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" Two triangles of the same altitude are to each other as their bases, and two triangles of the same base are to each other as their altitudes. And triangles generally, are to each other, as the products of their bases and altitudes. "
Elements of Geometry and Trigonometry: With Notes - Page 59
by Adrien Marie Legendre - 1828 - 316 pages
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The Modern Preceptor ; Or, a General Course of Education, Volume 1

John Dougall - 1810
...the same altitude, AE and CF. hoth equal 10 BG, the 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. 30. The area or surface of a...
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The Modern Preceptor Or a General Course of Education: Containing ..., Volume 1

John Dougall - 1810 - 580 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, as Well ...

Charles Hutton - Mathematics - 1816
...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 - 208 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
...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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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 618 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 - 574 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 - 280 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

Adrien Marie Legendre - Geometry - 1825 - 224 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

Adrien Marie Legendre - Geometry - 1825 - 224 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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