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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, based on Euclid, book i

Edward Atkins - 1877
...except AD ; Therefore AD is parallel to BF. Therefore, equal triangles, &c. Proposition 41. — 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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An elementary Greek grammar

James Hamblin Smith - 1878
...8vo. 3*. dd. LONDON, OXFORD, AND CAMBRIDGE. Book I.] PROPOSITION XLI. 67 PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double of Hie triangle. Let the ГЗ ABCD and the д ЕВС be on the...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...the parallelogram BF. Therefore, parallelograms upon the same &c. QED PROP. xiii. THEORE^T. (EI 41.) If a parallelogram and a triangle be upon the same base and between, the sami parallels, the parallelogram is double of the triangle. First, let ABCD be a "parallelogram and...
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A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 pagina’s
...parallels. Are the angles of these triangles equal, each to each? 41. Define a parallelogram. Prove that if a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle. Same proposition. Hence deduce that two...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...is parallel to B F. Therefore, equal triangles upon equal bases, etc. 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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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...intersection of the diagonals of a parallelogram will divide the parallelogram into two equal parts. 3. If a parallelogram and a triangle be upon the same base and upon the same parallels, the parallelogram shall be double of the triangle. Prove also the converse...
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The pupil teachers' handy mathematical and grammatical question-book, with key

Pupil teachers - 1880
...parallels. Are the angles of these triangles equal, each to each ? 41. Define a parallelogram. Prove that if a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle. Same proposition. Hence deduce that two...
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Moffatt's reprint of pupil teachers' questions, arranged by ed. of 'Papers ...

Moffatt and Paige - 1881 - 1880 pagina’s
..., +.] 1. Straight lines which are parallel to the same straight line are parallel to each other. 2. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. 3. If ABCD be a parallelogram and P...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...The argument would then rit I oc the *hsurdity of the l?is tri.-oigie being equal to the greater. D If a parallelogram and a triangle be upon the same base, and between tame parallelt , the parallelogram is double of the triangle, Let the parallelogram BD, and the triangle...
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The Cambridge Examiner, Volume 2

1882
...length between two given straight lines which meet so that it shall be equally inclined to each. 9. If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogram is double of the triangle. 10. Divide a given straight line into two parts,...
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