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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) cyclopŠdia, by J.M. Good, O. Gregory, and N ...
by John Mason Good - 1813
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 398 pages
...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." PROPOSITION XIII. 273. If four quantities be proportional according...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fouitl', when any equimultiples whatsoever of the first and third i being taken, ai;d any equimultiples...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879
...figures. 2. About a given circle describe a triangle equiangular to a given triangle. 3. If the first have the same ratio to the second which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the sixth, the first shall have to the...
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Elementary algebra: with brief notices of its history

Robert Potts - Algebra - 1879
...multiple of the third is abo 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. Conversely. If four magnitudes be proportional according to Eue. V.,...
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Elementary algebra, with brief notices of its history

Robert Potts - 1879
...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. Conversely. If four magnitudes be proportional according to Eue. V.,...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...together. [V. Definition 5. Wherefore, if any number &c. Q.EJ>. PROPOSITION 13. THEOREM. If the first have the same ratio to the second which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the si.cth, thefirst shall have to ths...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880
...and hexagon. 7. Give Euclid's definition of ratio. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 8. The sides about the equal angles of equiangular triangles are proportional. If a straight line...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...same kind, and so cannot have any ratio to each other. T. The Brst of four magnitudes is said to have the same ratio to the second, which the third has...of the first be less than that of the second, the mu'tiple of the third is also less than tlint of the fourth : or, if the multiple of the first be equal...
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Elements of Geometry

George Albert Wentworth - Geometry, Plane - 1881 - 250 pages
...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." PROPOSITION XIII. 273. If four quantities be proportional according...
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Elements of Geometry

George Albert Wentworth - Geometry, Plane - 1882 - 250 pages
...DBF. Euclid's test of a proportion is as follows :-•" The first of four magnitudes iń said to have the same ratio to the second which the third has to...equimultiples whatsoever of the second and fourth ; (l ▒ P] a : \ q/ : 0 ▒ -) V q/ :b▒Р-b \ b : : a : b, Q/ ~T~ — Cz ч Ч : : a : b. "If the multiple...
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