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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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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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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 548 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 F the same base BC, and between the same parallels BC, AE; the parallelogram ABCD is double of the...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...and of Triangles which are not equal 1/1 »II respects. (a) If a triangle and a parallelogram stand upon the same base, and between the same parallels, the parallelogram is double of the triangle . 17 (Í») Kvery triangle is equal to the half of a rectangle which has the same base and the same...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 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 the triangle EBC be upon the same base BC and between the same par- A TV T allels BC, AE; the parallelogram ABCD is double of the triangle EBC. Join...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 346 pages
...triangle be upon the same base, and between the same parallel ; the parallelogram is double of tlie 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 AI) E is double of the triangle EBC. Join...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...equal bases &c. Which was to be demonstrated. PROPOSITION XLI. THEOREM, — If a 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...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...; AD is therefore parallel to BF. Wherefore, equal triangles, &c. 9. ED PROPOSITION XLI. THEOR. — 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 base...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...Cor. The squares of equal straight lines are equal to one another: and conversely. PROP. 26. (Eue. i. 41.) If a parallelogram and a triangle be upon...and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle E В С be upon the same...
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