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" If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle. "
Elements of Euclid [selections from book 1-6] adapted to modern methods in ... - Page 50
by Euclides - 1874
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 351 pages
...parallelogram and a triangle be upon the fame bafe, and between the fame parallels ; the parallelogram fhall be double of the triangle. Let the parallelogram ABCD and the triangle EBC be upon the fame bafe BC, and between the fame parallels BC, AE ; the parallelogram ABCD is double of the triangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 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...and the triangle EBC be upon the same base BC, and between the same parallels BC, AE ; the parallelogram ABCD is double of the triangle EEC. Join AC ;...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 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 - 518 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 - 528 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 - Euclid's Elements - 1819 - 333 pages
...it but AD ; AD is therefore parallel to BF. Wherefore equal triangles., tc. Gi. ED PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same...Let the parallelogram ABCD and the triangle EBC be upoa the same base BC, and between the same parallels BC, AE ; the parallelogram ABCD A. DE is double...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 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...triangle. Let the parallelogram ABCD and the triangle EEC be upon the iiime base BC, and between^he same parallels BC,AE; the parallelogram ABCD &_ DE is...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...parallelogram and triangle be upon the same base, and between the same. parallels; the parallelogram shall be double of the triangle. , Let the parallelogram ABCD...and the triangle EBC be upon the same base BC, and between the same parallels BC, AE; the parallelogram ABCD is double of the triangle EBC. Join AC; then...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 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 - 272 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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