Page:The Whetstone of Witte.djvu/36

 other is still referred to that, that foloweth nexte. But this is the difference: that in the firste, there is a continuaunce of collation: and one terme is compared with twoo nombers: But in that forme of example, whiche you put, there is no nomber compared twise: For the first is referred to the seconde, and the second to the thirde. And so haue thei seueralle names to distincte theim a sonder.

Wherfore whē the first nomber is referred to the seconde, and that seconde to the thirde: the proportion is called continualle: and it maie consiste betwene 3. termes. As 5. 15. 45. doe procede in a continuall triple proportion. For as 5. is to 15: so is 15. to 45. as you doe see. But when I saie thus: as 5. is to 15. so 6. is to 18.

Here is a triple proportion, but not continualle. For the seconde terme beynge 15. is not compared with the thirde terme, that is 6. And therfore is it called a proportion discontinualle.

Scholar. Now I perceiue certainly their distinction: For in twoo poinctes these examples doe agree, and differ in a thirde poincte.

Firste thei agree in that (as you saied) that the formoste is referred to the other that foloweth it nexte: And secondly, thei agree in this also, that bothe are compared in a triple proportion. But in this thei differ, that the seconde terme, doeth not beare like proportion to the thirde, as the thirde doeth to the fourth or the firste to the seconde.

Master. Father more there is to bee noted, that in discontinualle proportion, there can bee no fewer than fower termes, or numbers: and so by euen formes still, as. 6. or. 8. and so forthe. Where as in continuall proportion, your termes maie bee of any number, euen or odde: aboue. 2.

And although I might saie more of the diuersities of proportions: as of Proportion conuersed or indirecte, Pro-