 XIII. Permutando, or alternando, by permutation, or alternately; this word is used when there are four proportionals, and it is inferred, that the first has the same ratio to the third, which the second has to the ,fourth; or that the first is to the...  Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Page 156by Euclides - 1861Full view - About this book
 | Robert Simson - Trigonometry - 1806 - 546 pages
...permutation, or alternately; this word is used when there are four proportionals, and it is See N. inferred, that the first has the same ratio to the...third, as the second to the fourth: as is shown in the 16th prop, of this 5th book. XIV. Invertendo, by inversion ; when there are four proportionals,... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...XIV. Permutando, or alternando, by permutation, or alternately ; this word is used when there are four proportionals, and it is inferred, that the first...first is to the third as the second to the fourth. See prop. 16th of this book. XV. Invertendo, by inversion : when there are four proportionals, and... | |
 | Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...products AD and BC still obtains. PROP. VIII. THEOR. Numbers are likewise proportional by alternation, or the first is to the third as the second to the fourth. Let A: B : : C : 1); then alternately A : C : : B : D. !For the extreme terms are here still retained,... | |
 | Euclid - Geometry - 1810 - 554 pages
...Permutando, or alternando, by premutation, or alternately; this See Note, word is used when there are four proportionals, and it is inferred, that the first...or that the first is to the third, as the second to |he fourth: as is shown in the 16th prop. of this sth book. XIV. luvertendo, by inversion: when there... | |
 | John Mason Good - 1813 - 714 pages
...or alternando, by permutation, or alternately; this word is ч-ed when there are four proportional*, and it is inferred, that the first has the same ratio to the third, « hicli the •econd has to the fourth; or that the first is to the third, as the second to the fourth:... | |
 | Euclides - 1814 - 560 pages
...alternando, by permutation, or alternately. This word is used when there are four proportionals, and See N. it is inferred, that the first has the same ratio...to the fourth; or that the first is to the third, us the second to the fourth : As is shown in the ICth prop. of this 5th book. XIV. Invertendo, by inversion... | |
 | Euclides - 1816 - 588 pages
...Permutando, or alternando, by permutation, or alternately. gee N. This word is used when there are four proportionals, and it is inferred, that the first...third, as the second to the fourth : As is shown in the 16th prop. of this 5th book. XIV. Invertendo by inversion ; when there are four proportionals,... | |
 | John Playfair - 1819 - 354 pages
...XIV. Permutando, or alternando, by permutation, or alternately ; this word is used when there are four proportionals, and it is inferred, that the first...first is to the third as the second to the fourth : See Prop. 16. of this Book. XV. Invertendo, by inversion : When there are four proportionals, and... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...XIII. Permutando, or alternando, by permutation, or alternately; this word is used when there are four proportionals, and it is inferred, that the first...third, as the second to the fourth; as is shown in the 16th prop. of this 5th book.* ' XIV. Invertendo, by inversion: when there are four proportionals,... | |
 | Euclides - 1821 - 294 pages
...alternando ; when it is concluded, that if there be four magnitudes of the same kind proportionals, the first is to the third as the second to the fourth. Note. In this the antecedents are compared with one another, and the consequents with one another;... | |
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