 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...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 - Astronomy - 1822 - 516 pages
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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,... | |
 | Euclides - 1838 - 264 pages
...fourth terms will be equal. PROP. X. THEOR. If the terms of a proportion are all of the same kind, they are proportional when taken ALTERNATELY, that is, the first is to the third as the second to the fourth. Let the proportion be A : B :: C : D; then also A : C :: B : D. For take mA, mB any... | |
 | John Radford Young - 1839 - 332 pages
...(Theor. 2) Ь : a : : d : c. 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 - Mathematics - 1841 - 144 pages
...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 - Algebra - 1844 - 568 pages
...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 pages
...and hence b: a=d:c. QED bd Ь а а с 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 - Algebra - 1846 - 300 pages
...is to the third. Let . a : b : : с : d, then 2 -t.. о а Whence — =f — or b : a : : d L с. ac 49. If four like quantities be proportional, they...fourth. Let a : b : : с : d, then a : с : : b : d ; a, b, c, and d being like quantities. For, since -r=>^, we have, by multiplying by -, о a " с Or, a... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...XL— TIIEOR-M. If the terms of a proportion are all of the sama kind, they also form a proportion •when taken ALTERNATELY ; that is, the first is to the third as the second is to the fourth. Let the homogeneous proportionals be A : В : : С : D ; then also A : С : : В : D. For let any equimultiples... | |
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Permutando, or alternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth. 
