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" If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...
by John Mason Good - 1813
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Elements of geometry, with ... trigonometry

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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

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...
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Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

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 '...
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Euclid, book v. proved algebraically, so far as it relates to commensurable ...

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 '...
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Euclidian Geometry

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...
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The Elements of Euclid, containing the first six books, with a selection of ...

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...
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The Elementary Geometry of the Right Line and Circle ... With Exercises

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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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...
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Elementary Algebra

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...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

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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