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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Seite 45
von Euclides - 1838
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877
...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
...= _. 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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Elements of Plane Geometry, Teil 1

Thomas Hunter - 1878 - 132 Seiten
...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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Complete guide to the certificate and scholarship examinations, by a head ...

J T. Amner - 1878
...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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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...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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Report of Her Majesty's Civil Service Commissioners, Together with ..., Band 23

Great Britain. Civil Service Commission - 1879
...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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Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

James Hamblin Smith - 1879 - 349 Seiten
...are on the same base EH and between the same || s ; .: lUABCD=OEFGH. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and 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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A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 Seiten
...angle. 36. Parallelograms upon equal bases and between the same parallels are equal to one another. 37. Triangles upon the same base and between the same parallels are equal to one another. Any point P is taken in the line joining an angular point A of a triangle to the middle point of the...
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Parliamentary Papers, Band 22

Great Britain. Parliament. House of Commons - 1879
...possible ? Show how the construction will fail if the condition is not observed. 4. Parallelograms upon the same base and between the same parallels are equal to one another. 5. In any right-angled triangle the square which is described upon the side subtending the right angle...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...opposite angles : these lines trisect the given line. PROPOSITION XXXV. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the / — 7s ABCD, EBCF be on the same base BC, and between the same ||s AF, BC. Then shall /— 7 ABCD...
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