A New System Of Geometry Successfully Applied To The Solution Of The Square Of The Circle - Softcover

William F. Gee

Softcover

ISBN 10: 0371406676 ISBN 13: 9780371406670

Publisher: HardPress, 2021

Synopsis

A New System Of Geometry Successfully Applied To The Solution Of The Square Of The Circle by William F. Gee is a nineteenth-century mathematical treatise focused on the quadrature of the circle. The work outlines a geometric program that brackets the circle’s contents with two constructions: inscribing 6,144 equal chords and surrounding the circle with 6,144 equal right lines parallel to those chords. Gee decomposes the circle into twelve right-angled triangles, using the circle’s radius as the hypotenuse and six segments cut off by chords equal to the radius. These pieces are assembled through a sequence of propositions (First through Fifteenth) and an extensive Appendix. Central to the method are auxiliary quantities labeled A, B, C, and D, whose interrelations are explored through analysis and induction to approximate the circle’s area. The text also includes numerical illustrations (e.g., for a circle of radius 10) and discusses a philosophy of numerical approximation and the powers of numbers. This book serves as a historical exploration of the efforts to square the circle through exhaustion and precise arithmetic.

Edition details

• Publisher: HardPress
• Publication date: 2021
• Language: English
• ISBN 10: 0371406676
• ISBN 13: 9780371406670
• Binding: Paperback
• Number of pages: 86