 | 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... | |
| |
When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. 
