Elements of Geometry With Practical Applications to Mensuration
The book Elements of Geometry With Practical Applications to Mensuration was written by author Benjamin Greenleaf Here you can read free online of Elements of Geometry With Practical Applications to Mensuration book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Elements of Geometry With Practical Applications to Mensuration a good or bad book?
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For the diagonals A C, B D bisect each other (Prop. XXXIV. Bk. I.) ; hence, in the trian- gle ABC, XB^ + BO^ = 2 AE^ + 2 BE® (Prop. XIV.) ; also, in the triangle A D C, ad' + DC' = 2 A E® + 2 D E^ 94 ELEMENTS OP GEOMETRY. Hence, by adding the corresponding sides together, and observing that, since B E and D E are equal, B E and D E^ must also be equal, we shall have, AB' + BC'' + ad' + DC' = 4 AB' + 4 D"e'. But 4 AE' is the square of 2 A E, or of A C, and 4 DE' is the square of 2 D E, or of B D... (Prop. VIII. Cor.) ; hence, BA' + BC' + CD' + ad' = A^' + BD'. Pkoposition XVI. — Theoeem. 249. In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diag- onals, plus four times the square of the straight line that joins the middle points of the diagonals. Let A B C D be any quadrilateral, the C diagonals of -whicli are AC, D B, and E P a straight line joining their mid- dle points, E, P ; then the sum of the squares of A B, B C, C D, A D is equiv- alent to AC' -f BD' + 4 EF', a Join E B and E D ; then in the triangle ABC, AB' -j- BC' = 2 AE' -f 2 BE^ (Prop.
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