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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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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 pagina’s
...AD (Bk. IV. Prop. 9) ; therefore the area of ABC is half the rectangle of BC and AD. Corollary. — If a parallelogram and a triangle be upon the same base and between the same parallels, the area of the triangle will be half the area of the parallelogram. PROPOSITION 1r. If...
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Elements of geometry, containing the first two (third and fourth ..., Deel 1

Euclides - 1871
...middle points of the sides of a triangle, divide it into four equal triangles. PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram it double of the triangle. Let the rjABCD and the A EBC be on the same...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - 1872
...parallel to AE, the line CF, which joins the vertices of the As, must be that line. PROPOSITION XLI. If a parallelogram and a triangle be upon the same base and between the same parallels (or have the same altitude), the parallelogram is the double of the triangle. For the construction...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 pagina’s
...points of the sides of a triangle, divide it into four equal triangles. PROPOSITION XLI. THEOREM. Jf a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double if the triangle. Let the EJABCD and the &EBC be on the same...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...therefore 4. AD is parallel to BF. Wherefore, equal triangles upon, &c. QED 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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Pure mathematics, Volume 1

Edward Atkins - 1874
...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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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...and DBF are both equal to ABC, which is impossible (Ax. 9.) PROP. XXXII. —THEOREM. (Euc. I. 41.) 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, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pagina’s
...except AD ; Therefore AD is parallel to BF. Therefore, eqxial 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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A graduated course of problems in practical plane and solid geometry

James Martin (of the Wedgwood inst, Burslem.) - 1876
...Ax. 7. From the foregoing notes the truth of the following theorem will be readily seen : — (E.) " If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogram shall be double of the triangle " (in area).— Euc. I., 41. Ex. ABCD...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1876 - 349 pagina’s
...middle points of the sides of a triangle, divide it into four equal triangles. PROPOSITION XLL THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is doubk of the triangle. Let the CU ABCD and the A EBC be on the same...
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