Liquor be geuen, hote in
the 4. degree: & one pound of Liquor be geuen, hote in the third
degree." I would gladly know the Forme resulting, in the Mixture of
these two Liquors. Set downe your numbers in order, thus.
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| | |
| {P}. _2._ | _Hote. 4._ |
| | |
| {P}. _1._ | _Hote. 3._ |
|____________|______________|

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
quantitie. 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 Aequation 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 Aequation, thus, 1{x}=11-2{x}. And yet againe, contracting,
or Reducing it: Adde to eche part, 2{x}: Then haue you 3{x} aequall to
11: thus represented 3{x}=11. Wherefore, diuiding 11. by 3: the Quotient
is 3-2/3: 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 3-2/3, resteth 2/3. Subtracte the same heigth of the
Forme resulting, (which is 3-2/3) from 4: then resteth 1/3: You see,
that 2/3 is double to 1/3: 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
Aequation, 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.
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