...of parallel planes, the cm-responding segments are proportional. 401. COR. 2. — If any number of lines are cut by three parallel planes, their corresponding segments are proportional. DIHEDRAL ANGLES. 402. A Dihedral Angle is the angle formed by two planes which intersect each other....

...under a given point in the ceiling be determined with a twelve-foot pole ? 6. If two straight lines be cut by three parallel planes, their corresponding...a spherical triangle whose angles are 65°, 75°, 80°, the radius of the sphere of which it forms a part being 10 feet. ALGEBRA TO QUADRATICS. JUNE,...

...are equal, and, according to the Proposition, their planes are parallel. PROPOSITION XVI. THEOREM. If two straight lines are cut by three parallel planes, their corresponding segments are proportional. Let the straight lines AB, CD be cut by Ml the parallel planes MN, PQ, RS in the points A, E, B, C,...

...to J/-V, for it would cut PQ, and therefore also .I/.V. PROPOSITION X. THEOREM 555. If two straiglit lines are cut by three parallel planes, their corresponding segments are proportional. GIVEN — the straight lines AB and CTcul by the parallel planes MN, PQ, and RS in the points A, E,...

...A could be parallel to MN. for it would cut PQ, and therefore also MN. PROPOSITION X. THEOREM 555. If two straight lines are cut by three parallel planes, their corresponding segments are proportional. GIVEN — the straight lines AB and CTcut by the parallel planes MN, PQ, and RS in the points A, E,...

...contain a given angle. 4. Define similar polygons and prove that the perimeters of two similar polygons are to each other as any two homologous sides. 5....radius of the sphere of which it forms a part being 10 feet. JUNE 1886. PLANE. 1. Prove that the three perpendiculars from the vertices of a triangle to...

...MN. PQ, the plane of AB and AC, will be parallel to MN. GEOMETRY OF SPACE PROPOSITION X. THEOREM 555, If two straight lines are cut by three parallel planes, their corresponding segments are proportional. GIVEN — the straight lines AB and CTcut by the parallel planes MN, PQ, and RS in the points A, E,...

...these lines. §183 §150 §128 § 522 § 533 / | p. 1 < e==:,r=^^\i . \ PROPOSITION XV. THEOREM. 535. If two straight lines are cut by three parallel planes, their corresponding segments are proportional. Let AB and CD be intersected by the parallel planes MN, PQ, RS, in the points A, E, B, and C, F, D....

...Therefore, PQia II to MN, the plane of these lines. § 533 p ; i ' ^-^^"^\ : \ PROPOSITION XV. THEOREM. 535. If two straight lines are cut by three parallel planes, their corresponding segments are proportional. Let AB and CD be intersected by the parallel planes MN, PQ, RS, in the points A, E, B, and C, F, D....

...lines. § 533 1 , I ^5T\ \ ,, \ Vr I , ^^^^C'^\ ,_ \ PROPOSITION XV. THEOREM. 535. If two strait/ht lines are cut by three parallel planes, their corresponding segments are proportional. Let AB and CD be intersected by the parallel planes MN, PQ, RS, in the points A, E, B, and C, F, D....