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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... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 105
by Euclides - 1816 - 528 pages
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...the sixth, is of the fourth D. If, therefore, &c. PROP. IV. THEOR. IF the first of four magnitudes have the same ratio to the second which the third has to the fourth ; then any like multiples whatever of the first and third have the same ratio to any like multiples...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 318 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...
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The Elements of Algebra: Designed for the Use of Students in the University

John Hind - Algebra - 1837 - 539 pages
...there being taken any equimultiples whatever of the first and third, and any equimultiples whatever of the second and fourth : if the multiple of the first be greater than the multiple of the second, the multiple of the third will be greater than that of the...
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The Principles and Practice of Arithmetic: Comprising the Nature and Use of ...

John Hind - Arithmetic - 1840 - 224 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 third has to the fourth, when any equimultiples whatever of the^rst and third being taken, and any equimultiples whatever of the second anA fourth...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...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,...
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Euclid's Elements - 1841 - 98 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...
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - Ratio and proportion - 1841 - 98 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,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...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...second and " fourth ; if the multiple of the first be equal to, greater " than, or less than the multiple of the second, the multiple " of the third is also...
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The principles of arithmetic. [Followed by] The principles of algebra

Wales Christopher Hotson - 1842
...:: 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...first and third being taken, and any equimultiples whatsover of the second and fourth ; if the multiple of the first, be less than that of the second,...
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