| Robert Simson - Trigonometry - 1762 - 488 pages
...Proportion confifts in three terms at leaft. X. When three magnitudes are proportionals, the firft: rs **faid to haVe to the third the duplicate ratio of that which it has to the** fecond. XI. When four magnitudes are continual proportionals, the firft is faid to have to the fourth... | |
| Benjamin Donne - Geometry, Plane - 1775 - 336 pages
...the Product will be equal to the Antecedent. 161. Def. ro. When three Magnitudes are Proportionals, **the firft is faid to have to the third the duplicate Ratio of that which, it has to the fécond.** 162. Def. ii. When four Magnitudes are continual Proportionals, the firft is faid to have to the fourth... | |
| Robert Simson - Trigonometry - 1775 - 534 pages
...ratios." lA.* Proportion confifts in three terms at lead. X, When three magnitudes are proportionals, **the firft is faid to have to the third the duplicate ratio of that which it has to the** fecond. XL re N. When four magnitudes are v>nt'nual proportionals, the firft is faid to have to the... | |
| Euclid, James Williamson - Euclid's Elements - 1781 - 324 pages
...fixth, eighth, and ninth definitions are fufficiently obvious. When three magnitudes are proportionals; **the firft is faid to have to the third the duplicate ratio, of that which it has to the** fecond. But this definition and the next I fhall have occafion to explain afterwards. When we fay that... | |
| Euclid - 1781 - 552 pages
...fo EF to BG ; and that if three ftraight lines be pro- BGCEF portionals, the firft is f i0. def. 5. **faid ' to have to the third the duplicate ratio of that which it has** tothefecond; BC therefore has to BG the duplicate ratio of that g r. 6. which BC has to EF : But as... | |
| John Playfair - Euclid's Elements - 1795 - 462 pages
...becaufe as BC is to EF, fo EF to BG; and that if three ftraight linesbe proportionals, the firft has **to the third the duplicate ratio of that which it has to the** fecond ; BC therefore has to BG the duplicate ratio of that i i. 6. which BC has to EF : but as BC... | |
| Alexander Ingram - Trigonometry - 1799 - 374 pages
...called the Extremes, and the others are called Means, X. X. .. BOOK V. The firft of three proportionals **is faid to have to the third the duplicate ratio of that which it has to the** fecond. XI. Of four continual proportionals, the" firft is faid to have to the fourth the triplicate... | |
| Robert Simson - Trigonometry - 1804 - 528 pages
...ratios." IX. Proportion confifts in three terms at leaft. X. When three magnitudes are proportionals, **the firft is faid to have to the third the duplicate ratio of that which it has to the** fecond. XI. See N. When four magnitudes are continual proportionals, the firft is faid to have to the... | |
| Isaac Dalby - Mathematics - 1806 - 526 pages
...And in like manner it is proved that a -f : -. a* : A*. And so of others. And the first term is said **to have to the third, the duplicate ratio of that which it has to the** second ; and to the fourth, the triplicate ratio of that which it has to the second ; and so on. NB... | |
| Robert Simson - Trigonometry - 1806 - 548 pages
...EF, so EF to BG ; and that if three straight lines be proportionals, the first is f 10.def.5. said f **to have to the third the duplicate ratio of that which it** h»s to the second ; BC therefore has to BG the duplicate ratio of 1 6 that which BC has to EF : but... | |
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