| 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,... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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,... | |
| 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... | |
| 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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