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" PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 36
by Euclid, James Thomson - 1837 - 390 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 516 pages
...BCD, and the diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. PARALLELOGRAMS upon the same base, and between the...to one another.* "Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC; the parallelogram ABCD shall be equal...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...triangle DBC. Wherefore triangles, &c. QED Propoķiķion XXXVIII. Theorem. 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...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 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....
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...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
...and the 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 - 272 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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A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - Astronomy - 1831
...shall be equal to an nth part of the weight of the body. TRINITY COLLEGE, 1827. 1. PARALI/ELLOGRAMS upon the same base, and between the same parallels, are equal to one another. 2. If a straight line be divided in extreme and mean rate, the parts into which it is divided are incommensurable...
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On the study and difficulties of mathematics [by A. De Morgan].

Augustus De Morgan - 1831
...BGHA and BPKD are four- sided figures &c. (Construction.) .-. BGHA and BPKD are parallelograms. IX. Parallelograms upon the same base and between the same parallels are equal. (Proved.) EBAFandBGHA, are parallelograms &c. (Construction.) .•. EBAF and BGHA are equal. X. Parallelograms...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...parallelograms upon equal bases, &c. Which was to be demonstrated. PROPOSITION XXXVII. THEOREM. — Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be upon the same base BC, and between the same paral- EADF lels AD, BC. The triangle...
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