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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 for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle EBC be on the same base SC, and between the same parallels BC, AE : the parallelogram ABCD shall be double...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...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...and between the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram ABCD, and the triangle EBC be upon the same...
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Papers for the schoolmaster, Volume 4

1868 - 344 pages
...the least perimeter. 2. Triangles upon the same base, and between the stime parallels, are equal. 3. If a parallelogram and a triangle be upon the same...and between the same parallels, the parallelogram shall be double of the triangle. If through the angles of a parallelogram straight lines be drawn parallel...
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868 - 132 pages
...determinate area when its base and altitude are given. COR. 3. If a parallelogram and a triangle are on the same base and between the same parallels, the parallelogram is double of the triangle. For the parallelogram ACHE is double of the triangle ABC, and therefore of any other triangle DBC which...
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Logic, Volume 1

Alexander Bain - Logic - 1870 - 304 pages
...construction, establish two minors under the proposition — ' A parallelogram and a triangle being on the same base and between the same parallels, the parallelogram is double of the triangle ; ' and then proceed to the main steps, the application of the axioms. We first apply the axiom —...
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The Acharnians: The Knights

Aristophanes - 1870 - 264 pages
...'PROPOSITION XLI. 67 PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same case, and between the same parallels, the parallelogram is double of the triangle. Let the O ABCD and the A EEC be on the same base BO and between the same [|s AE, BC. Then must £7 ABCD be...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...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...and between the same parallels, the parallelogram it double of the triangle. Let the rjABCD and the A EBC be on the same base BCand between the same...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...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 there be two straight...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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,...between the same parallels, the parallelogram is double if the triangle. Let the EJABCD and the &EBC be on the same base .8(7 and between the same IIs AE,...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...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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