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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... "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 149
von Euclides - 1861
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Report of the ... Meeting, Band 10

ANZAAS (Association) - 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 of the Australian and New Zealand Association ..., Band 10

ANZAAS. - 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 - 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 - 1912 - 370 Seiten
...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 Calvert Kneale, William Kneale, Martha Kneale - 1962 - 761 Seiten
...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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