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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Seite 45
von Euclides - 1838
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 Seiten
...; 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 - 1837 - 318 Seiten
...parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH. P PROP. XXXVII. THEOR. Triangles upon the same base,...between the same 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 Seiten
...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 - 240 Seiten
...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 - 215 Seiten
...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 - 88 Seiten
...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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 Seiten
...PROP. XXXVII. THEOR. TRIANGLES upin the same base, and between the same parallels, are equal to bne another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, E AD F BC : the triangle ABCjs equal to the triangle DBC. Produce AD both witys to the points E, F,...
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A complete treatise on Practical Land-Surveying, etc

Thomas Holliday - 1838 - 80 Seiten
...figure be equal, they will alto be parallel, and the figure will be a parallelogram. 3. Parallelograms upon the same base and between the same parallels are equal to one another. 4. A parallelogram is double the area of a triangle of the same base and altitude. See fig. 22, plate...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...XXXVI. THEOR. Parallelograms on equal bases and between the. same parallels, are equal. DG _H a )•: PROP. XXXVII. THEOR. Triangles upon the same base and between the same parallels, are equal. BC__DP PROP. XXXVIII. THEOR. Triangles upon equal bases and between the same parallels, are equal....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 Seiten
...the same EBCH: therefore the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. Triangles upon the same base,...between the same parallels, are equal to one another. BC, and between the same parallels AD, BC: the triangle ABC shall be equal to the triangle DBC. Produce...
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