 | Cambridge Philosophical Society - 1842 - 458 sider
...himself with the first twenty-six propositions of Euclid, and not till then, it becomes evident to him, that parallelograms on the same base and between the same parallels are equal ; and he cannot even conceive the contrary. When he has a little further cultivated his geometrical... | |
 | Pierre Simon de Marquis Laplace, Thomas Young - 1821 - 372 sider
...DCB (105), and A BC is common, therefore they are equal (102), and AB=CD, and AC=BD. 115. THEOREM. Parallelograms on the same base, and between the same parallels, are equal. ABC __ T> Since AB=CD, botli being cqnal to EF, AC=BD (15, or 16), and the triangle AEC is equiangular... | |
 | Walter Henry Burton - 1828 - 84 sider
...ix. jj_ The next proposition is very important, and the truth of it is not obvious at first sight. Parallelograms on the same base, and between the same parallels, are equal. A.. I perceive that it is so in your first figure, where the diagonal of one parallelogram serves for... | |
 | John Playfair - 1829 - 210 sider
...the figure is a parallelogram, therefore the opposite angles are equal. PROPOSITION XXXV. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another; that is, their surfaces are equal. Let the parallelograms ABCD, DBCF be on the same... | |
 | Euclides - 1833 - 304 sider
...other, as being together with these equal angles = to two right angles (prop. 29.) PROP. 35, THEOR. Parallelograms on the same base and between the same parallels are equal. Connect the sides opposite the base, (if necessary,) then there are two triangles formed (viz. the... | |
 | Alexander Smith (M.A.) - 1835 - 750 sider
...and the mathematicians teach us that the three angles of a triangle are equal to two right angles ; that parallelograms on the same base, and between the same parallels, are equal, and the like ; and they likewise teach us why this is true ; ie they shew how these truths necessarily... | |
 | Alexander Smith - 1835 - 350 sider
...and the mathematicians teach us that the three angles of a triangle are equal to two right angles ; that parallelograms on the same base, and between the same parallels, are equal, and the like ; and they likewise teach us why this is true ; ie they shew how these truths necessarily... | |
 | George Darley - 1836 - 172 sider
...common to the two triangles ABC, BDC. Hence, by ART. 7, these triangles are equal. This, &c. ART. 23. Parallelograms on the same base, and between the same parallels, are equal. A JS D IT Let A BCD, EBCF, be two parallelograms on the same base BC, and between the same parallels... | |
 | Euclid, James Thomson - 1837 - 410 sider
...preceding books. 1. Thus it was proved in the 37th proposition of the first book, that all triangles on the same base, and between the same parallels, are equal in area : and hence, if only the base and area of a triangle be given, its vertex may be at any point in a... | |
 | Scotland free church, gen. assembly - 1847 - 554 sider
...the same point in the given line. GEOMETRY -3D CLASS. Define a parallelogram, and similar figures. Prove that parallelograms on the same base and between the same parallels are equal. The square on one side of a triangle is equal to the squares on the other two sides, what kind of a... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
