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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 ...

Euclides - 1834
...equal parts. QED PROPOSITION XXXV. THBOR. — Parallelograms upon t he same base, and between See N, the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base See the 2d BC, and between the same parallels AF, BC : the parallelo- and sd...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...former, there 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...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 ; the parallelogram ABCD...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...parallelogram ABCD is equal to EFGH. Wherefore, " pa" rallelograms," &c. QED PROP. XXXVII. THEOR. 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 parallels AD, BC : The triangle ABC...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...equal to one another, and the diameter bisects it, that is, divides it into two equal parts. XXXV. Parallelograms upon the same base and between the same parallels, are equal to one another. XXXVI. Parallelograms upon equal bases, and between the same parallels, are equal to one another. XXXVII....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 471 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...
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Library of Useful Knowledge: Mathematics I.

Mathematics - 1836
...BGHA and 3 PKD 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.) EB AF and BGH A, are parallelograms &c. (Construction.) .: EBAF and BGHA are equal. X. Parallelograms...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...EBCH ; therefore also the parallelogram ABCD is equal to EFGH. PROPOSITION XXXVII. THEOREM. Triangles upon 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 ABO...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 215 pages
...likewise—what ? P.—The same perpendicular height; they have the same altitude. M.—And, since parallelograms upon the same base and between the same parallels are equal to each other, what may be inferred of equal parallelograms which are upon the same base ? P.—Equal...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...and Z CAB = BDC, 3. that whole Z ^BD = whole Z DCA, 4. that A ABC = A BCD. PROPOSITION XXXV. Theorem. Parallelograms upon the same base, and between the same parallels, are equal to each other. (In Jig. 1, the ams are equal, because each is double of A BDC.) Steps of the Demonstration,...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 215 pages
...are about the diagonal of a square are, likewise, squares. 6. Parallelograms and triangles which are upon the same base and between the same parallels are equal to each other. 7. Parallelograms and triangles which are upon equal bases and between the same parallels...
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