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 be ...
... 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 be ...
Page 178
... volume bounded by polygons . The bounding polygons are called faces of the polyedron ; the lines in which the faces ... equal in all their parts , and having their homologous sides parallel . The other faces are parallelograms ( B. I. , P.
... volume bounded by polygons . The bounding polygons are called faces of the polyedron ; the lines in which the faces ... equal in all their parts , and having their homologous sides parallel . The other faces are parallelograms ( B. I. , P.
Page 181
... VOLUME OF A POLYEDRON is its numerical value expressed in terms of some other polyedron as a unit . The unit ... equal to the perim eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex surface ...
... VOLUME OF A POLYEDRON is its numerical value expressed in terms of some other polyedron as a unit . The unit ... equal to the perim eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex surface ...
Page 188
... equal to FA2 plus AH2 or FC2 : bence , FD2 = FB2 + FA2 + FC2 . B Cor . 3. A parallelopipedon may be constructed on three straight lines AB , AD , and AE , intersecting in a common point A , and not lying in the same ... volume . For , through ...
... equal to FA2 plus AH2 or FC2 : bence , FD2 = FB2 + FA2 + FC2 . B Cor . 3. A parallelopipedon may be constructed on three straight lines AB , AD , and AE , intersecting in a common point A , and not lying in the same ... volume . For , through ...
Page 189
... equal ( P. II . ) : edron Badc - g is a right prism ( D. 2 , 4 ) , polyedrons Bad - h and Bcd - h . hence , the poly ... volume . In like manner , it may be shown that the prisms BCD - II and Bcd - h are equal in volume . The prisms Bad ...
... equal ( P. II . ) : edron Badc - g is a right prism ( D. 2 , 4 ) , polyedrons Bad - h and Bcd - h . hence , the poly ... volume . In like manner , it may be shown that the prisms BCD - II and Bcd - h are equal in volume . The prisms Bad ...
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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