei de5icai. -2All6a m6hn ka6i d4uo k4uklwn 24ontwn t5wn A, B 2e6an 2ap' a2ut5wn 2iso7uye5i@ k4wnou@ 26h kul4indrou@ 2anagr4aywmen, 24esontai pr6o@ 2all4hlou@ 3w@ a3i b4asei@, tout4estin 3w@ o3i A, B k4ukloi. ka6i e2i m6en s4ummetro4i e2isin o3i k4ukloi, s4ummetroi 24esontai ka6i o34i te k5wnoi pr6o@ 2all4hlou@ ka6i o3i k4ulindroi, e2i d6e 2as4ummetro4i e2isin o3i k4ukloi, 2as4ummetroi 24esontai ka6i o3i k5wnoi ka6i o3i k4ulindroi. ka6i faner6on 3hm5in g4egonen, 34oti o2u m4onon 2ep6i gramm5wn ka6i 2epifanei5wn 2esti summetr4ia te ka6i 2asummetr4ia, 2all6a ka6i 2ep6i t5wn stere5wn sxhm4atwn.>3>