Rational Geometry a Text book for the Science of Space Based On Hilberts Foun

Cover Rational Geometry a Text book for the Science of Space Based On Hilberts Foun
Rational Geometry a Text book for the Science of Space Based On Hilberts Foun
George Bruce Halsted
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Ex. 376. AH-HD=BH-HE.
Ex. 377. The area of a -I- r't A is $c 2 .
Ex. 378. Construct i A =given a with same b and hb.
Ex. 379. Bisect any quad' by a st' from any vertex; from any point in a side.
Ex. 380. Any st' through the bisection-point of a diag- onal bisects the ||gm.
Ex. 381. 3(a 2 + 6 2 + c 2 ) =4(m a 2 + m 2 + wc 2 ).
Ex. 382. Upon any st' the sum of the ±s from the vertices of a a is thrice the 1 from its centroid.
Ex. 383. In r't A, $c 2 ■=4(wo, + Wt 2 ).
Ex. 384. Trisect a quad'.
Ex.
... 385. Find a =aABC, but with sides m, n; with side m and adjoining ^ d; and opposite ^ 8.
EQUIVALENCE. 137 Ex. 386. Find -I- A = A ABC, but with base m\ with side m.
Ex. 387. Find a = given polygon.
Ex. 388. From any point in an equilateral a the three ±s on the sides together =the altitude.
Ex. 389. Sects from the bisection-point of a non-|| side of a trapezoid to oppsite vertices bisect it.
Ex. 390. If the products of the segments of two inter- secting sects are =, their ends are concyclic.


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