The Mathematicall Praeface to Elements of Geometrie of Euclid of MegaraDee, John
Philosophy
The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara
Dee, John
Geometry -- Early works to 1800; Mathematics -- Early works to 1800; Philosophy -- Early works to 1800
Counting then from _B_, 2. degrees, toward _A_: you finde it to be _Dry_
in the first degree: So is the _Forme resulting_ of the Mixture of _A_,
and _B_, in our example. I will geue you an other example. Suppose, you
haue two thinges, as _C_, and _D_: and of _C_, the Heate to be in the 4.
degree: and of _D_, the Colde, to be remisse, euen vnto the
_Temperament_. Now, for _C_, you take 4: and for _D_, you take a Ciphre:
which, added vnto 4, yeldeth onely 4. The middle, or halfe, whereof, is
2. Wherefore the _Forme resulting_ of _C_, and _D_, is Hote in the
second degree: for, 2. degrees, accounted from _C_, toward _D_, ende
iuste in the 2. degree of heate. Of the third maner, I will geue also an
example: which let be this:
[Note.]
I haue a liquid Medicine whose Qualitie of heate is in the 4. degree
exalted: as was _C_, in the example foregoing: and an other liquid
Medicine I haue: whose Qualitie, is heate, in the first degree. Of eche
of these, I mixt a like quantitie: Subtract here, the lesse frõ the
more: and the residue diuide into two equall partes: whereof, the one
part, either added to the lesse, or subtracted from the higher degree,
doth produce the degree of the Forme resulting, by this mixture of _C_,
and _E_. As, if from 4. ye abate 1. there resteth 3. the halfe of 3. is
1½: Adde to 1. this 1½: you haue 2½. Or subtract from 4. this 1½: you
haue likewise 2½ remayning. Which declareth, the _Forme resulting_, to
be _Heate_, in the middle of the third degree.
[The Second Rule.]
“But if the Quantities of two thinges Commixt, be diuerse, and the
Intensions (of their Formes Miscible) be in diuerse degrees, and
heigthes. (Whether those Formes be of one kinde, or of Contrary kindes,
or of a Temperate and a Contrary, _What proportion is of the lesse
quantitie to the greater, the same shall be of the difference, which is
betwene the degree of the Forme resulting, and the degree of the greater
quantitie of the thing miscible, to the difference, which is betwene the
same degree of the Forme resulting, and the degree of the lesse
quantitie_. As for example. Let two pound of 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 nũbers in order, thus.
___________________________
| | |
| {P}. _2._ | _Hote. 4._ |
| | |
| {P}. _1._ | _Hote. 3._ |
|____________|______________|
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