The College Euclid; Comprising the First Six and the Parts of the Eleventh and Twelfth Books Read at the Universities, by A.K. Isbister (Paperback)

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. 1865 Excerpt: ...the rectangle contained by A, C, is equal to that contained by B, D; but the rectangle contained by B, D is the square on B, because B is equal to D; therefore the rectangle contained by A, C, is equal to the square on B. Next, if the rectangle contained by A, C, be equal to the square on B. Then A shall be to B, as B to C. DEMONSTRATION The same construction being made, because the rectangle contained by A, C, is equal to the square on B, and the square on B is equal to the rectangle contained by B, D, because B is equal to D; therefore the rectangle contained by A, and C, is equal to that contained by B, and D. But if the rectangle contained by the extremes be equal to that contained by the means, the four straight lines are proportionals; (vi. 16.) therefore A is to B, as D to C; but B is equal to D; wherefore, as A to B, so B to C. Therefore, if three straight lines, &c. Q. & D. PROP. XVIIL--Pboblem. Upon a given straight line to describe a rectilineal figure similar, and similarly situated, to a given rectilineal figure. (References--Prop. I. 23, 32; v. 22; vi. 4.) First, let AB be the given straight line, and CDEF the given rectilineal figure of four sides. It is required upon the given straight line AB to describe a rectilineal figure similar, and similarly situated, to CDEF. CONSTRUCTION Join DF, and at the points A, B, in the straight line AB make the angle BAG equal to the angle at C, and the angle ABG equal to the angle CDE; (i. 23.) and at the points G, B, in the straight line GB, make the angle BGH equal to the angle DFE, and the angle GBH equal to the angle FDE. (i. 23.) Tnen the figure ABHG snail be similar and similarly situated to CDEF. DEMONSTRATION Because the angle BAG is equal to C, and the angle ABG to the angle CDF; (constr.) t...