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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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...therefore parallel to BF. Wherefore, equal triangles, &c. QED PROP. XLJ. THEOR. IF a paralellogram 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 figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...side of it, are between the same parallels. PROP. XLI. THEOR. If a parallelogram and a triangle are upon the same base and between the same parallels, the parallelogram is double of the triangle. DF PROP. XLII. PROB. To construct a parallelogram equal to a given triangle, and having an angle equal...
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Lectures Against Socialism: Delivered Under the Direction of the Committee ...

London city mission - Christian socialism - 1840 - 620 pages
...themsehes are unknown." We know, for example, that if a parallelogram and a triangle be constructed on the same base, and between the same parallels, the parallelogram is double of the triangle : (Euc. 1.41 :) though we may know nothing more, whatever, about either of the figures. 2. " Two lines...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...parallelogram and a triangle be upon the same bose, 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 shall be 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 - 1842 - 332 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. ID Let the parallelogram ABCD and the triangle...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 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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A course of practical geometry for mechanics

William Pease - Geometry - 1843 - 80 pages
...BK equal to A B. Join DK, when ADK will be the triangle required. Reason : " If a parallelogram and triangle be upon the same base, and between the same...parallels, the parallelogram is double of the triangle." But the base AB is only half of the base AK ; therefore ADK is equal to ABC D. PROBLEM LXm. Any isosceles...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...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...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. ID PROP....
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...BF, but AD : AD is therefore parallel to BF. Wherefore, if equal triangles, &c. 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 parallels BC, AE ; the parallelogram is double of the triangle. • In this proposition...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...AD : AD is therefore parallel to BF. Wherefore equal triangles, &c. QED PROPOSITION XLI. THEOB. — 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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