Elements of Geometry With Practical Applications to Mensuration
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In our eReader you can find the full English version of the book. Read Elements of Geometry With Practical Applications to Mensuration Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of Geometry With Practical Applications to Mensuration
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To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Elements of Geometry With Practical Applications to Mensuration?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Greenleaf to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Elements of Geometry With Practical Applications to Mensuration?
You can find similar books in the "Read Also" column, or choose other free books by Benjamin Greenleaf to read onlineMoreLess
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