 | Adrien Marie Legendre - 1819 - 574 σελίδες
...alternando, by permutation or alternately, when, with respect to four proportionals, it is inferred that the first is to the third as the second is to the fourth ; invertendo, by inversion, when it is inferred that the second is to the first as the fourth is to... | |
 | Rev. John Allen - 1822 - 516 σελίδες
...names, 16. Alternating ; when it is inferred, if four magnitudes of the same kind be proportional, that the first is to the third, as. the second is to the fourth; as is shewn in the 16 prop, of tins hook. 17. Inverting; when it is inferred, if four magnitudes he... | |
 | John Radford Young - 1832 - 408 σελίδες
...c. THEOREM^. If four quantities be proportional, they are proportional also when taken alternately ; that is, the first is to the third, as the second is to the fourth. For if a : b : : с : d, then - = - ; and multiplying by y, their recd suits — =—,.: a : с : :... | |
 | Andrew Bell - 1837 - 290 σελίδες
...terms of an analogy, so that they continue still to be proportionals :— 21. By alternation, when the first is to the third, as the second is to the fourth. 22. By inversion, when the second is to the first, as the fourth is to the third. 23. By composition,... | |
 | John Radford Young - 1839 - 332 σελίδες
...THEOREM 4. If four quantities be proportional, they are proportional also when taken alternately ; that is, the first is to the third as the second is to the fourth. For if о : ft : : с : d, then — = - ; and multiplying by -7, there re, cd , , suits - = •=-,.•.... | |
 | Oliver Byrne - 1841 - 144 σελίδες
...inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second is to the fourth : as is shown in the following proposition : — Let • : A : Г О : Д, by ' ' permuntando " or... | |
 | William Scott - 1844 - 568 σελίδες
...that if four quantities are proportional, they are also proportional when taken alternately, or that the first is to the third as the second is to the fourth. win tn Tn . _ . e. Since ^=^=1> an"^"=«' it follows that, if ae b=if acm me then also 5=rfX-=^oro... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...105. Prop. 4. If four quantities be proportional they are also proportional when taken alternately; that is, the first is to the third as the second is to the fourth. For tor on both sides, we have -•=-,'. a: c=b:d. QED '-' a 106. Prop. 5. When four quantities are... | |
 | Samuel Alsop - 1846 - 300 σελίδες
...с. ac 49. If four like quantities be proportional, they are proportional when taken alternately ; that is, the first is to the third as the second is to the fourth. Let a : b : : с : d, then a : с : : b : d ; a, b, c, and d being like quantities. For, since -r=>^, we have,... | |
 | Samuel Alsop - 1848 - 336 σελίδες
...c. <a с 49. If four like quantities be proportional, they are proportional when taken alternately ; that is, the first is to the third as the second is to the fourth. Let a : b : : с : d, then a : с : : b : d ; a, o, c, and d being like quantities. For, since -7- = -., we have,... | |
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If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Let... 
