 | Euclid - 1845 - 218 σελίδες
...C ; that is, C is the same part of D, that A is of B. Therefore, if the first, &c. QED PROPOSITION 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... | |
 | Euclides - 1845 - 546 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 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... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...the same multiple of C, that is, C is the same part of D, that A is a part of B. It, therefore, &c. PROP. VII. THEOR. — Equal magnitudes have the same ratio to the same magnitude of the same kind: and the same has the same ratio to equal magnitudes of the same kind. ABC DBF DA... | |
 | Euclid, John Playfair - 1846 - 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...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... | |
 | Patrick James Stirling - 1846 - 416 σελίδες
...constantly to the same level. This might be demonstrated as strictly as the mathematical proposition that " equal magnitudes have the same ratio to the same magnitude,...the same has the same ratio to equal magnitudes." Increase the supply of corn, its money price will be depressed, and continue so till mankind (in Paley's... | |
 | Euclides - 1846 - 292 σελίδες
...multiple of C — that is, C is the same part of D that A is of B. Wherefore, If the first %c. QED PROP. VII. THEOR. Equal magnitudes have the same ratio to the same magnitudes : and the same has the same ratio to equal magnitudes. Let A and B be equal magnitudes,... | |
 | Euclides - 1848 - 52 σελίδες
...of the second ; the third is the same multiple, or the same part of the fourth. PROP. VII. THEOREM. Equal magnitudes have the same ratio to the same magnitude;...and the same Has the same ratio to equal magnitudes. PROP. VIII. THEOREM. Of two unequal magnitudes, the greater has a greater ratio to any other magnitude... | |
 | John Playfair - 1849 - 332 σελίδες
...is the same multiple of C, and therefore C is the same part of D that A is of B. PROP. VII. -HHEOR. 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 : : B : C. Let mA, mB, be any equimultiples... | |
 | Euclides - 1853 - 176 σελίδες
...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 same has the same ratio to equal magniiudes. LET a and b be equal magnitudes, and c any other. a and b have each of them the same ratio... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...A is of B. Therefore, if the first, etc. QED B E D r PROPOSITION VII. THEOR. Equal magnitudes hare 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 each of them the same ratio to C, and... | |
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Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes. 
