 | Euclides - 1855 - 230 σελίδες
...BSEM.O, or-. E (a) Hvpoth. D F (b) V.'cor. 4. (c) VA ABCD (d) V. B. PROPOSITION VII. THEOEEM.—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 each of them have the same ratio to... | |
 | Eucleides - 1860 - 396 σελίδες
...m' Hypoth. V. cor. 4. VA and multiplying by 6, B = m . b, or — . . PROPOSITION VII. THEOBEM. — 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 each of them have the same ratio to... | |
 | John Playfair - 1860 - 334 σελίδες
...is shewn above, D is the same multiple of C, and therefore C is the same part of D that A is of B. PROP. VII. THEOR. Equal magnitudes have the same ratio to the same magnitude ; and I In- samtt has the same ratio to equal magnitudes. Let A and B be equal magnitudes, and C any other;... | |
 | Robert Potts - 1860 - 380 σελίδες
...C is the same part of D, that A is of B. Therefore, if the first, &c. QED PROPOSITION VII. THEOREM. Equal magnitudes have the same ratio to the same magnitude : and the raflu has the same ratio to equal magnitude!. Let A and B be equal magnitudes, and Cany other. Then... | |
 | George Sturton Ward - 1862 - 104 σελίδες
...n ie с is the same part of d that a is of b. Therefore, if the first, &c.— QED PROPOSITION VII. Equal magnitudes have the same ratio to the same magnitude...and the same has the same ratio to equal magnitudes. a, b, c. Let a =- b. Then shall a : с ; : b : c, and с : a : : с : b. First, because a = b, therefore... | |
 | Euclides - 1865 - 402 σελίδες
...or a part of the second ; the third is the same multiple, or the same part of the fourth. Prop. 7. Equal magnitudes have the same ratio to the same magnitude...and the same has the same ratio to equal magnitudes. Prop. 8. Of two unequal magnitudes, the greater has a greater ratio to any other magnitude than the... | |
 | Robert Potts - 1865 - 528 σελίδες
...is the same part of D, that A is of B. Therefore, if the first, &c. QEI). PROPOSITION VII. THEOREM. Equal magnitudes have the same ratio to the same magnitude : and the »ame has the same ratio to equal magnitudet. Let A and B be equal magnitudes, and C any other. Then... | |
 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...is, C is the same part of D that ^ is of B. Wherefore, if the first &c. QED PROPOSITION 7. THEOREM. Equal magnitudes have the same ratio to the same •magnitude; and the same hat the same ratio to equal magnitudes. Let yl and B be equal magnitudes, and C any other magnitude:... | |
 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...equal, equal ; if less, less. .'. A is to B as E is to F. . V. Def. 5. QED PROPOSITION VI. (EucL v. 7.) 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 magnitude. Then must Abe to C as Bis to C, and C must... | |
 | Euclides - 1874 - 342 σελίδες
...is the same part of D, that A is of B. Therefore, if the first, &c. QED PROPOSITION 7. — Theorem. 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. Then A and B shall each of them have the same ratio... | |
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Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes. 
