| André Darré - 1872
...multiple of the third is also 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." THEOREM. 77. If lines which intersect tiro sides of a triangle and... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...be proportionals, and any equimultiples be taken of the first and third, and also any equimultiples **of the second and fourth, if the multiple of the first be** greater than that of the second, the multiple of the third must be greater than that of the fourth... | |
| Euclid, Lewis Carroll - Euclid's Elements - 1874 - 62 pages
...The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have **the same ratio to the second which the third has to the fourth, when** the first is the same multiple, part, or fraction of the second which the third is of the fourth '... | |
| Charles Lutwidge Dodgson - 1874
...The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have **the same ratio to the second which the third has to the fourth, when** the first is the same multiple, part, or fraction of the second which the third is of the fourth '... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...latter by less than any assignable quantity. DEFINITION. 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 same... | |
| Euclides - 1874
...ratio to the second, than the fifth has to the sixth. PROPOSITION 14.— Theorem. If the first has **the same ratio to the second which the third has to the fourth** ; then, if the first be greater than the third, the second shall be greater than the fourth ; ana if... | |
| William Alexander Willock - Circle - 1875 - 172 pages
...OAv OB, be proportional, and the following statement hold good:— If there be four magnitudes, and **any equimultiples whatsoever of the first and third...equimultiples whatsoever of the second and fourth** being taken, if the equimultiples of the first and third together exceed, or are equal to, or are less... | |
| Robert Potts - Geometry, Plane - 1876 - 403 pages
...any integers, m,*l. mA. or m/ll : na, : : m/f, : na,. That i«, if the first of four magnitudes has **the same ratio to the second which the third has to the fourth** ; then any equimultiples whatever of the first and third shall have the game ratio to any equimultiples... | |
| James Hamblin Smith - Algebra - 1877 - 398 pages
...test is given in Book v. Def. 5, where it stands thus : " The first of four magnitudes is said to have **the same ratio to the second which the third has to...of the third is also less than that of the fourth** : " If the multiple of the first be equal to that of the second, the multiple of the third is also... | |
| Samuel H. Winter - 1877 - 413 pages
...into three, and also into five equal parts. 6. When is the first of four magnitudes said to have the **the same ratio to the second which the third has to the fourth** ? Prove that triangles which have the same altitude are to one another as their bases. Show also that... | |
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