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" ... two triangles are to each other as the products of their bases by their altitudes. "
New Elementary Algebra: in which the First Principles of Analysis are ... - Page 294
by Benjamin Greenleaf - 1863 - 324 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...Now, &ABC= \EHASEC. §220 But ED ABEC = axb. § 229 Hence &.ABC = I a X b. QED 232. COR. 1. — Two triangles are to each other as the products of their bases by their altitudes. COR. 2.— Two triangles having equal bases are to each other as their altitudes. COR. 3. — Two triangles...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...solid AG : solid AZ : : AE x AD x AE : AO X AM X AX. Therefore any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. 405. Scholium. Hence we may take for the measure of a...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. Fig. 213. Demonstration. Having placed the two solids...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...same altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelopipeds are to each other as the products of their bases by their altitudes, or as the products of their three dimensions. Fig. 213. Demonstration. Having placed the two solids...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...altitude are to each other as their bases. THEOREM. 404. Any two rectangular parallelepipedons are to each other as the products of their bases by their altitudes, that is to say, as the products of their three dimensions. For, having placed the two solids AG, AZ,...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 pages
...area of a triangle Is half the product of the base multiplied by the height. Consequently airy two triangles are to each other as the products of their bases by their heights. 161. If we designate the height of a rectangle by #, and the base by 6, the area will be expressed...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 pages
...of the preceding demonstrations. COR. — Two prisms, two pyramids, two cylinders, or two rones are to each, other as the products of their bases by their altitudes. If the altitudes are the same, they ore as their bases. If the bases are the same, thty are as t/icir...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 212 pages
...in the last query ; namely, triangles upon the same basis, and of equal heights. 4th. The areas of triangles are to each other as the products of their bases by their heights : for the halves of these products being the areas of the triangles, the whole products must...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...to each other as their bases. PROPOSITION XIII. THEOREM. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes, that is to say, as the products of their three dimensions. c EH \K \ i L I V 6 A B > \ ro\ I3 \ t C...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...denotes its ratio to the unit of surface. 241. Theorem. Two rectangles, as ABCD, AEFG (fig. 127) are to each other as the products of their bases by their altitudes, that is, ABCD : AEFG = AB X AC : AS X AF. Demonstration. Suppose the ratio of the bases AB to AE to...
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