Of the vse of the Trigon in measuring of Plaines by the foot.

TO measure by this Table, is, by two numbers knowne, to finde the third vnknowne. Things here to be measured, are magnitudes. And magnitudes or bignesses, are quantities which haue either one or more dimensions, to wit, length, breadth, or thicknesse. These dimensions are here represented by numbers. Of the two numbers assigned, the one must be sought amongst those on the out side of the Tri­gon: The other amongst those vnderneath the base of the same. The numbers, as you see, doe stand against the spaces enclosed betweene two parallell lines. Hauing found your numbers giuen, let your eye direct you through the opposite spaces against which they stand, from the one ascending; from the other sidewaies, or contrarily, vntill you obserue both the spaces to meet, or fall into one. The number there found, is the dimension sought. Plaines are magnitudes long and broad: Or, Surfaces are magnitudes of two dimensions, namely, length and breadth. Here the two numbers giuen, are that of the breadth, and the number of 12; 1 A Board of 18 inches broad, and 24 foot long, is to be measured. Here the breadth 18 taken amongst those vnder the base, and 12 amongst those on the side, doe in the quadrate where their spaces meet, giue 8 inches for the length desired. Now because 8 inches is contained in 84 foot 36 times▪ therefore the board giuen, doth containe 36 foot of plaine measure. 2 A pane of Glasse is 8 inches broad. Here 8 taken amongst those on the side; and 12 vnderneath the base, doe set vs out 18 inches for the length. If the breadth bee greater then 24, that is, then any number enclosing the Trigon, then take the halfe, one third part, one quarter, &c. and the number found shall be two, three, or foure foot, &c of plaine measure. 3 A Table of one yard and a quarter (or 45 inches) broad is to be measured. Here 45 inches is grea­ter then any number about the Trigon; therefore I take 15 the third part of the breadth, and 15 and 12 I finde to point to 9 and 3/5 for the length desired. Therefore I auerre, that euery 9 inches, and 3/5 parts of an inch in length of that table, shall conteine 3 foot of plaine measure. 4 A roome of 16 foot broad, and 48 foot long is to be floored; I would know how many foot of Board it will aske to couer it. Here 16 foot, that is, 196 inches is greater then any about the Trigon; therefore I take 16 the 12 part thereof: and 16 and 12 doe allow 9 inches for the length. Now because 9 inches are conteined in 48 foot 64 times; and 64 times 12 are 768. Therefore I say, the floore will require 768 foot of board to couer it.

The vse of the Trigon in the measuring of Solids by the fo [...].

SOlids or bodies haue three dimensions, to wit, length, breadth, and thick [...]e. And of these commonly the breadth and thicknesse are giuen; the length is so [...] 1 A square timber stick of 12 inches broad, and 12 inches thick, is to bee [...]asured. Here 12 and 12 doe point out 12 inches for the length desired. 2 [...] [...]one is 18 inches broad, and 16 thick. Here I finde 6 inches for the length [...]ght. If either one or both of numbers giuen, be greater then any about the Trigon, ta [...]s afore, either the one halfe, one third, and the number found shall answere in a pr [...]tion, as afore. 3 Suppose a stone were 4 foot (or 48 inches) ouer, and 8 in [...] thick. Here 24 the halfe of 48, and 8, doe assigne 9 inches for the leng [...] desired. Therefore say, that euery 9 inches in length of that stone, shall [...]eine 2 foot of solid measure. 4 Admit the stone were a yard square, that is, [...] inches broad, and 36 inches thick. Here both the dimensions, to wit, be [...] [...]readth and thicknesse, are greater then any of those about the Trigon. [...]efore I take 18 and 18, the halfe of each; and I finde them to meet in the [...] where you haue 5 inches and 1/3. Therefore I say, that euery 5 inches, and [...] of an inch doth conteine 4 foot of stone.

To measure by that our Rular, being by the crossing of two lines giuen, to finde out the third; And the eye not able in many cases precisely to discerne at what parts of an inch that crossing is; some haue desired that these seuerall meetings might bee noted on the verge of the Rular, either aboue or beneath; but th [...] being not to be done without confusion, I doe aduise them to haue recourse to this our Table, where they shall receiue satisfaction: And withall it shall teach them how to doe it. Other vses of this our Trigon, shall, God willing, shortly bee de­clared: for this straightnesse of roome will ad­mit of no long discourse. Vale.