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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... "
A system of practical mathematics; being no.xvi. of a new series of school-books - Page 111
1845
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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
...Art. 67. Def. 13. EUCLID'S TEST FOR EQUAL RATIOS. Euclid states this Test in the 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 whatsoever of the first and third being taken,...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 777 pages
...definition. Euclid's definition of a proportion is: ' 'The first of four magnitudes is said to hare the same ratio to the second that the third has to...fourth, when any equimultiples whatever of the first and the third being taken, and any equimultiples whatever of the second and the fourth, if the multiple...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - Mathematics - 1901
...quadrilateral (i) inscribed in, (2) described about, a circle. 9. When is the first of four magnitudes said to have the same ratio to the second that the third has to the fourth ? Illustrate this definition by giving Euclid's proof of the proposition that triangles of the same...
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The Teaching of Elementary Mathematics

David Eugene Smith - Mathematics - 1902 - 312 pages
...Teaching. One has but to read the Euclidean definition of equal ratios to be assured of this fact : " 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,...
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Ellen: or, Whisperings of an old pine, Volume 1

Joseph Battell - Force and energy - 1903
...that the third has to the fourth. ' 6. Magnitudes are said to be proportionals, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth, and so on whatever be...
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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 ratio to the second which the third has to the fourth when, if the first be divided into any number whatever of equal parts,...
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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 ratio to the second which the third has to the fourth when, if the first be divided into any number whatever of equal parts,...
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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 same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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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...fourth, when any equimultiples whatever of the first and the third being taken, and any equimultiples whatever of the second and the fourth, if the multiple...
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Pass school, group A (-D).

Oxford univ, exam. papers, 2nd publ. exam
...circle describe a triangle equiangular to a given triangle. 6. When is the first of four magnitudes said to have the same ratio to the second that the third has to the fourth ? Explain the terms — invertendo, ex aequali. Define reciprocal figures. *i '. If a straight line...
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