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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 - 1819 - 317 pagina’s
...it but AD ; AD is therefore parallel to BF. Wherefore eqaal triangles, tc. Q, ED 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 Arithmetic, Algebra, and Geometry

George Lees - 1826
...parallelograms ; hence triangles upon the same base, and between the same parallels, are equivalent. Cor. 2. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double of the triangle. Cor. 3. Equivalent triangles upon the same...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 pagina’s
...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 bet-ween the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram A BCD and the...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...; AD is therefore parallel to BF. Wherefore, equal triangles, &c. 9. ED PROPOSITION XLI. THEOR. — 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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...The squares of equal straight lines are equal to one another: and conversely. PROP. 26. (Eue. i. 41.) 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 System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 pagina’s
...way, it may be proved that BG is not greater than EH. Hence BG and EH are equal. This, &c. ART. 31. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double of the triangle. on the same base AC as the triangle ABC, and...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 pagina’s
...side of bases, which are equal and in the same straight line, are between the same parallels. XLI. If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle. XLIII. The complements of the parallelograms...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 pagina’s
...parallel to BF, but AD: AD is therefore parallel to BF. Wherefore 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 A BCD and the triangle...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 pagina’s
...= greater, which shows the supposition to be false, 3. that .'. AD || BF. 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. Proved by showing that C3m BD = 2 A ABC,...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 pagina’s
...are equal ; and if the areas and altitudes be equal, the bases are equal. 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. X 3<5 ELEMENTS OF PLANE GEOMETRY. AE,...
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