Elements of Geometry, Conic Sections, and Plane Trigonometry

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Harper & Bros., 1877 - Geometry - 443 pages
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Page 68 - Any two rectangles are to each other as the products of their bases by their altitudes.
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 64 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Page 71 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 23 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
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 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 177 - THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let...
Page 27 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

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