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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...
Euclidian Geometry - Page 157
by Francis Cuthbertson - 1874 - 349 pages

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

John Playfair - Geometry - 1837 - 332 pages
...7nB=77inC, and by hypothesis A=mB, therefore A=7nnC. PROP. IV. THEOR. If the first 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 the first and third, and any whatever of the second and...

## The Principles and Practice of Arithmetic: Comprising the Nature and Use of ...

John Hind - Arithmetic - 1840 - 252 pages
...in iheJifth Book of Euclid's Elements, that " Proportion is the Similitude of Ratios; and theJirst of four magnitudes is said to have the same ratio...the second, which the third has to the fourth, when any equimultiples whatever of the^rst and third being taken, and any equimultiples whatever of the...

## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...multiples or submultiples which are equal, those pairs of numbers are proportional, or the first has the same ratio to the second which the third has to the fourth. But it must be remembered that there are incommensurable magnitudes, the relative values of which,...

## The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Euclid's Elements - 1841 - 144 pages
...understand this definition before proceeding further. с 2 PROP. IV. THEO. If the first of four magnitudes have the same ratio to the second, which the third has to the fourth, then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples...

## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...the fourth. If, therefore, the first, &c. QED PROP. IV. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples...

## The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Ratio and proportion - 1841 - 140 pages
...a, artd (m — n) b с = b, when m — n = 1. PROP. A. THEO. If the first of the four magnitudes has the same ratio to the second, which the third has to the fourth, then, if the first be greater than the second, the third is also greater than the fourth ; and if equal,...

## The principles of arithmetic. [Followed by] The principles of algebra

Wales Christopher Hotson - 1842 - 306 pages
...:: a + c + e ... : 6 + d +/... 149. Geometrical Definition of Proportion. (Euclid, book v. def. 5). The first of four magnitudes is said to have the same...the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsover of...

## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...the ratio of the third to the fourth. Definition of proportion according to Euclid, (Def. V., Book " The first of four magnitudes is said to have the same...the second, which the third has to the fourth, when any " equimultiples whatsoever of the first and third being " taken, and any equimultiples whatsoever...