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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 111
by Thomas Perronet Thompson - 1833 - 150 pages
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877 - 72 pages
...two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the same parallels AF, BC ; The parallelogram...
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Inventional Geometry: A Series of Problems : Intended to Familiarize the ...

William George Spencer - Geometry - 1876 - 118 pages
...make two triangles that shall be equal to each other, and yet not similar ? 137. Can you show that all triangles upon the same base and between the same parallels are equal to one another ? 138. Can you place a circle, whose radius is \\ inch, so that its circumference may touch two points...
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Inventional Geometry: A Series of Problems, Intended to Familiarize the ...

William George Spencer - Geometry - 1877 - 108 pages
...make two triangles that shall be equal to each other, and yet not similar ? 137. Can you show that all triangles upon the same base and between the same parallels are equal to one another ? 138. Can you place a circle, whose radius is 1J inch, so that its circumference may touch two points...
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877 - 126 pages
...not intersect, and therefore the construction for the triangle required would fail. 2. Parallelograms upon the same base, and between the same parallels, are equal to one another. Shew that if two triangles have two sides of the one equal to two sides of the other, each to each,...
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John Heywood's complete guide to the standard examinations, consisting of 24 ...

Alfonzo Gardiner - 1878 - 146 pages
...= _. 7. The difference of two numbers is 14, and their sum is 48 : find the numbers. 8. Prove that triangles upon the same base, and between the same parallels, are equal to one another. 9. What do you mean by the " complements of a parallelogram " and by " applying a parallelogram to...
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Complete guide to the certificate and scholarship examinations, by a head ...

J T. Amner - 1878 - 226 pages
...equal to two right angles. What ratio does the angle of a regular hexagon bear to a right angle ? 2. Triangles upon the same base and between the same parallels are equal. A line drawn through the middle points of the sides of a triangle is parallel to the base. 3. In any...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...same reason EFGH is equal to ABGH. Hence ABCD and EFGH are equal (Ax. 1). PROPOSITION VIII.—THEOREM. Triangles upon the same base, and between the same parallels, are equal ABC and ABD have the same base, AB, and be between the same parallels, AB and CD; then will these two...
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Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

James Hamblin Smith - Euclid's Elements - 1879 - 378 pages
...EBCH=CJEFGH, I. 35. v they are on the same base EH and between the same || s ; .: lUABCD=OEFGH. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same...between the same parallels, are equal to one another. O Let A a ABC, DBC be on the same base BC and between the same \\a AD, BC. Then must A ABC= &DBC. From...
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Report of Her Majesty's Civil Service Commissioners, Together ..., Volume 23

Great Britain. Civil Service Commission - 1879 - 622 pages
...same side ; and also the two interior angles on the same side together equal to two right angles. 3. Triangles upon the same base and between the same parallels are equal to one another. Let ABC, ABD, be two equal triangles upon the same base AB, and on opposite sides of it ; if CD be joined...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879 - 474 pages
...ACD B. Therefore, the opposite sides and angles, etc. . QED Proposition XXXV. Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, B C. Then the...
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