| George Darley - 1836 - 172 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.... | |
| John Playfair - 1837 - 332 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... | |
| Euclid, James Thomson - 1837 - 410 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... | |
| Andrew Bell - 1837 - 290 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... | |
| Charles Reiner - 1837 - 246 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... | |
| Euclides - 1837 - 112 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,... | |
| Robert Simson - 1838 - 434 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,... | |
| Thomas Holliday - 1838 - 404 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... | |
| Euclides - 1840 - 82 Seiten
...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.... | |
| Euclides - 1841 - 378 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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