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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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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...same EBCH : Therefore also the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED Proposition, XXXVII. Theorem. Triangles upon the same base, and between the same parallels, are eqnal to one another. Let the triangles ABC,DBC, be upon the same base BC, and between the same parallels...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC, be constituted upon the same base вс, and between the same parallels AD, вс. The triangle...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. 3i. i. parallel to сл, " and through c draw CF, parallel to в D. Therefore each of them EBCA,...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...diameter BC divides the parallelogram ACDB into two equal parts.' ei. ED PROP. XXXV. THEOR. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parnllelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC : the parallelogram...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 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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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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...triangle d 7. Ax. DBC. Wherefore, " triangles," &c. QED PROP. XXXVIII. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : The triangle ABC is equal to...
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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 to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels, AD, BC : The triangle ABC is equal to...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 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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