Elements of Geometry, Conic Sections, and Plane Trigonometry

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Harper & Brothers, 1880 - Geometry - 443 pages
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Page 35 - 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 187 - 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 124 - The area of a circle is equal to the product of its circumference by half the radius.* Let ACDE be a circle whose centre is O and radius OA : then will area OA— ^OAxcirc.
Page 64 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Page 180 - ... and is measured by the arc of a great circle described from its vertex as a pole, and included between its sides.
Page 20 - 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 31 - 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 147 - ... are greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB. Any two of them are greater than the third. If...
Page 73 - 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 73 - THEOREM. The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines.

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