Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students |
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Common terms and phrases
adjacent angles altitude angles formed apothem bisect called chord circle circumference coincide Corollary Corollary.-The Cosine Cotang curve demonstration diagonals diameter dicular diedral angles distance divided equal angles equally distant equivalent extent faces figure four right angles frustum Geometry given angle given line given point given straight line gles greater Hence homologous lines hypotenuse hypothesis inscribed intercepted intersection isosceles triangle Join less let fall line parallel logarithm M. M. Sine mantissa measured by half number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular plane polyedral polyedron principle prism Problem.-To PROBLEMS IN DRAWING proportion proposition pyramid quadrilateral quantities radii radius ratio regular polygon respectively equal right angled triangle secant similar similar triangles similarly arranged slant hight sphere spherical triangle student subtracted surface symmetrical Tang tangent tetraedrons theorem Theorem.-The triangle ABC triangles are equal triedral vertex vertices
Popular passages
Page 86 - If two triangles have two sides of the 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.
Page 40 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 170 - ... the plane at equal distances from the foot of the perpendicular, are equal...
Page 129 - 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 239 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.
Page 79 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Page 161 - S' denote the areas of two circles, R and R' their radii, and D and D' their diameters. Then, I . 5*1 = =»!. That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Page 125 - 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.
Page 295 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 225 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.