Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 17
... angles . A SQUARE is an equilateral rectangle . 2d . A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral rhomboid . 29. SPACE is indefinite extension . 30. A VOLUME is 2 BOOK I. 17.
... angles . A SQUARE is an equilateral rectangle . 2d . A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral rhomboid . 29. SPACE is indefinite extension . 30. A VOLUME is 2 BOOK I. 17.
Page 18
... VOLUME is a limited portion of space , combining the three dimensions of length , breadth , and thickness . AXIOMS . 1. Things which are equal to the same thing , are equal to each other . 2. If equals are added to equals , the sums are ...
... VOLUME is a limited portion of space , combining the three dimensions of length , breadth , and thickness . AXIOMS . 1. Things which are equal to the same thing , are equal to each other . 2. If equals are added to equals , the sums are ...
Page 189
... volume bounded by polygons . The bounding polygons are called faces of the poly- edron ; the lines in which the faces meet , are called edges of the polyedron ; the points in which the edges meet , are called vertices of the polyedron ...
... volume bounded by polygons . The bounding polygons are called faces of the poly- edron ; the lines in which the faces meet , are called edges of the polyedron ; the points in which the edges meet , are called vertices of the polyedron ...
Page 191
... edges , or angles , are called homologous . 17. A DIAGONAL of a polyedron , is a straight line join- ing the vertices of two polyedral angles not in the same face . 18. The VOLUME OF A POLYEDRON is its numerical value BOOK VII . 191.
... edges , or angles , are called homologous . 17. A DIAGONAL of a polyedron , is a straight line join- ing the vertices of two polyedral angles not in the same face . 18. The VOLUME OF A POLYEDRON is its numerical value BOOK VII . 191.
Page 192
... VOLUME OF A POLYEDRON is its numerical value expressed in terms of some other polyedron taken as a unit . The unit generally employed is a cube constructed on the linear unit as an edge . PROPOSITION I. THEOREM . The convex surface of a ...
... VOLUME OF A POLYEDRON is its numerical value expressed in terms of some other polyedron taken as a unit . The unit generally employed is a cube constructed on the linear unit as an edge . PROPOSITION I. THEOREM . The convex surface of a ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence