| John Playfair - 1806 - 320 ÆäÀÌÁö
...multiple of C. Therefore C is the same part of D that A is of B. Therefore, &c. QED PROP. VII. THEOR. EQUAL magnitudes have the same ratio to the same magnitude...magnitude has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other; A : C ; : B : C. Let >»A, wB be any equimultiples of A... | |
| Robert Simson - 1806 - 546 ÆäÀÌÁö
...&c. QED aCor.4.5. b A. 5. See the figure at the foot of the preceding page. cB. 5. PROP. VII. THEOR. EQUAL magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other. A and B have... | |
| Euclides - 1816 - 588 ÆäÀÌÁö
...the firsX, &c. QED D'A.5. See the figure at the loot of the preceding page. 'B.5. PROP. VII. THEOR. EQUAL magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes. * « " • • Let, A and B be equal magnitudes, and C any... | |
| John Playfair - 1819 - 350 ÆäÀÌÁö
...of C, and therefore C is the same part of D that A is of B. Therefore, &c. Q, ED PROP. VII. THEOR. Equal magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other; A : C : :... | |
| James Ryan - 1824 - 550 ÆäÀÌÁö
...same integer, and therefore rA, rB, are the same parls of A and B. ^7 QED "7 *>,/fy PROP. VII. THEOR. Equal magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes. DEMONSTRATION. Let A and B be any two equal magnitudes, and... | |
| James Ryan, Robert Adrain - 1824 - 542 ÆäÀÌÁö
...is, to the same integer, and therefore rA, rB, are the same parts of A and B. Q, ED PROP. VII. THEOR. Equal magnitudes have the same ratio to the same magnitude ; and the same has the same ratio to equal magnitudes. DEMONSTRATION. Let A and B be any two equal magnitudes, and... | |
| Euclides - 1826 - 226 ÆäÀÌÁö
...— bm is the same multiple of m as a — bn is of n. Q. ¬Ü. D. 8.5. • PROPOSITION VII. THEOREM. Equal magnitudes have the same ratio to the same magnitude,...has the same ratio to equal magnitudes. Let A, B, be equal magnitudes, and c some other magnitude, then A, B, have the same ratio to c, and also c has... | |
| Euclid - 1826 - 234 ÆäÀÌÁö
...b times in n, a — bm is the same multiple of m as a —bn is of n. QKD PROPOSITION VII. THEOREM. Equal magnitudes have the same ratio to the same magnitude,...has the same ratio to equal magnitudes. Let A, B, be equal magnitudes, and ¬ã some other magnitude, then A, B, have the same ratio to ¬ã, and also c... | |
| Robert Simson - 1827 - 546 ÆäÀÌÁö
...that is, C is the same part of D, that A is of B. Therefore, if the first, &c. QED PROP. VII. THEOR. Equal magnitudes have the same ratio to the same magnitude : and the same has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other. A and B shall... | |
| Euclid, Dionysius Lardner - 1828 - 542 ÆäÀÌÁö
...the same submultiple of D that A is of B. ABCD EP ABCD PROPOSITION VII. THEOREM. (484) and of n A EB Equal magnitudes have the same ratio to the same magnitude : and the same has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other. A and B shall... | |
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