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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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Ellen: Or, Whisperings of an Old Pine, Volume 1

Joseph Battell - Force and energy - 1903
...must contain 2, 3 X 3, or 9 times. See Axiom 6. PROPOSITION IV. ' If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiple whatever is taken of the first and third, and any whatever of the second and...
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First Stage Practical Plane and Solid Geometry

G. F. Burn - Geometry - 1903 - 255 pages
...is the equality of two ratios. Four quantities are therefore in true proportion when the first has the same ratio to the second which the third has to the fourth ; thus, since 3 : 6 and 1 : 2 are equal ratios, we have a true proportion in 3 : 6 : : 1 : 2 (read...
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Report of the Meeting of the Australian and New Zealand ..., Volume 10

ANZAAS. - Science - 1905
...geometrically as sound as Euclid's, and infinitely more natural. I need only quote it to enforce the point: " The first of four magnitudes is said to have the same...the second which the third has to the fourth when, if the first be divided into any number whatever of equal parts, and the third be divided into the...
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Report of the Meeting - ANZAAS., Volume 10

ANZAAS (Association) - Science - 1905
...geometrically as sound as Euclid's, and infinitely more natural. I need only quote it to enforce the point : " The first of four magnitudes is said to have the same...the second which the third has to the fourth when, if the first be divided into any number whatever of equal parts, and the third be divided into the...
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Books 3-9

Euclid - Mathematics, Greek - 1908
...unnecessary. Simson added, in place of Theon's corollary, the following : " 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 same ratio to the second and fourth...
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The Teaching of Mathematics in Secondary Schools

Arthur Schultze - Mathematics - 1912 - 370 pages
...has only to read Euclid's definition* to be convinced that it is utterly unfit for young students. * "The first of four magnitudes is said to have the...fourth ; if the multiple of the first be less than that The fact that the arithmetical view of ratio leads to a product of two lines is no serious objection,...
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The Development of Logic

William Kneale, William Calvert Kneale, Martha Kneale - Nature - 1962 - 761 pages
...of mathematics. The essence of it is a new definition of the equality of ratios between magnitudes : 'The first of four magnitudes is said to have the same ratio to the second that the third has to the fourth, when any equimultiples whatever of the first and the third being...
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Pass school, group A (-D).

Oxford univ, exam. papers, 2nd publ. exam - 1884
...rectilineal figures. Explain homologous, alternando, ex aequali. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 7. In a right angled triangle, if a perpendicular be drawn from the right angle to the base, the...
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