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" Any two rectangles are to each other as the products of their bases by their altitudes. "
Elements of Geometry and Conic Sections - Σελίδα 60
των Elias Loomis - 1858 - 234 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Elements of Geometry

Adrien Marie Legendre - 1819 - 208 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1825 - 224 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1825 - 224 σελίδες
...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...

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - 316 σελίδες
...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,...

Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - 1829 - 172 σελίδες
...its height, and CE X CG is the product of the base of the rectangle CEFG by its height. Therefore — Two rectangles are to each other as the products of their bases by their heights. 159. It is usual to estimate areas by square feet, square yards, square rods, &c. By a square...

Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 σελίδες
...AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes. SCHOLIUM. Hence the product of the base by the altitude may be assumed...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 σελίδες
...ABCD, AEFD, of the same altitude, are to each other as theii bases AB, AE. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases multiplied by their altitudes. Let ABCD, AEGF, be two rectangles ; then will the rect angle, ABCD :...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1837 - 159 σελίδες
...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...

Elements of Geometry

Adrien Marie Legendre - 1841 - 235 σελίδες
...solid AG : solid AZ : : AB 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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