...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...

...be the least, the fourth €hall be the ! greatest. ....'• ' : .' .• •.. . u ,'t .. ..-.•; , Let A, B, C, D, be four magnitudes of the same kind, which are proportionals ; and, first, let A be the greatest; then D shall be. the least of them. For,...

...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...

...magnitudes of the same kind be proportionals, they shall also be proportionals when taken alternately. Let A, B, C, D be four magnitudes of the same kind, which are proportionals, viz. as A to B, so C to D: they shall also be proportionals when taken alternately;...

...four magnitudes of the same kind be proportionals, they are also proportionals when taken alternately. Let A, B, C, D be four magnitudes of the same kind, and let A : B = C : D : they are also proportionals when taken alternately ; that is, A : C = B : D....

...magnitudes of the same kind be proportionals, they shall also be proportionals when taken alternately. Let A, B, C, D be four magnitudes of the same kind, which are proportionals ; viz. as A to B, so C to D : they shall also be proportionals when taken alternately...

...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,...

...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 - = •=-,.•....

...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...

...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...