Plane and Solid Geometry

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Century Company, 1906 - Geometry - 418 pages
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Page 168 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 41 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 35 - Any side of a triangle is less than the sum of the other two sides...
Page 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Page 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 171 - 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 199 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 192 - The areas of two rectangles having equal altitudes are to each other as their bases.
Page 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...

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