The quadrature of the circle discovered ... / Submitted to the consideration of the Royal Society.

  • Parsey, Arthur, 1791-1857.
Date:
1832
Catalogue details

Licence: Public Domain Mark

Credit: The quadrature of the circle discovered ... / Submitted to the consideration of the Royal Society. Source: Wellcome Collection.

    17/26 (page 15)
    Again I say, the circumference multiplied by half the radius, or half the circumference multiplied by half the diameter, or, which is the same thing, half the circumference multiplied by half the diameter, is not the area of a circle. As the ratio 1 to 3,1415926 has been assented to, and em¬ ployed by mathematicians of every country for ages down to the present time, from successive examination and de¬ monstration, it will no doubt be a matter of surprise when I suggest that not one place of decimal is true. The ratio employed is to compute areas of circles. Be the peri¬ meter of the circle what it may, 3,1415926 is not the true working decimal, neither are any of the computations cor¬ rect, resulting from a radical error. By Prop. 8. (Page 6.), the perimeters of polygons are to one another as the radii (AO, ao) of the circles circumscribed, and also as the radii (DO, do) of the circles inscribed. AB : ab ; AO : ao DO : do Q. E. D. By Prop. 7- (Page 7), the area of a regular polygon is equal to its perimeter, multiplied by half the radius of the inscribed circle. . •. The area of all the triangles of which the polygon is composed is = (GH 4- III 4- IK + KL LM ■+■ MG) x £ OT, which is = the perimeter X £ the radius of the inscribed circle Q. E. D. Prop. 11. (Page 8), the circumferences of circles are as their radii, and their surfaces are as the squares of their radii. Q. E. D. Prop. 12. (Page 9), the area of a circle is equal to the product of the circumference and half the radius, whicli it is said has been demonstrated. By Euclid, (Prop. iv. Book i.) it is demonstrated that, if two triangles have two sides of the one z= 2 sides of the other, each to each, and have like¬ wise the angles contained by those sides equal to one another,