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" Equal magnitudes have the same ratio to the same magnitude; and the same has the same ratio to equal magnitudes. "
An Elementary Treatise on Algebra, Theoretical and Practical ... - Σελίδα 496
των James Ryan, Robert Adrain - 1824 - 516 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 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;...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 σελίδες
...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...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1819
...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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 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;...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...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...

An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - 1826 - 383 σελίδες
...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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