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" The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple... "
An Elementary Treatise on Algebra: Theoretical and Practical ... - Σελίδα 331
των James Ryan - 1826 - 383 σελίδες
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 σελίδες
...therefore E is to G, so is c F to H. Therefore, if the first, &c. QED See N. C0R. Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third have the same ra- Boox V. tio to the second...

Easy Introduction to Mathematics, Τόμος 1

Charles Butler - 1814 - 540 σελίδες
...comparison of one number to another is called their ratio ; and when of four giren numbers the first has the same ratio to the second which the third has to the fourth, these four numbers are said to be proportionals. Hence it appears, that ratio is the comparison of...

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

Euclides - 1816 - 588 σελίδες
...the less can be multiplied so as to exceed the other. y. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever...

Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - 456 σελίδες
...in the reduction of equations. According to Euclid, " The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever...

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

John Playfair - 1819 - 354 σελίδες
...= mnC ; whence also mB = mnC, and by hypothesis A = mB, therefore A— m«C. Therefore, &c. Q,. ED PROP. IV. THEOR. If the first of four magnitudes has...ratio to the second which the third has to the fourth, and if any equimultiples whaterer be taken of the first and third, and any whatever of the second and...

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

John Mason Good - 1819 - 800 σελίδες
...the other uf the I'nuiih. Prop. IV. Theor. If the first of four magnitude« ha» the same ratio lo the second which the third has to the fourth; then any equimultiples whatever of the first and third sh.ill have the sain« ratio to any equimultiples of the second and fourth, viz. the equimultiple of...

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

John Playfair - 1819 - 350 σελίδες
...mnC, and by hypothesis A = mB, therefore A~mn C. Therefore, &c. Q, ED PROP. IV. THEOR. If thefirst of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of thefirst and third, and any whatever of the second and...

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

Euclid, Robert Simson - 1821 - 514 σελίδες
...which GH the third, together with the sixth, is of the fourth D. If, therefore, the first, &c. QED PROP. IV. THEOR. IF the first of four magnitudes has...whatever of the first and third shall have the same ratio to any equimultiples of the second and fourlji, viz. ' the equimultiple of the first shall have the...

The First Six Books with Notes

Euclid - 1822 - 222 σελίδες
...controversy among geometers. Euclid defines them thus: The Jirst of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever...

Universal Technological Dictionary: Or, Familiar Explanations of ..., Τόμος 2

George Crabb - 1823 - 704 σελίδες
...15 to 5, which is expressed thus : as 6 : 2 : : 15 : 5. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever...




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