 | Robert Simson - 1806 - 546 σελίδες
...Therefore, if the first, &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...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 each of them the same ratio to C, and... | |
 | John Playfair - 1806 - 320 σελίδες
...above, D is the same 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 ; and the same magnitude has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other;... | |
 | Euclid - 1810 - 554 σελίδες
...the first, &c. QED 1 a Cor. 4. 5. b A. 5. See the figure at the loot of the preceding page. cB. 5. PROP. VII. THEOR. EQUAL magnitudes have the same ratio to the same magnitude; and the same ha§ the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other. A and B... | |
 | Euclides - 1816 - 588 σελίδες
...B : Therefore, if 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...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 each. of them the same... | |
 | John Playfair - 1819 - 350 σελίδες
...the same multiple 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...and the same has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other; A : C : : B : C. Let mA, mB, be any equimultiples... | |
 | John Mason Good - 1819 - 800 σελίδες
...a multiple, or part of the second ; the third is the same multiple, or the same part of the fourth. Prop. VII. Theor. Equal magnitudes have the same ratio to the same mapnituilc ; and the same im. magnitude is to the secend of the first rank, haï the same ratio tu... | |
 | Euclid, Robert Simson - 1821 - 514 σελίδες
...part of D, that A is of B; therefore, if the first, &c. QED PROP. VII. THEOR. EQUAL magnitudes h<jve the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes. t» Let A and B be equal magnitudes, and C any other. A and B have each of them the same ratio to C;... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...equal to -, that 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...and that C has the same ratio to A and B. Because hy hypothesis A=B, therefore by division g-=p-; that is, A : C : : B : C. Again, since by hypothesis... | |
 | Euclides - 1826 - 226 σελίδες
...— bm is the same multiple of m as a — bn is of n. Q. к. D. 8.5. • PROPOSITION VII. THEOREM. Equal magnitudes have the same ratio to the same magnitude, and the same magnitude has the same ratio to equal magnitudes. Let A, B, be equal magnitudes, and c some other magnitude,... | |
 | Euclid - 1826 - 234 σελίδες
...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, and the same magnitude has the same ratio to equal magnitudes. Let A, B, be equal magnitudes, and с some other... | |
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Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes. 
