 | Cambridge Philosophical Society - 1842 - 458 pagine
...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 pagine
...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 pagine
...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 pagine
...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 pagine
...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 pagine
...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 pagine
...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 pagine
...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... | |
 | Scotland free church, gen. assembly - 1847 - 554 pagine
...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... | |
 | 1843 - 582 pagine
...are either two right angles, or are together equal to two right angles. 2. Define a parallelogram. Parallelograms on the same base and between the same parallels are equal to one another. Shew that if any quadrilateral figure be bisected by both its diagonals it is a parallelogram.... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
