Elements of Geometry, Conic Sections, and Plane Trigonometry

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Harper & Brothers, 1895 - Geometry - 436 pages
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Page 42 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 194 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 187 - ... and is measured by the arc of a great circle described from its vertex as a pole, and included between its sides.
Page 71 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Page 27 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 184 - THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let...
Page 310 - II. Given two sides of a triangle and an angle opposite one of them, to find the other two parts.
Page 38 - BAC equal to the third angle EDF. For if BC be not equal to EF, one of them must be greater than the other. Let BC be the greater, and make BH equal to EF, [I.
Page 80 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 91 - Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig. 128. which contain the equal angles; thus the triangle ABC (fig.

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