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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
Statistics of Land-grant Colleges and Universities - Σελίδα 227
των United States. Office of Education - 1917
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Transactions of the Cambridge Philosophical Society

Cambridge Philosophical Society - 1842 - 458 σελίδες
...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...

Elementary Illustrations of the Celestial Mechanics of Laplace: Part the ...

Pierre Simon de Marquis Laplace, Thomas Young - 1821 - 372 σελίδες
...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...

Dialogues on the First Principles of the Newtonian System, Τόμος 4

Walter Henry Burton - 1828 - 84 σελίδες
...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...

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

John Playfair - 1829 - 210 σελίδες
...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...

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

Euclides - 1833 - 304 σελίδες
...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...

The philosophy of morals

Alexander Smith (M.A.) - 1835 - 750 σελίδες
...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...

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

Alexander Smith - 1835 - 350 σελίδες
...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...

A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 172 σελίδες
...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...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 σελίδες
...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...

Proceedings

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