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" ... multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth... "
Elementary Algebra - Page 232
by James Hamblin Smith - 1870
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...the third is also equal to that of the fourth; or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. 6. Magnitudes which have the same ratio are called proportionals. NB When four...
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A Philosophical and Mathematical Dictionary: Containing an ..., Volume 2

Charles Hutton - Astronomy - 1815 - 686 pages
...third is also equal to that of the fourth ; or if when the multiple of the first is greater than that of the second, the multiple of the third is also greater than that of the fourth : then, the first X)f the four magnitudes shall be to the second as the third to...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 456 pages
...the third is also equal to that of the fourth ; or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." This definition, however perplexed and verbose, is yet easily derived from that...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...also equal to that of the fourth; or, if the multiple of the * SBP note. first be greater than that of the second, the multiple of the third is also greater than that of the fourth. VL Magnitudes which haye the same ratio are called proportionals. NB ' When four...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...the third is also equal to that of the fourth ; or if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. SCHOLIUM. We shall demonstrate towards the close of this essay, that this definition...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...the third is also equal to that of the fourth ; or if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. SCHOLIUM. We shall demonstrate towards the close of this essay, that this definition...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...the third is also equal to that of the fourth ; or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. VI. Magnitudes which have the same ratio are called proportionals. NB ' When four...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...third is also equal to that of the fourth ; or if when the multiple of the first is greater than that of the second, the multiple of the third is also greater than that of the fourth; then, the first of the four magnitudes is to the secoud as the third is to the...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...third is also equal to that of the fourth ; or if when the multiple of the first is greater than that of the second, the multiple of the third is also greater than that of the fourth ; then, the first of the four magnitudes is to the second as the third is to the...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...the third is also equal to that of the fourth : or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. VI. Magnitudes which have the same ratio are called proportionals. 'NB When four...
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