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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 ... - Strona 35
autor: John Playfair - 1855 - Liczba stron: 318
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - Liczba stron: 150
...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
...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 - Liczba stron: 513
...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 is equal to...
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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, В С ;...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - Liczba stron: 472
...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 - 1837 - Liczba stron: 318
...same EBCH : Therefore also the parallelogram ABCD is equal to EFGH. P PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels,...parallels, AD, BC : The triangle ABC is equal to the trian- jE ' A gle DBC. Produce AD both ways to the points E, F, and through B draw (31. 1.) BE parallel to...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - Liczba stron: 390
...given, however, it is so useful, that the student should be early acquainted with it. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF (figs. 2. and 3.) be upon the same base BC, and between the same parallels...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - Liczba stron: 240
...line, they are between the same parallels. (1. 33, Cor.) PBOPOSITION XXXV. THEOREM. Parallelograms upon the same base and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF (see the 2d and 3d figures), be upon the same base BC, and between the same...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - Liczba stron: 215
...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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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - Liczba stron: 88
...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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