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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. "
The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ... - Side 42
av Benjamin Donne - 1775 - 159 sider
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 364 sider
...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,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 sider
...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...
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Instructions Given in the Drawing School Established by the Dublin Society ...

Joseph Fenn - 1769
...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...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 sider
...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...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 sider
...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...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ...

Euclid, James Williamson - 1781 - 309 sider
...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;...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 400 sider
...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...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 sider
...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...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...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...
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A Course of Mathematics ...: Designed for the Use of the Officers ..., Volum 2

Isaac Dalby - 1806
...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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