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 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 equa to each other . 2. If equals be added to equals , the sums will ...
... 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 equa to each other . 2. If equals be added to equals , the sums will ...
Page 178
... volume bounded by polygons . The bounding polygons are called faces of the polyedron ; 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 . 2 ...
... volume bounded by polygons . The bounding polygons are called faces of the polyedron ; 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 . 2 ...
Page 180
... 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 180 GEOMETRY .
... 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 180 GEOMETRY .
Page 181
... VOLUME OF A POLYEDRON is its numerical value expressed in terms of some other polyedron 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 right ...
... VOLUME OF A POLYEDRON is its numerical value expressed in terms of some other polyedron 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 right ...
Page 188
... volume . For , through the vertices F and B let planes be passed perpendicular to FB , the former cutting the other lateral edges in the points e , h , 9 , and the latter cutting those edges produced , in the points a , d , and C. The ...
... volume . For , through the vertices F and B let planes be passed perpendicular to FB , the former cutting the other lateral edges in the points e , h , 9 , and the latter cutting those edges produced , in the points a , d , and C. The ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence