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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: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...BF. Wherefore, " equal triangles," &c. QED PROP. XLI. THEOR. If a parallelogram and a triangle are upon the same base, and between the same parallels ; the parallelogram is double the triangle. a 37. I. Let the parallelogram ABCD and the triangle EBC be up- Book I. on the same base...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...to BF. Wherefore, " equal triangles" &c. QED PROP. XLI. THEOR. If a parallelogram and a triangle are upon the same base, and between the same parallels ; the parallelogram is double the triangle. DE Let the parallelogram ABCD and the triangle EBC be up- Book I. on the same base BC,...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 172 pages
...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...parallels, the parallelogram is double of the triangle. on the same base AC as the triangle ABC, and between the same parallels AC, BE. Then ACED is double...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...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...parallels; the parallelogram is double of the triangle. XLIII. The complements of the parallelograms which are about the diameter of any parallelogram, are...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...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...parallelogram is double of the triangle. Let the parallelogram A BCD and the triangle EBC be upon the same base BC, and between the same parallels BC, AE; the parallelogram...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...= 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...and between the same parallels; the parallelogram shall be double of the triangle. Proved by showing that C3m BD = 2 A ABC, which = 2 A EBC. PROPOSITION...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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...and between the same parallels, the parallelogram shall be double of the triangle. X 3<5 ELEMENTS OF PLANE GEOMETRY. AE, the parallelogram ABCD is double...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...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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The First Six Books of the Elements of Euclid: With a Commentary and ...

Dionysius Lardner - Geometry - 1838 - 382 pages
...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...parallels, the parallelogram is double of the triangle. Proposition. In a right-angled triangle the square of the hypotenuse is equal to the sum of the squares...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...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...and between the same parallels ; the parallelogram shall be iluu'ile of the triangle. Let the parallelogram ABCD and the A triangle EBC be npon the same...
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