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
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 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 - Euclid's Elements - 1806 - 311 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 - 493 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 - 518 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
...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
...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 - Euclid's Elements - 1816 - 528 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 - 317 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 - 516 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
...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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