| Cambridge Philosophical Society - Philosophy - 1842 - 458 pages
...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 - Celestial mechanics - 1821 - 372 pages
...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 - Astronomy - 1828 - 84 pages
...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 - Geometry - 1829 - 210 pages
...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 pages
...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 pages
...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 - Ethics - 1835 - 350 pages
...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 - Euclid's Elements - 1836 - 172 pages
...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 pages
...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... | |
| Education - 1843 - 582 pages
...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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