| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...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... | |
| Euclides - 1834 - 518 pages
...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... | |
| Euclid - 1835 - 540 pages
...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... | |
| Mathematics - 1835 - 684 pages
...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 ;... | |
| Mathematics - 1836 - 488 pages
...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.... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...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... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...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... | |
| Charles Reiner - Geometry - 1837 - 246 pages
...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 - Euclid's Elements - 1837 - 112 pages
...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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