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.)

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    great number of sides, we know the limit above which the num- ber must be situated.* The shortest way now to calculate the periphery of those poly- gons is to rii.d a formula i'or the side of a polygon of double the number of sides of a given polygon, and also for the side of the circumscribed polygon of the same number of sides as the inscri- bed one, the latter being given. Calling the side of the inscribed polygon s, and of the polygon of double the numberof sides s', we easily obtain, taking the diameter of the circle = 1, the expression *'= V ' [1 -V 0-r)] and calling S the side of the inscribed polygon of the same num- ber as the inscribed one of s sides, we have X Polygons of 6 Sides . If now we commence with a polygon of six sides, then if the diameter of the circle being =1,.*= \ and 1 \ 1 Q -i 2_ — * — 1 ./q The periphery of the inscribed polygon of 6 sides is therefore 6 X i = 3. of the circumscribed =C x |\/3 =2/3. The length of the circumference of the circle is between these two numbers, and by doubling the sides we inclose it between nar- rower limits. Polygons of 12 Sides ■ So we will find the side of the inscribed polygon of 12 sidea • As this essay is not intended for an elementary treatise on Geometry, we have no space to copy the demonstrations of these truths, or of the next fol- lowing formulae, they may be found in many of the larger works on Geome- try, as I.F.r.KvriHK. !,.*<' ;oix. and others