Elements of Geometry, Conic Sections, and Plane Trigonometry

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Harper & brothers, 1877 - 443 sider
 

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Side 68 - Any two rectangles are to each other as the products of their bases by their altitudes.
Side 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.
Side 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...
Side 64 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Side 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.
Side 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.
Side 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.
Side 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.
Side 177 - THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let...
Side 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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