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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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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 576 pages
...equimultiples whatever of tiie first and third being taken, and any equimultiples whatever of the 2d iind'4lh ; if the multiple of the first be less than that of the 2(1, the multiple of the 3d is also less than that of the •!• h ; or if the multiple of the I -i...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...treat of propov\\ov\, i the method of PROP. IV. THEOR. -4' •* ,' It'tlictirft 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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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - Algebra - 1824 - 516 pages
...method of demonstration adopted in this essay. 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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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...and С have been taken certain equimultiples K, L ; and of В and О COR. 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 sam ratio to the second and...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - Algebra - 1826 - 383 pages
...that the ratio of C to D is less than the ratio of A ta B. The Fiftli Definition according to Euclid. The first of four magnitudes is said to have the same ratio to the second which the tnird has to the four h, when any equimultiples whatsoever of the first and third being taken, and...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...- Оr r— = — Оr - = -r. QEI. • 1 Ax. 5. PROPOSITION XXIV. THEOREM. If the first magnitude have the same ratio to the second which the third has to the fourth; and the fifth, the same ratio to the second, which the sixth has to the fourth; then the first and...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...— = T- or - = TQKI>. • 1 Ax. 5. be/ e be fe cf PROPOSITION XXIV. THEOREM. If the first magnitude have the same ratio to the second which the third has to the fourth, ; and the fifth, the same ratio to the second, which the sixth has to the fourth ; then the first and...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...greater ratio to the second, than the fifth has to the sixth. PROP. XIV. THEOR. See N. If the Jirst have 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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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 6

Perry Fairfax Nursey - Industrial arts - 1827
...the proposition <>f Euclid. Book 5, " If the first of four magAbGEBBAIUAL BQtATIOX. 537 nitudes has the same ratio to the second, which the third has to the fourth, theu, if the first be greater thiin the second, the third is also greater than the fourth ; and if...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...Propositions are introduced by SIMSON. PROPOSITION A. THEOREM. (480) If the first of four magnitudes have 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...
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