 | 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... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...the area of the triangle is equal to half this product : that is, to half the product of AB x CDCor Two triangles of the same altitude are to each other...same base are to each other as their altitudes- And generally, triangles are to each other as the products of their bases and altitudes. x THEOREM XThe... | |
 | William Smyth - Navigation - 1855 - 234 pages
...field ABC equally among three persons, by lines proceeding from the vertex C of the triangle. Since triangles of the same altitude are to each other as their bases, it will be sufficient, it is evident, to divide the -" base AB into three equal parts, and then to... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...ADE have A common ; have the angle at then we shall THIRD BOOK. For, joining D and 0, we have, since triangles of the same altitude are to each other as their bases, ABC : ADC : : AB : AD, ADC : ADE : : AC : AE. Multiplying together the corresponding terms of these... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 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... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...triangle is equal to one half of the product of BC by AD. Therefore, the area of a triangle, &c. Cor. 1. Triangles of the same altitude are to each other as their bases, and triangles of the same base are to each other as their altitudes. Cor. 2 Equivalent triangles, whose... | |
 | Popular educator - 1860 - 536 pages
...the diff. of the segments of the base. 5 0+14 Hence — % — =32, AD, 50—82=18, D B. Again, since triangles of the same altitude are to each other as their bases, and the triangle ABC contains 320 nun* 60 : 32 : : 820 : 204-8 parts in AD c. 820—204-8=115-2 parti in... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...parallelogram ABCF (T. XIX.). the triangle is measured by the base BC into half the altitude AD. ' Cor. I. Triangles of the same altitude are to each other as their bases ; and triangles of the same or equal bases are to each other as their altitudes. Cor. II. The area of a trapezoid... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1860 - 332 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... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...the product of BC by AD. Cor. 1. Triangles of the same altitude are to each other as their bases, and triangles of the same base are to each other as their altitudes. Cor 2 Equivalent triangles, whose bases are equal, have equal altitudes; and equ ivalent triangles,... | |
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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. 
