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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 CONTENTS OF THE FIFTH AND SIXTH BOOKS OF EUCLID

M. J. M. HILL - 1900
...following manner : — The first of four magnitudes is said to have the same ratio to the second, as the third has to the fourth, when any equimultiples...equimultiples whatsoever of the second and fourth being taken; if the multiple of the first be less than that of the second, the multiple of the third...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 143 pages
...multiple of the third is also equal to that of the fourth : and, 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. The statement of the above Test in symbols has already been given...
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The Teaching of Elementary Mathematics

David Eugene Smith - Mathematics - 1900 - 312 pages
...OF ELEMENTARY MATHEMATICS 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."1 The other extreme is the purely algebraic plan, the one adopted...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 777 pages
...multiple of the third is also equal to that of the fourth, and 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." (Euclid, Book V.) ac For, let a : b = c ; d; then — oa £2=£5....
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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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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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Report of the Meeting of the Australian and New Zealand ..., Volume 10

ANZAAS. - Science - 1905
...natural. I need only quote it to enforce the point: " The first of four magnitudes is said to have the same ratio to 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
...natural. I need only quote it to enforce the point : " The first of four magnitudes is said to have the same ratio to 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
...convinced that it is utterly unfit for young students. * "The first of four magnitudes is said to have the same ratio to the second, which the third has...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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