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