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" ... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes. "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 165
by George Roberts Perkins - 1856 - 235 pages
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...BE1. Cor. 2. Parallelograms of the same base are to each other as their altitudes ; and parallelograms of the same altitude are to each other as their bases : for if A and B are the altitudes of two parallelograms, and C their base ; then A x C is equal to the area...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...partial triangles, which constitute their bases, multiplied by the common altitude. Hence the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. 1. Comparing two prisms, which have the same altitude, the products of their bases by their altitudes...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...partial triangles which constitute their bases, multiplied by the common altitude. Hence the solidity of any polygonal prism is equal to the product of...the same base are to each other as their altitudes. PROPOSITION XII. THEOREM. Similar prisms. are to one another as the cube of ., • • their homologous...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...altitude, the products of the bases by the altitudes, will be as the bases (Prop. VIII., B. II.); hence prisms of the same altitude are to each other as their bases. For the same reason, prisms of the same base are to each other as their altitudes ; and prisms generally...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...BE A & Cor. Parallelograms of the same base are to each other as their altitudes; and parallelograms of the same altitude are to each other as their bases: for, let B be the common base, and C and D the altitudes of two parallelograms: is equal to the area of...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...partial triangles which constitute their bases, multiplied by the common altitude. Hence the solidity of any polygonal prism is equal to the product of...the same base are to each other as their altitudes. PROPOSITION XIITHEOREM. Similar prisms are to one another as the cube of their homologous sides. Let...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the triangles which constitute their bases, multiplied by the common altitude. Hence, the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...the triangles which constitute their bases, multiplied by the common altitude. Hence, the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...the triangles which constitute their bases, multiplied by the common altitude. Hence, the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since any two prisms are to each other as the products of their bases and altitudes, if the altitudes...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...ABxAF. Cor. Parallelograms of the same base are to each other as their altitudes, and parallelograms of the same altitude are to each other as their bases ; for magnitudes have the same ratio that their equimultiples have (Prop. VIII., B. II.). PROPOSITION VI....
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