Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students. Written for the Mathematical Course of Joseph Ray, M.D.

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Sargent, Wilson & Hinkle, 1868 - 420 sider
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Side 183 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Side 238 - The volume of any parallelopiped is equal to the product of its base by its altitude.
Side 72 - Problem. — To draw a line through a given point parallel to a given line.
Side 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Side 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Side 173 - The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary. — When the radius is unity, the area is expressed by -. 503. Theorem — The area of a sector is measured by half the product of its arc by its radius.
Side 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Side 260 - 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...
Side 137 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Side 274 - The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.

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