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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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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...that the area of the triangle is equal to half this product : that is, to half the product of AB x CD. Cor. Two triangles of the same altitude are to each...same base are to each other as their altitudes. And generally, triangles are to each other as the products of their bases and altitudes. THEOREM X. The...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...that the area of the triangle is equal to half this product : that is, to half the product ofABxCD. Cor. Two triangles of the same altitude are to each...same base are to each other as their altitudes. And generally, triangles are to each other as the products of their bases and altitudes. THEOREM X. The...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...altitude ; and the two triangles ADF, CDF, on the bases AF, FC, have also the same altitude ; and because triangles of the same altitude are to each other as their bases, (B. IV, Prop, iv, Cor.) therefore, ADF : BDF : : AD : DB; ADF : CDF : : AF : FC. But BDF = CDF; consequently,...
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Young Scientist: A Practical Journal for Amateurs, Volume 1

1851 - 716 pages
...two legs half the diagonals of the rhombus (fig. 51). The areas of two parallelograms as well as of two triangles of the same base, are to each other as their altitudes ; of the same altitude, as their bases ; and generally, parallelograms are to each other as the products...
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Iconographic Encyclopaedia of Science, Literature, and Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...two legs half the diagonals of the rhombus (fig- 51). The areas of two parallelograms as well as of two triangles of the same base, are to each other as their altitudes ; of the same altitude, as their bases ; and generally, parallelograms are to each other as the products...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 340 pages
...that the area of the tri angle is equal to half this product : that is, to half the product of ABX CD Cor- Two triangles of the same altitude are to each...same base are to each other as their altitudes- And generally, triangles are to each ntho-r as the products of their bases and altitudesTHEOREM XThe area...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...Two triangles of equal altitudes are to each other as their bases, and two triangles of equal bases are to each other as their altitudes. And triangles...other, as the products of their bases and altitudes. PROPOSITION VII. THEOEEM. The area . of a trapezoid is equal to the product of its altitude, ~by half...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...Two triangles of equal altitudes are to each other as their bases, and two triangles of equal bases are to each other as their altitudes. And triangles...other, as the products of their bases and altitudes. PROPOSITION VII. THEOREM. The area of a trapezoid is equal to the product of its altitude, by half...
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The Collected Works of Dugald Stewart, Volume 2

Dugald Stewart - 1854 - 536 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 must...
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The Collected Works of Dugald Stewart: Elements of the philosophy of the ...

Dugald Stewart - 1854 - 538 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 must...
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