Plane and Solid Geometry

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American book Company, 1908 - Geometry - 340 pages

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Page 158 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 128 - 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 63 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 134 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The two triangles thus formed are similar to each other and to the whole triangle. II. The perpendicular is a mean proportional between the segments of the hypotenuse.
Page 42 - If two triangles have two sides of one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side. If two triangles have two sides of...
Page 118 - In any proportion, the product of the means is equal to the product of the extremes.
Page 221 - If the product of two numbers -is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Page 120 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 223 - Prove that in any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares on the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 270 - If a pyramid is cut by a plane parallel to the base : 1. The edges and altitude are divided proportionally. 2. The section is a polygon similar to the base. Let V-ABCDE be cut by a plane parallel to its base, intersecting the lateral edges in a, b, c, d, e, and the altitude in o.

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