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acute adjacent altitude applied arranged base called chord circle circumference coincide common cone construct Corollary corresponding Cosine Cotang curve demonstrated described diagonals diameter diedral difference direction distance divided draw edges equal equivalent example EXERCISES expressed extend faces fall figure formed formula four functions Geometry given greater half Hence homologous hypotenuse included inscribed intersection Join length less limit logarithm mantissa means measured meet method opposite parallel pass perimeter perpendicular places plane polygon positive principles prism problem proportional pyramid radius ratio regular polygon remaining right angles secant sides similar similarly sine solution sphere spherical triangle square straight line student subtract Suppose surface Tang tangent tetraedrons theorem Theorem.-The third triangle triedral true unit vertex vertices volume whole
Page 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.
Page 72 - Problem. — To draw a line through a given point parallel to a given line.
Page 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.
Page 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Page 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.
Page 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Page 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...
Page 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.