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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
Examination Papers for Science Schools and Classes - Page 23
by Great Britain. Education Department. Department of Science and Art - 1882
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...the opposite sides are parallel, and the diagonal joins opposite angles. DEMONSTRATION. — P. 35. Parallelograms on the same base and between the same parallels are equal. P. 34. The opposite sides and angles of parallelograms are equal, and the diameter bisects them. Ax....
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...simple interest ? Euclid 1. The greater side of every triangle is opposite to the greater angle. 2. Parallelograms on the same base and between the same parallels are equal to one another. VOLUNTARY PORTION. (1 .) "When are two magnitudes said to be equimultiples of two other...
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On the Philosophy of Discovery: Chapters Historical and Critical

William Whewell - Philosophy - 1860 - 604 pages
...himself with the first twenty-rix 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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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...intervenes ; 5, to divide a / — 7 into two eq. pts. from a • in one of the sides, &c. 35. 113. Parallelograms on the same base and between the same parallels are equal, or rather equivalent, to one another. SCH. — The equality of / 7s proved by the Method of Indivisibles....
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Christmas examinations [examination papers].

Dublin city, academic inst - 1862 - 32 pages
...line apply a parallelogram equal to a given triangle, and having an angle equal to a given one. 3. Parallelograms on the same base and between the same parallels are equal. 4. Suclid says the external angles of any rectilinear figure are together equal to two right angles...
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Responsions

University of Oxford - Education, Higher - 1863 - 316 pages
...rectangle contained by the whole and one of the parts may be equal to the square on the other part. 9. Parallelograms on the same base and between the same parallels are equal to one another. 10. In any right-angled triangle, the square which is described on the side subtending...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...parallelogram ACDB into two equal parts. Wherefore, the opposite sides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...parallelogram ACDB into two equal parts. Wherefore, the opposite aides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the sameparallels...
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Induction

Alexander Bain - Logic - 1870 - 478 pages
...of Deduction. Let us assume that a certain proposition has been arrived at, "no matter how, say, ' Parallelograms on the same base, and between the same parallels, are equal.' Now any one considering this proposition might readily see, that the axiom of mediate equality applied...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...the four triangles, into which a parallelogram is divided by its diagonals, are equal to each other. Parallelograms on the same base and between the same parallels are equal. Let the OĢ ABCD, EBCF be on the same base BC, and between the same \\s AF, BC. Then must rjABCD= CASE...
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