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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 33
by Euclid, John Playfair - 1846 - 317 pages
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...to each other. Therefore, parallelograms &c. QED ED. PROPOSITION XXXVII. THEOREM, Triangles on the same base, and between the same parallels, are equal to one another; that is, their surfaces are equal. Let the triangles ABC, DBC be on the same base BC, and between the...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...a rectangle of the same base and altitude. PROP. 25. (Eue. i. 36.) Parallelograms upon equal bases, and between the same parallels, are equal to one another. Let the parallelogramsABCD, E FGH, be upon equal bases BC, FG, and between the same parallels AH, BG. The parallelogram...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...same EBCH: Therefore also the parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. QED PROP. XXXVII. THEOR. Triangles upon the same base,...parallels, AD, BC: The triangle ABC, is equal to the triangle DBC. Produce AD both ways to the points E, F, and through B draw (31. 1.) BE parallel to CA;and...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...originally meant ' the line determined by a plummet.' PROPOSITION XXXV. THEOREM. — Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms AC, BF, be upon the. same base BC, and between the same parallels AF, BC. The parallelograms...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...and between the same parallels, arc equal to one another. Let the triangles ABC, DBC be upon E AD K the same base BC, and between the same parallels AD, BC : the triangle ABC shall be equal to the triangle DBC. Produce t AD both ways to the points E, F ; and through B, draw...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...EBCH: Therefore also the parallelogram ABCD is equal to EFGH. Wherefore, " pa" rallelograms," &c. QED PROP. XXXVII. THEOR. Triangles upon the same base,...parallels, are equal to one another. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels AD, BC : The triangle ABC is equal to...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...remains (ax. 3.) the complement AE equal to E C. Therefore, &c. PROP. 24. (Eue. i. 35.) Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, E В С F, be upon the same base BG and between the same parallels AF, В С ;...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...EFGH is equal to the same EBCH: Therefore also the parallelogram ABCD is equal to EFGH. PROP. XXXI. THEOR. Triangles upon the same base, and between the same parallels, are equivalent to one another. Let the triangles ABC, DBC be upon the same base BC, and between the flame...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...parallelogram ABCD is equal to EFGH. W||crefore, parallelograms, &c. QED XXXVII. THEOJl. Triangles ufon the same base, and between the same parallels, are equal...parallels, AD, BC : The triangle ABC is equal to the triangle DBC. Produce AD both ways to the points E, F, and through B draw a 31, 1. a BE parallel to...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...Parallelograms upon equal bases, and between the same parallels, are equal to one another. XXXVII. Triangles upon, the same base, and between the same parallels, are equal to one another. XXXVIII. Triangles upon equal bases, and between the same parallels, are equal to one another. XXXIX....
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