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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
The Elements of Plane Geometry ... - Page 101
by Association for the improvement of geometrical teaching - 1884
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Transactions of the Cambridge Philosophical Society

Cambridge Philosophical Society - Philosophy - 1842 - 458 pages
...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...
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Elementary Illustrations of the Celestial Mechanics of Laplace: Part the ...

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...
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Dialogues on the First Principles of the Newtonian System, Volume 4

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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

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...
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The Philosophy of Morals: An Investigation by a New and Extended ..., Volume 1

Alexander Smith - Ethics - 1835 - 350 pages
...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...
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The philosophy of morals

Alexander Smith (M.A.) - 1835 - 750 pages
...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...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

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...
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General Report on Public Instruction in the Bengal Presidency

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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Proceedings

Scotland free church, gen. assembly - 1847 - 554 pages
...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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