Plane and Solid Geometry

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Macmillan, 1913 - Geometry, Plane - 321 pages
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Page 168 - 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 140 - 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 154 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 53 - If two parallel lines are cut by a transversal, the alternate interior angles are equal.
Page 133 - 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 66 - If two triangles have two sides of the one equal to two sides of the...
Page 309 - 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 294 - 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 134 - 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.
Page 67 - The perpendicular is the shortest line that can be drawn from a point to a straight line.

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