| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| |