| Robert Simson - 1806 - Liczba stron: 518
...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, which...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 - 1806 - Liczba stron: 311
...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...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 - 1809 - Liczba stron: 524
...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 - 1810 - Liczba stron: 518
...or alternately; this See Note, word is used when there are four proportionals, and it is inferred, **that the first has the same ratio to the third, which...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
...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: as is** shewn in the XVI. Prop, of this Book V. 14. Invertendo, by inversion: when there are four proportionals,... | |
| Euclides - 1814
...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 third, which...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 - Liczba stron: 528
...permutation, or alternately. gee N. This word is used when there are four proportionals, and it is inferred, **that the first has the same ratio to the third, which...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 - Liczba stron: 333
...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...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... | |
| 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;... | |
| George Crabb - 1823
...order or magnitude of the proportionals, as — Alternate proportion, when the first of four magnitudes **has the same ratio to the third which the second has to the fourth** ; thus the ratio of A to C, fig. 32, being the same as B to D, the proportion is alternate. — Inverse... | |
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