Books Books
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.
Instructions Given in the Drawing School Established by the Dublin Society ... - Page 165
by Joseph Fenn - 1769

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...

## The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - Geometry, Plane - 1775 - 338 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...

## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

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...

## The Elements of Euclid: With Dissertations Intended to Assist and Encourage ...

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...

## The First Six Books: Together with the Eleventh and Twelfth

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...

## Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, 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...

## The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

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...

## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 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...