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" Two triangles of the same altitude are to each other as their bases ; and... "
Elementary Geometry: With Applications in Mensuration - Page 90
by Charles Davies - 1850 - 216 pages
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The Modern Preceptor Or a General Course of Education: Containing ..., Volume 1

John Dougall - 1810 - 554 pages
...altitude of the triangle. Corollary. Triangles on the same base are to each other as their altitudes ; and triangles of the same altitude are to each other as their bases. PROP. XVI. fig. SO. The area or surface of a trapezoid, that is, of an irregular quadrilateral, of...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816 - 610 pages
...tude ; and the two triangles ADE, CDE, on the bases AE, EC, have also the same altitude ; and because triangles of the same altitude are to each other as their bases, therefore the triangle ADE = BDE : '• AD : DB, jj g and triangle ADE : CDE : : *E : EC. Bui BDE is...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...parallelogram = BC x AD (174) ; therefore the area of the triangle = | BC X AD, or BCx^AD. 177. Corollary. Two. triangles of the same altitude are to each other as their hases, and two triangles of the same base are to each other as their altitudes. THEOREM. X 178. The...
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Elements of the Philosophy of the Human Mind, Volumes 1-2

Dugald Stewart - Psychology - 1821 - 706 pages
...circumference on the same base, we ascertain a relation between two quantities. When we demonstrate, that triangles of the same altitude are to each other as their bases, we ascertain a connexion between two relations. It is obvious, how much the mathematical sciences mu...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...finally, the solidity of a cylinder is equal to the product of its base by its altitude. Cor. 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of the same base are to each other as their altitudes. Cor. 9,. Similar cylinders are to...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...fade ; and the two triangles ADE, CDE, on the bases AE, EC, have also the same altitude , and because triangles of the same altitude are to each other as their bases, therefore the triangle ADE : BDE : : AD : on, and triangle ADE : CDE : : AE : EC. But BDE is =CDE ratio...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 pages
...parallelogram = BCx AD (174); therefore the area of the triangle = BC x AD, or BC x AD. 177. Corollary. Two triangles of the same altitude are to each other...the same base are to each other as their altitudes. THEOREM. 178. The area of a trapezoid ABCD (fig. 105) is equal to tfie Fig. 105. product of its altitude...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...Every pyramid is a third of a prism of the same base and same altitude. 418. Corollary n. Two pyramids of the same altitude are to each other as their bases, and two pyramids of the same base are to each other as their altitudes. 419. Scholium. The solidity of any...
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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
...solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders of the same base are to each other as their altitudes. 518. Corollary n. Similar cylinders...
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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
...solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders of the same base are to each other as their altitudes. 518. Corollary n. Similar cylinders...
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