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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any...
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 149
von Euclides - 1861
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 Seiten
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED Cos, 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 shall have the same ratio to the second...
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## The elements of algebra. [With] Answers

Robert Fowler - 1861
...those m = 16 j cases. PROPOKTION. 133. Def. — If there be four quantities, such that the first has the same ratio to the second which the third has to the fourth, then the four quantities are said to be proportionals. Thus if а, Ъ, с, d be the four quantities,...
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## The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 79 Seiten
...and therefore e ; / : ; g : A. Therefore, if the first, &c.— QED COR. 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...
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## The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same...whatsoever of the first and third being taken, and auy equimultiples whatsoever of the second and fourth; if the multiple of the first b« IMS than that...
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## The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...being any integers, no, no, ' or mAl : na, : : mAt : no,. That is, 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 same ratio to any equimultiples...
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## The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...has to the second a greater ratio than the fifth has to the sixth . . . . . V. 13. 10. If the first have the same ratio to the second which the third has to the fourth ; then if the first be greater than the third, the second is greater than the fourth ; and if equal,...
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## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 Seiten
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. 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...
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## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 Seiten
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. 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...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 Seiten
...fourth D. If, therefore, the first, &c. QED PROPOSITION IV. THEOREM. If the first of four magnitudes hat 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 same ratio to any equimultiples...
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## Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI

Euclid - 1868 - 141 Seiten
...Sivripov Kai rfrápruv, кaQ' ùiroiovovv iro\\air\aaia.afièv, rbv àvrbv ejfi Xóyo»< If the first has the same ratio to the second which the third has to the fourth; any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of...
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