| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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... | |
| 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.... | |
| 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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