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" If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle. "
Skeleton propositions &c. of Euclid, books i and ii, with references, by H ... - Pagina xl
door Euclides - 1868
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 pagina’s
...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- AT*...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...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 base, and between the same parallels ; the parallelogram shall be iluu'ile of the triangle. Let the parallelogram ABCD and the...
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The First Six Books of the Elements of Euclid: With a Commentary and ...

Dionysius Lardner - 1838 - 332 pagina’s
...triangles have two sides, and the included angle respectively equal, the two triangles are equal. b If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double of the triangle. Proposition. In a right-angled triangle the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 pagina’s
...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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 pagina’s
...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 base, and between the same parallels; the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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 base, and between the same parallels; the parallelogram shall be double of the triangle. Let the parallelogram ABCD, and the triangle...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 pagina’s
...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 base, and between the same parallels, the parallelogram is double of the triangle. Let the parallelogram ABCD and the triangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 pagina’s
...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 Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 base, and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCB and the triangle...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847
...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 base, and between the same parallels, the parallelogram is double of the triangle. PART. ENUN. — Let the A j .,. nm ABCD and...
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