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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Elements of Plane Geometry - Page 57
by Thomas Hunter - 1878 - 132 pages
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...a parallelogram is divided into two equal parts by either of its diagonals. (Prop. XXXIV.) 2. That parallelograms upon the same base and between the same parallels are equal. (Prop. XXXV.) 3. That the halves of equals are equal. (Ax. VIII.) Let ABC and ABD be two As upon the...
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Introduction to quaternions, by P. Kelland and P.G. Tait

Philip Kelland - 1873 - 248 pages
...Ex. 1, Art. 7, DA=a-ß; and, changing all the signs, we get (20) for the corresponding lines, Ex. 4. Parallelograms upon the same base and between the same parallels are equal. It is necessary to remind the reader of what we have already stated, that examples such as this are...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...parallelogram ABCD into two equal parts. Therefore, the opposite sides, <fec. QED Proposition 35. — Theorem. Parallelograms upon 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 same parallels...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...diameter BC divides the parallelogram ACDB into two equal parts. ~ QED PROPOSITION 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels...
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The American House-carpenter: A Treatise on the Art of Building, and the ...

Robert Griffith Hatfield - Architecture - 1874 - 452 pages
...is equal to the parallelogram, B. a tt « / Fie. 103. 145. — Proposition. Parallelograms standing upon the same base and between the same parallels, are equal. Let abed and cfcd, (Fig. 103,) be given purallelograms, standing upon the same base, cd, and between the...
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Edinburgh Medical Journal, Volume 21, Part 1

Medicine - 1876 - 610 pages
...contained angles are equal, and if the third sides are unequal, the contained angles are unequal. 3. Parallelograms upon the same base and between the same parallels are equal. 2. If a straight line falling upon two other straight lines makes the alternate angles equal, those...
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A graduated course of problems in practical plane and solid geometry

James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pages
...student enters on the following problems he should thoroughly master the subjoined theorems.) (A.) "Parallelograms upon the same base, and between the same parallels, are equal to each other" (in area). — Euc. I., 35. Ex. ABCD, DBCF— NOTE 1. — " Between the same parallels...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 pages
...side together equal to two right angles, the two straight lines shall be parallel to one another. 8. Parallelograms upon the same base, and between the same parallels, are equal to one another. Are the parallelograms equal in all respects ? 1. Simplify 1£ — | -j 1 — *-(*—...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...parallelogram ABCD into two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms upon 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 same parallels...
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877 - 72 pages
...parallelogram ABCD into two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms upon 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 same parallels...
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