The philosopher's stone / by P.H. Vander Weyde.

  • Peter Henri Van Der Weyde
Date:
1861 [i.e. 1862]
Catalogue details

Licence: Public Domain Mark

Credit: The philosopher's stone / by P.H. Vander Weyde. Source: Wellcome Collection.

Provider: This material has been provided by the National Library of Medicine (U.S.), through the Medical Heritage Library. The original may be consulted at the National Library of Medicine (U.S.)

    14/42
    and its periphery = 12x1. 7(2— V-i) = 6x V[2— ^3] The side of the circumscrihed polygon of 12 sides is now found by placing in the formula s —. for s the value \ 7 (2 — 7 3), and we obtain S = v/(l-0 i 7L2-73] 7[2- 73] 7[2- 73] X 7[2 + 73] 7[l-£(2-V3)] 712+73] 7[2+73]x 7[2+73] 7[4-3] 1 1 x [2- ^3] 2- v/3 2+73 2+ x/3 [2+ v/3]x[2- ^/3] 4-3 and its periphery = 12 X [2 — y/ :'>]. The periphery of the inscribed polygon of 12 sides is thus 6x 7 [2 — 7 3], and of the circumscribed 12 X [2 — / 3], and the circumference of the circle again between the two. Polygons o£ more Sides . This calculation may be shortened in the consecutive opera- tions; we have, however, no room for the details, and will give only the results in the following table. Number Side of Polygon ; Sides. Inscribed Circumscribed 6 0.3 0.577350269etc. 12 0.258819045102 0.267949192 •• 24 0.130526182220 0.1316525 48 0.063403129230 0.0655435 96 0.032710082821 0.0327190 192 0.016361731625 0.0163617 384 0.008181139604 0.00818113 M 768 0.004090604026 0.00409060 1536 0.002045306291 0.0020462 3072 0.001022653680 0 00102265 . 6144 0.000511326907 0.00051132 « 12288 O.CO0255663162 0.000255663 163 Periphery of Polygon; Inscribed 3.0000000 3.105S285 3.1326286 3.1393502 3.1410319 3.1414525 3.1415576 3.1415839 3.1415904 3.1415921 3.1415925 3.1 115926 Cicumscri'd 3.4641016 3.2153903 3.1596600 3.1460362 3.1427146 3.1418731 3.141C630 3.1416102 3.1415970 3.1415937 3.1415429 3.1415927