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" If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ...
by John Mason Good - 1813
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The Principles and Practice of Arithmetic: Comprising the Nature and Use of ...

John Hind - Arithmetic - 1840 - 224 pages
...Elements, that " Proportion is the Similitude of Ratios; and theJirst of four magnitudes is said to have the same ratio to 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 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
...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 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
...Definition of proportion according to Euclid, (Def. V., Book " The first of four magnitudes is said to have the same ratio " to the second, which the third has...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
...Geometrical Definition of Proportion. (Euclid, book v. def. 5). The first of four magnitudes is said to have the same ratio to the second which the third has to...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...mB=mnC, and by hypothesis A=mB, therefore A=wmC 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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A Treatise on Algebra: Arithmetical algebra

George Peacock - Algebra - 1842
...of the second, the multiple of the thii will be equal to that of the fourth : and if the multiple of first be less than that of the second, the multiple of the will be less than that of the fourth. It is this proposition which is deduced as a necessary consequence...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION XIV. THEOR. — If the first has the same ratio to the second which the third has to the fourth; then, if the first be greater than the third, the second shall be greater than the fourth ; and if...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED COB. 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 shall have the*same ratio to the second...
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