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" If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ratio which the first of the others has to the last. NB This is usually... "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 217
von Euclides - 1861
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 Seiten
...greater than C, D will be greater than F ; if equal, equal ; and if less, less. tt. PROI'. XXII. THEOB. If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first rank of magnitudes, the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 Seiten
...to F: A is to D. as E to H. Because А, В, С, яге three magnitudes, and F, G, H, other three, which, taken two and two in a cross order, have the same ratio ; by the first case, A is to C, as F to H: But с is to D, as E to F ; wheretbre again. by the first...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

James Ryan - 1826 - 383 Seiten
...greater than C, D will be greater than F ; if equal, equal ; and if less, less. PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, •which, take two and two in order, have the same ratio ; the first shall have to the last of the first rank...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 Seiten
...Therefore, if there be three, &c.. SeeN. * 4.'5. * 20. 5. •f- Constr. *5Def. 5. PROP. XXII. THEOR. If there be any number of magnitudes, and as many others, which taken two and two in order have the same ratio ; theJirst shall have to the last of the Jirst magnitudes the same ratio...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 Seiten
...greater than A' (by the first case) ; that is A' is less than C'. PROPOSITION XXII. THEOREM. (501) If there be any number of magnitudes, and as many others, which taken two and two in order have the same ratio ; the first has to the last of the first magnitudes the same ratio which...
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A Treatise on Algebra

George Peacock - 1830 - 685 Seiten
...perturbatfi. A similar demonstration will apply when there are more than three magnitudes in each set. 413. " If there be any number of magnitudes and as many others, which, taken two and two in a cross order, jlaye ^ same rati0; namely, if the first be to the second of the first set of magnitudes, as the last...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 Seiten
...therefore, by the first case, since C> A, F>D, that is, D^_F. Therefore, &c. QED PROP. XXII. THEOR. Jf there be any number of magnitudes, and as many others, which, taken two and two in order, have (he same ratio; the Jirst will have to the lust of the first magnitudes, the same ratio...
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Band 19

Perry Fairfax Nursey - 1833
...ist propositions. Solution by l In- Hon. Lionel Smytke, the Proposer. I. The 22d Proportion, Book V. If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio, the first will have to the last of the first magnitudes the same ratio...
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The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Band 19

1833
...2ist propositions. Solution ty the Hon. Lionel Smythe, the Proposer. I. The 22d Proposition, Book V. If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio, the first will have to the last of the first magnitudes the same ratio...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 Seiten
...ex sequo," PROP. XXIII. THEOR. If there be any number of magnitudes, and as many others, — „.., taken two and two, in a cross order, have the same ratio ; the first will have to the last of the first magnitudes the same ratio which the first of the others has to the...
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