Plane and Solid Geometry

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Page 160 - The area of a rectangle is equal to the product of its base and altitude ; that is, A = ab. 443. Corollary 1. The area of a square is equal to the square of its side. 444. Corollary 2. Tiro rectangles are to each other as the products of their bases and altitudes.
Page 132 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 132 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 125 - If the product of two numbers is equal to the product of two other numbers, either two may be made the means, and the other two the extremes of a proportion.
Page 301 - 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 - If two triangles have two sides of the one equal to two sides of the...
Page 286 - The axis of a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.
Page 222 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Page 310 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.
Page 126 - If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third.

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