Plane and Solid Geometry

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American Book Company, 1912 - Geometry - 488 pages
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Page 281 - ... that the bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.
Page 76 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 232 - Prove that the square described on the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides.
Page 179 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.
Page 455 - 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 397 - The lateral area of a cylinder is equal to the product of the perimeter of a right section of the cylinder by an element. Hyp. S is the lateral area, P the perimeter of a right .section, and E an element of the cylinder AK; S...
Page 449 - The area of a zone is equal to the product of its altitude and the circumference of a great circle.
Page 195 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. 3. In a right triangle the square of either leg is equal to the square of the hypotenuse minus the square of the other leg.
Page 83 - How many sides has a polygon, the sum of whose interior angles is equal to the sum of its exterior angles ? 51.
Page 12 - LET it be granted that a straight line may be drawn from any one point to any other point.

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