 | John Keill - 1723 - 444 σελίδες
...Fourth. Vllf. Analogy is a Similitude of Proportionsi IX. Analogy at leaft conjifts of three Terms. X. When three Magnitudes are Proportionals, the Firft • is faid to have to the Third, a Duplicate Ratio to -what it has to the Second• XI. But when four Magnitudes are Proportionals,... | |
 | Robert Simson - 1762 - 488 σελίδες
...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... | |
 | Joseph Fenn - 1769 - 524 σελίδες
...progrefTion,/«f¿ are tbe numbers i, 2, 4, 8, 16, 32, 64, £Л. X. When three magnitudes are proportional the firft is faid to have to the third the duplicate ratio of that which it has to the fécond. XI. When four magnitudes are continual proportionals, the firft is faid to have to the fourth the triplicate... | |
 | Robert Simson - 1775 - 534 σελίδες
...Analogy, or proportion, is the fimilitude of ratios." lA.* Proportion confifts in three terms at lead. X, When three magnitudes are proportionals, the firft...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 - 1781 - 552 σελίδες
...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... | |
 | Euclid, James Williamson - 1781 - 324 σελίδες
...And proportion is a fimilitude of ratios. 9. But proportion confifts in three terms at leaft. 10. And when three magnitudes are proportionals ; the firft is faid to have to the third a duplicate ratio of that which it has to the fecond. n. And when four magnitudes are proportionals;... | |
 | Euclid, John Playfair - 1795 - 462 σελίδες
...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 - 1799 - 374 σελίδες
...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 - 1804 - 530 σελίδες
...Analogy, or proportion, is the fimilitude of ratios." IX. Proportion confifts in three terms at leaft. X. When three magnitudes are proportionals, the firft...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 - 1806 - 526 σελίδες
...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... | |
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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. 
