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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 equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple...
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Page 458
by Sir John Leslie - 1809 - 493 pages

The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...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...

The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...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...

The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...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,...

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

Robert Potts - 1865 - 528 pages
...is to G, so is Fto H. (v. def. 5.) 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 shall have the same ratio to the second...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 426 pages
...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...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 424 pages
...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...

Manual of Euclid: Books IV, V, VI.

Euclid - 1868 - 138 pages
...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...

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

Robert Potts - 1868 - 434 pages
...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...

A Treatise on Elementary Algebra

James Hamblin Smith - 1869 - 412 pages
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus : " The first of four magnitudes is said to have the same...being taken and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be less than that of the second, the multiple of...

Elementary Algebra

James Hamblin Smith - 1870 - 478 pages
...representing the ratios must be equal. Euclid's test is given in Book Y. Def. 5, where it stands thus: " The first of four magnitudes is said to have the same...being taken and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be less than that of the second, the multiple of...