Some General Theorems of Considerable Use in the Higher Parts of Mathematics - Softcover

Stewart, Matthew

9781151602053: Some General Theorems of Considerable Use in the Higher Parts of Mathematics

Softcover

ISBN 10: 1151602051 ISBN 13: 9781151602053

Publisher: General Books LLC, 2012

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated.1746 Excerpt: ... ber of the points A, B, C, &c. E. D. Cor. I. Let there be two circles having the fame centre, and let the circumference of one of the circles be divided into any number of equal parts, and from the points of divifi- on let there be drawn right lines to any point in the circumference of the other, the fum of the fquares of thefe lines will always be the lame. Cor. II. Let there be two regular figure infcribed in a circle, and from all the angles of both figures let there be drawn right lines to any point, the fum of the fquares of the lines drawn from the angles of the one, will be to the fum of the fquares of the lines drawn from the angles of the other, as the number of the fides of the one to the. num/r ber of the fides of the other, LEMMA II. Fig, 8. 9. Let there be any number of right lines AB, AC, AD, AE, &c. interfering each other in the point A, and making all the angles. about the point A equal., let there be an circle pajfing through the point A; the cirtumference of the circle will be divided bf the lines intersecting each other in the point A into as many equal parts as there are lines. 1. When the circle does not touch any of the lines intersecting each other in the point A. Fig. 8. Let AB, AC, AD, AE, &c. meet the circles in B, C, D, E, &e. Because the angles BAC, CAD, DAE, &c. are equal, the segments BC, CD, DE, &c. will be equal. Let BE be the segment in which the point A is; draw BD, ED to any point D in the circle; the angle BDE will be equal to the angle adjacent to the angle BAE, that is, to the angle BAF, or BAC j therefore the segment BAE is equal to the segment BC. 2. When the circle touches one of the lines intersecting each other in the point A. & 9- Let it touch AB, and let AC, AD, AE meet the circle in C, D, E. Because the angle C...

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About the Author

Matthew Stewart is the author of Nature's God: The Heretical Origins of the American Republic, The Courtier and the Heretic: Leibniz, Spinoza, and the Fate of God in the Modern World and The Management Myth: Debunking the Modern Philosophy of Business. He lives in Boston, Massachusetts.

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