Elements of Geometry

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Harper & brothers, 1897 - Geometry - 354 pages
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Page 106 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 290 - 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 177 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Page 83 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 54 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 125 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 122 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 51 - Two oblique lines cutting off equal distances from the foot of the perpendicular are equal.
Page 318 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 139 - Any two rectangles are to each other as the products of their bases by their altitudes.

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