An Excellent TABLE for the finding the Periferies or Circumferences of all Elleipses or Ovals, so near the Truth as any Mechanical Practice can require,

AxisPerife­riesDiff.AxisPerife­riesDiff.
 2.0000 502.4218 
12.001212512.4342124
22.002816522.4467125
32.004820532.4594127
42.007226542.4723l29
52.010028552.4852129
62.013333562.4983131
72.017037572.5114131
82.021343582.5245131
92.026148592.5377133
102.031453602.5510133
112.037056612.5644134
122.043262622.5779135
132.049664632.5915136
142.056468642.6052137
152.063470652.6189137
162.070874662.6327138
172.078476672.6465138
182.086278682.6604139
192.094280692.6744140
202.102482702.6884140
212.110682712.7025141
222.119286722.7166141
232.128189732.7309143
242.137392742.7453144
252.146794752.7599146
262.156194762.7745146
272.165897772.7891146
282.175698782.8038147
292.1856100792.8186148
302.1956100802.8334148
312.2057l01812.8482148
322.2160103822.8630148
332.2264104832.8779149
342.2368104842.8929150
352.2474106852.9080150
362.258l107862.9231151
372.2692111872.9382151
382.2803111882.9534152
392.2915112892.9686152
402.3028113902.9839153
412.3142114912.9993154
422.3256114923.0147154
432.3371115933.0302155
442.3488117943.0458156
452.3607119953.0614156
462.3726119963.0771157
472.3848122973.0928157
482.3970122983.1086158
492.4094124993.1244158
502.42181243.1402158

EXAMPLE I.

WHere the longer Axis of the Elleipsis is 1, and the shorter .78; Because the Table is made for such Elleips's, enter with .78, the Perifery of that Elleipsis will be 2.8038.

EXAMPLE II.

The longer Axis 1, the shorter .4382, I enter with .43, gives 2.3371: Then to find the part answering to .71, say, If 100 give .117; what shall .71 give? Answ. .83, which added to 2.3371, gives 2.3454 for the Perifery desired.

EXAMPLE III.

Where the longer Axis is 388, the shorter 280, first say, 388 : 280 :: 1.000 : Answ. .721, seek in the Table for .72, it gives 2.7166; then say, 1.0000:2.7166 :: 388 : Answ. 1054.06, which is the Circumference desired.

EXAMPLE IV.

The longer Diameter 32.54, the shorter 18.64; say; 32.54 : 18.64 :: 1.000 : 572; to which in the Table answers 2.5114, and the part proportional for 2 is 26, which makes the whole 2.5140; then 1.000 : 2.5140 :: 32.54 : 81.805 the Perifery required. The Area or Superficies of an Elleipsis is easily got by this Rule. As the longer Diameter, is to the shorter: So is the Circle of the longer Diameter, to the Elleipsis.

I have made above 45000 Arithmetical Operations for this Table, and am now well pleased it is finished. Some perhaps may find shorter ways, as I believed I had my self, 'till advised otherwise by the truly Honourable the Lord BRUNCKER. I therefore pursued the Rules given by me, in that Contemplation of the Elleipsis Printed in my Arithmetick, taking 100 Elleipsis betwixt that which falls upon the Diameter equal in this case to 2.0000 the first in the Table, and the greatest which is the Circle 3.1402 the last.

SOLI DEO GLORIA.

LONDON, Printed by W. G. for N. Brooke, at the Angel in Cornhill, 1676.

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