Page:The Whetstone of Witte.djvu/35

 acchiued. For of the Arte of Proportios, dependenth all the subtilties, and fine workes, not onely of Arithmetike, but also of Geometre besides father mater that as now I will not toche. But as for the workes of Proportions, I will omitte them til an other tyme: consideryng not onely the troublesome condition, of my vnquiete estate: but also the conuenient order of teachynge, whereby it is required that the extraction of rootes, should go orderly before the arte of Proportions: whiche without those other, cā not be wrought.

Therfore will I now onely declare these kindes of proportion, whiche yet are not spoken of: to the intente that you maie haue here, the generall diuision of numbers, somewhat sufficiently touched.

As you see that betwene any two numbers, there maie be a conference of proportion: so if any one proportion be continued in more then. 2. nombers, there maie be then a conference also of these proportions, in their seuerall terms:

and that conference or comparison is named Analogie: whiche some delighte to call proportionalitie: As in this example, where 3 nōbers beare like proportion in their progression: 4. 6. 9. You see that 6. to 4. is in proportion sesquialter: and so is 9. to 6. and therfore is there a like proportion betwene the. 2. laste, as there is betwene the. 2. firste.

Scholar. This I consider well by progression in Arithmetike.

Master. Likewaies where fower termes or more be set in order of proportion, as here 2. 6. 18. 54.

Scholar. I perceiue this wel: for here the proportiō is triple. But what saie you to this forme of comparison in Proportion? As 6. is to 2: So 30. is to. 20.10. [sic] Is it not all one kinde of Analogie?

Master. It is one kinde of Analogie generalle, whiche maie be called directe Analogie: bicause the first is compared to him that doeth folowe nexte: & so each