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. 1898 Excerpt: ...( 111.) Prop. XXXIX. Problem. 220. Given two sides and the included angle of a parallelogram, to construct the parallelogram. Given m and n two sides, and A' the included Z, of a O. (The construction and proof are left to the pupil.) Prop. XL. Problem. 221. To inscribe a circle in a given triangle. Given A ABC. Required to inscribe a O in A ABC. Construction. Draw lines AD and BE bisecting A A and B, respectively ( 207). From their intersection O, draw line OM AB ( 204). With O as a centre and OM as a radius, describe a O. This (c) will be tangent to AB, BC, and CA. (The proof is left to the pupil; see 135.) Ex. 80. To construct a right triangle, having given the hypotenuse and an acute angle. (The other acute Z is the complement of the given Z.) Prop. XLI. Problem. 222. To circumscribe a circle about a given triangle. C Given A ABC. Required to circumscribe a O about A ABC. Construction. Draw lines DF and EG to AB and AC, respectively, at their middle points ( 205). Let DF and EG intersect at O. With O as a centre, and OA as a radius, describe a O. The circumference will pass through A, B, and C. (The proof is left to the pupil; see 137.) 223. Sch. The above construction serves to describe a circumference through three given points not in the same straight line, or to find the centre of a given circumference or arc. EXERCISES. 81. To construct a right triangle, having given a leg and the opposite acute angle. (Construct the complement of the given Z.) 82. Given the base and the vertical angle of an isosceles triangle, to construct the triangle. (Each of the equal d is the complement of one-half the vertical Z.) 83. Given the altitude and one of the equal angles of an isosceles triangle, to construct th.