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" If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle. "
A System of Popular Geometry: Containing in a Few Lessons So Much of the ... - Page 25
by George Darley - 1836 - 128 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...equal triangles, &c. Q, ED PROP. XLI. THEOR. IF a parallelogram and a triangle be upon the same \V base, and between the same parallels, the parallelogram is double of the triangle. Let the parallelogram ABCD and the triangle EBC be upon the same base BC, and between the same parallels...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...parallel to BF. Wherefore, equal triangles, &c. QED a 31. I PROP. XLI. THEOR. y, IF a parallelogram and triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. Book I. Let the parallelogram ABCD and the triangle EBC be upon v—...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 554 pages
...to BF. Wherefore, equal triangles, &c. QED a 31. 1. b38.I. PROP. XLI. THEOR. IF a parallelogram and triangle be upon the same base, and between the same parallels ; the parallelo, gram shall be double of the triangle. Book I. Let the parallelogram ABCD and the triangle...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...therefore parallel to BF. Wherefore equal triangles, &c. QED PROP. XLI. THEOR. IF a parallelogram and triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. .•BouK I. Let the parallelogram ABCD and the triangle EBC be. '*—...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...it but AD ; AD is therefore parallel to BF. Wherefore eqaal triangles, tc. Q, ED PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same...parallels ; the parallelogram is double of the triangle. Let the parallelogram ABCD and the triangle EEC be upon the iiime base BC, and between^he same parallels...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...parallel to BF. Wherefore equal triangles, &c. QED .Proposition XL/. Theorem. If a parallelogram and triangle be upon the same base, and between the same parallels ; the parallelogiam shall be double of the triangle, j; | Let the parallelogram ABCD and the triangle EBC...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...parallelograms ; hence triangles upon the same base, and between the same parallels, are equivalent. Cor. 2. If a parallelogram and a triangle be upon the same...parallels, the parallelogram is double of the triangle. Cor. 3. Equivalent triangles upon the same base, and upon the same side of it, are between the same...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...it but AD ; AD is therefore parallel to BF. Wherefore equal triangles, &e. QED -f" PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same base, and between the same parallel,; the parallelogram is double of the triangle. Let the paralellogram ABCD and the triangle...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...to it but AD: AD is therefore parallel to BF. Wherefore equal triangles, &c. QED PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same...and bet-ween the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram A BCD and the triangle EBC be upon the same...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...equal bases, and between the same parallels, are equal. If a parallelogram and a triangle stand on the same base and between the same parallels, the parallelogram is double of the triangle. The complements of the two parallelograms which are about the diagonal of any parallelogram are equal...
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