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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 43
av Benjamin Donne - 1775 - 159 sider
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Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - 1874 - 80 sider
...three terms at least. This is an Axiom. X. 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. • XL When four magnitudes are continual proportionals, the first is said to have to the fourth,...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 sider
...Proportion consists in three terms at least. 10. 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. 11. When four magnitudes are continual proportionals, the first is said to have to the fourth,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 sider
...because as .BCis to EF, so EFto BG; and that if three straight lines be proportionals, the first is said to have to the third, the duplicate ratio of that which it has to the second : (v. def. 10.) therefore BChas to BG the duplicate ratio of that whichSChasto EF: but as BCis...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 sider
...Proportion consists in three terms at least. 10. 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 second magnitude is said to bo a mean proportional between the first and the third.] 11....
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The Competitor, Volumer 1-2

1882 - 480 sider
...duplicate ratio of their homologous sides. (a) "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. (Definition, Book V.) (b) Euclid, Book VI., Prop. 19. 6. If the four sides of any quadrilateral...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 sider
...Proportion consists in three terms at least. 10. "When three magnitudes are proportionals, the first Ja said to have to the third the duplicate ratio of that which it has to the second. [The second magnitude is said to be a mean proportional between the first and the third.] 1...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885 - 340 sider
...proportion is 4 : 6 : : 6 : 9. x. When three magnitudes are continual proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. xi. When four magnitudes are continual proportionals, the first is said to have to the fourth...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 340 sider
...proportion is 4 : 6 : : 6 : 9. x. When three magnitudes are continual proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. xi. When four magnitudes are continual proportionals, the first is said to have to the fourth...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 sider
...Proportion consists in three terms at least 10. 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. Thus if A : B :: B : C, then the ratio of A : C is called the ' duplicate ' of the ratio A:...
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A Text-book of Euclid's Elements for the Use of Schools, Bok 1

Euclid - 1904 - 488 sider
...T, -, -, - we ocae HSE , Definition 13. 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. Thus if a : b : : b : c, then a : c is said to be the duplicate of the ratio a : 6. NOTE. In...
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