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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 Adapted to Modern Methods in Geometry - Page 50
by Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 216 pages
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...AD is therefore parallel to BF. Wherefore, equal triangles upon, &c. QED PROPOSITION XLI. THEOREM. If a 'parallelogram and a triangle be upon the same...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...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...PROPOSITION XXVIII. — THEOREM. If a parallelogram ABCD, and a triangle A n E EBC, be upon the same base BC, and between the same parallels, the parallelogram is double of the triangle. For, join AC, and the AABC is = the AEBC, (Prop. 26), but the CZ7ABCD is double of tinAABC (Prop. 24),...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...parallel to BF : Therefore AD is parallel to BF. Wherefore, Equal triangles S,c. QED PROP. XLI. THEQR. If a parallelogram and a triangle be upon the same...and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCB and the triangle EEC be upon the game base...
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A course of practical geometry for mechanics

W. PEASE - 1846 - 86 pages
...before,) join IE, when AIE shall be the right-angled triangle sought. Reason : " If a parallelogram and triangle be upon the same base, and between the same parallels, the parallelogram is double the triangle." But the base AB is only half of the base AE ; therefore ADE is equal to ABC D. EXAMPLES....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...demonstrated that there is no other parallel to it but AD ; AD is therefore parallel to BF. 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 parallelogram ABCD and the tri- \ ~r\...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 pages
...unequal to EF, ie it is = to it. Wherefore trapeziums &c. — QED PROP. XLI. THEOR. GEN. ENUN. — If a parallelogram and a triangle be upon the same...parallels, the parallelogram is double of the triangle. PART. ENUN. — Let the A j .,. nm ABCD and the A EBC be upon the same base BC, and between the same...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1847 - 340 pages
...upon the same base, and between the same parallel ; the parallelogram is double of the triangle. D 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 ;...
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Minutes of the Committee of Council on Education: with Appendices, Volume 1

Great Britain. Committee on Education - Education - 1848 - 514 pages
...extent of Palestine, and what was its population in the time of David? GEOMETRY.— (Inverness.) 1. If a parallelogram and a triangle be upon the same...same parallels, the parallelogram is double of the trianslc. 2. The sum of the squares of the diameters of any parallelogram is equal to the sum of the...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...same straight line, and towards the same parts, are between the same parallels. PROP. XLI. THEOREM. If a parallelogram and a triangle be upon the same...and between the same parallels ; the parallelogram shall be double of the triangle. PROP. XLII. PROBLEM. To describe a parallelogram that shall be equal...
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Report of the Committee of Council on Education (England and Wales ..., Issue 1

Great Britain. Council on Education - Education - 1848 - 532 pages
...diameters of any parallelogram is equal to the sum of the squares of the sides of the parallelogram. 1. If a parallelogram and a triangle be upon the same base, and betweerf the same parallels, the parallelogram is double of the triansle. 3. In a circle, the angle...
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