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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Inventional Geometry: A Series of Problems, Intended to Familiarize the ... - Página 43
por William George Spencer - 1877 - 97 páginas
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 páginas
...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 Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 páginas
...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....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...the 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...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...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,...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...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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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 páginas
...; and by the same ART. CGHD is also equal to CABD. Hence, EABF is equal to CGHD. This, &c. ART. 25. Triangles upon the same base and between the same parallels are equal. on the same base AC, and between —-77 the same parallels AC, DF. Then these triangles are equal....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 471 páginas
...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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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 páginas
...the same 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 páginas
...the parallelogram AC is equal (I. ax. 1.) to EG. Wherefore parallelograms, &c. PROP. XXXVII. THEOR.* 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 ; ABC is...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 páginas
...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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