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" And if the first have a greater ratio to the second, than the third has to the fourth, but the third the same ratio to the fourth, which the fifth has to the sixth... "
A Supplement to the Elements of Euclid - Σελίδα 284
των Daniel Cresswell - 1819 - 410 σελίδες
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 σελίδες
...(a.) The centres of equal straight lines in a circle. 9. When is the first of four magnitudes said to have a greater ratio to the second than the third has to the fourth? When is a straight line said to be cut in extreme and mean ratio ? Define alternando, componendo, and...

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

Euclid, Isaac Todhunter - 1883 - 428 σελίδες
...therefore A has a greater ratio to B than E has to F. EUCLID'S ELEMENTS. COROLLARY. And if the first have a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth that tha fifth has to the sixth, it may be shewn, in the...

Books 3-9

Euclid - 1908 - 456 σελίδες
...(from above) me^nf. Therefore a : b> e :/. Simson adds as a corollary the following : " If the first have a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth which the fifth has to the sixth, it may be demonstrated...

A History of Greek Mathematics: From Thales to Euclid

Sir Thomas Little Heath - 1921 - 474 σελίδες
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth ' ; this (possibly for brevity's sake) states only one criterion, the other possible criterion being...

A History of Greek Mathematics, Τόμος 1

Sir Thomas Little Heath - 1921 - 482 σελίδες
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has. to the fourth ' ; this (possibly for brevity's sake) states only one criterion, the other possible criterion being...

Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - 1990 - 434 σελίδες
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth. The definition states that if for even one m and one n,ma>nb but mc is not greater than nd, then ajb >...
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The Thirteen Books of Euclid's Elements

Euclid - 452 σελίδες
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth. 8. A proportion in three terms is the least possible. 9. When three magnitudes are proportional, the...
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