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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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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 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. Let the parallelogram ABCD and the triangle EBC be upon the same base...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1849 - 332 pages
...XLl. 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- A y» « angle EBC be upon the same base BC and =^- -*" between the same parallels BC, AE ; the...
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An elementary course of practical mathematics, Part 2

James Elliot - 1851 - 152 pages
...the given triangle. PROPOSITION LIX. THEOREM. If a Parallelogram and a Triangle are upon equal Bases, and between the same Parallels, the Parallelogram is double of the Triangle. EXERCISE 1. Draw any triangle, and make a parallelogram equal to it. 2. Make a triangle whose area...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...triangles, &c. QED BOOK I. * xxxi. 1. b xxxviii. 1. BOOK I. PEOP. 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. Let the parallelogram ABCD and the triangle EEC be upon the same base...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...but AD; therefore 4. AD is parallel to BF. Wherefore, equal triangles, &c. aED 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. Let the parallelogram ABCD and the triangle EBC be upon the same base...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...area to half the same. PROPOSITION XII. THEOREM. — If a -parallelogram (ABCD) and, a triangle (E BC) be upon the same base, and between the same parallels, the parallelogram is double of the triangle. CONSTRUCTION. Draw the diagonal AC. DEMONSTRATION. Then, because the two triangles ABC and EBC are...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...and a triangle be on the same base and between the same parallels : then the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle EBC be on the same base BC, and between the same parallels BC, AE. Then the parallelogram ABCD shall be double...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...parallel to bf Wherefore equal triangles, ta. QED 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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...between the same parallels ; the parallelogram shall be double of the triangle. Let the paralellogram 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Geometry - 1853 - 336 pages
...that there is no other parallel to it bul AD ; AD is therefore parallel to BF. , / ' PROP. XLfTTHEOR. If a parallelogram and a triangle be upon the same base, and betioeen the same parallel ; the parallelogram is double of the triangle. D Let the parallelogram ABCD...
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