...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...

...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...

...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,...

...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,...

...second is to the fourth. OBS. This prop" is usually cited by the word " alternando," or " permutando." Let A, B, c, D be four magnitudes of the same kind, and let A be to B as c is to D. G Then shall A be to c as B is toD. Of A, B take any equimulti- P pies...

...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...

...A : y. Rut by a former proposition, " If the first be to the second as the third is to the fourth, then the first is to the third as the second is to the fourth ; " hence the last proposition may take the form, 1 : A :: В : y,butby(I.)l : A : : В : x. Hence,...

...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 be to B as C is to D: they are also proportionals when taken alternately : that is, A is...

...the 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,...

...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...