 | Robert Simson - Trigonometry - 1806 - 546 pages
...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 - Mathematics - 1806 - 320 pages
...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 - Geometry - 1810 - 554 pages
...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 pages
...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 - Circle-squaring - 1819 - 350 pages
...above, D is 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...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 Playfair - 1819 - 354 pages
...the same multiple of C, and 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...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 pages
...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 - Geometry - 1821 - 514 pages
...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 - Algebra - 1824 - 550 pages
...that is, to the 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...and that C has the same ratio to A and B. Because by hypothesis A=B, AB therefore by division pr^p"! that is, A : C : : B : C. Again, since by hypothesis... | |
 | James Ryan - Algebra - 1826 - 430 pages
...integer, and therefore rA, rB, are the same parts of A and BQED PROP. VII. THEOR. Equal magnitudes hare the same ratio to the same magnitude ; and the same...and C any other, we are to prove that A and B have ea<-b the same ratio to C, and that C has the same ratio to A and B. Because by hypothesis A=B, .1.... | |
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Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes. 
