Now by the rule of Algiebar, haue I deuised a very easie, briefe, and generall maner of working in this case. Let vs first, suppose that _Middle Forme resulting_, to be 1{x}: as that Rule teacheth. And because (by our Rule, here geuen) as the waight of 1. is to 2: So is the difference betwene 4. (the degree of the greater quantitie) and 1{x}: to the difference betwene 1{x} and 3: (the degree of the thing, in lesse quãtitie. And with all, 1{x}, being alwayes in a certaine middell, betwene the two heigthes or degrees). For the first difference, I set 4-1{x}: and for the second, I set 1{x}-3. And, now againe, I say, as 1. is to 2. so is 4-1{x} to 1{x}-3. Wherfore, of these foure proportionall numbers, the first and the fourth Multiplied, one by the other, do make as much, as the second and the third Multiplied the one by the other. Let these Multiplications be made accordingly. And of the first and the fourth, we haue 1{x}-3. and of the second & the third, 8-2{x}. Wherfore, our Æquation is betwene 1{x}-3: and 8-2{x}. Which may be reduced, according to the Arte of Algiebar: as, here, adding 3. to eche part, geueth the Æquation, thus, 1{x}=11-2{x}. And yet againe, contracting, or Reducing it: Adde to eche part, 2{x}: Then haue you 3{x} æquall to 11: thus represented 3{x}=11. Wherefore, diuiding 11. by 3: the Quotient is 3⅔: the _Valew_ of our 1{x}, _Coss_, or _Thing_, first supposed. And that is the heigth, or Intension of the _Forme resulting:_ which is, _Heate_, in two thirdes of the fourth degree: And here I set the shew of the worke in conclusion, thus. The proufe hereof is easie: by subtracting 3. from 3⅔, resteth ⅔. Subtracte the same heigth of the Forme resulting, (which is 3⅔) frõ 4: then resteth ⅓: You see, that ⅔ is double to ⅓: as 2.{P}. is double to 1.{P}. So should it be: by the rule here geuen. Note. As you added to eche part of the Æquation, 3: so if ye first added to eche part 2{x}, it would stand, 3{x}-3=8. And now adding to eche part 3: you haue (as afore) 3{x}=11. _________________________ | | | _ | {P}. _2._ | _Hote. 4._ | ⅓ _ _The forme_ | | | _ _3⅔ resulting._ | {P}. _1._ | _Hote. 3._ | _ ⅔ |___________|_____________| And though I, here, speake onely of two thyngs Miscible: and most commonly mo then three, foure, fiue or six, (&c.) are to be Mixed: (and in one Compound to be reduced: & the Forme resultyng of the same, to serue the turne) yet these Rules are sufficient: duely repeated and iterated. [Note.]