regulam supra eam jaceant: seligo terminos æqua-
tionis per parallelogramma contingentia regulam designatos
et inde quæro quantitatem quotienti addendam.

Sic ad extrahendam radicem $\mathrm{y}$ ex ${\mathrm{y}}^6-5\mathrm{x}{\mathrm{y}}^5+\frac{{\mathrm{x}}^3}{\mathrm{a}}{\mathrm{y}}^4-$
$7\mathrm{a}\mathrm{a}\mathrm{x}\mathrm{x}\mathrm{y}\mathrm{y}+6{\mathrm{a}}^3{\mathrm{x}}^3+\mathrm{b}\mathrm{b}{\mathrm{x}}^4=0$; parallelogramma
hujus terminis respondend |t|ia signo nota aliqua $\ast$ ut vides
in schem. 2. Dein applico regulam $\mathrm{DE}$ ad inferiorem
e locis \signatis/ in sinistra columna, eámqꝫ ab inferioribus
dextrorsum ad superiora dextrorsum gyrare facio
donec alium similiter vel fortè plura e reliquis
signatis locis quam primum attinget \cœperit attingere/, videóqꝫ loca
sic attracta esse ${\mathrm{x}}^3$, ${\mathrm{x}}^2{\mathrm{y}}^2$, & ${\mathrm{y}}^6$. E terminis itáqꝫ
${\mathrm{y}}^6-7\mathrm{a}\mathrm{a}\mathrm{x}\mathrm{x}\mathrm{y}\mathrm{y}+6{\mathrm{a}}^3{\mathrm{x}}^3$ tanquam nihilo æqualibus
(et insuper si placet reductis ad ${\mathrm{v}}^6-7\mathrm{v}\mathrm{v}+6=0$
ponendo $\mathrm{y}\times \sqrt{}\mathrm{a}\mathrm{x}$) quæro valorem $\mathrm{y}$, et invenio quadruplicem $+\sqrt{}\mathrm{a}\mathrm{x}$, $-\sqrt{}\mathrm{a}\mathrm{x}$, $+\sqrt{}2\mathrm{a}\mathrm{x}$
& $-\sqrt{}2\mathrm{a}\mathrm{x}$, quorum quemlibet pro initio quotientis accip [illeg] |er|e \liceat/ prout e radicibus
quampiam extrahere decre [illeg] |tu|m est

Sic ex ${\mathrm{y}}^5-\mathrm{b}\mathrm{y}\mathrm{y}+9\mathrm{b}\mathrm{x}\mathrm{x}-{\mathrm{x}}^3=0$ seligo $-\mathrm{b}\mathrm{y}\mathrm{y}+9\mathrm{b}\mathrm{x}\mathrm{x}$, et inde obtineo $+3\mathrm{x}$ pro
initiali termino quotientis

Et ex ${\mathrm{y}}^3+\mathrm{a}\mathrm{x}\mathrm{y}+\mathrm{a}\mathrm{a}\mathrm{y}-{\mathrm{x}}^3-2{\mathrm{a}}^3=0$ seligo ${\mathrm{y}}^3+\mathrm{a}\mathrm{a}\mathrm{y}-2{\mathrm{a}}^3$, et radicem
ejus $+\mathrm{a}$ scribo in quotiente.

Et ex $\mathrm{x}\mathrm{x}{\mathrm{y}}^5-3{\mathrm{c}}^4\mathrm{x}\mathrm{y}\mathrm{y}-{\mathrm{c}}^5\mathrm{x}\mathrm{x}+{\mathrm{c}}^7=0$ seligo $\mathrm{x}\mathrm{x}{\mathrm{y}}^5+{\mathrm{c}}^7$, quod exhibet
$\sqrt{}5:\frac{{\mathrm{c}}^7}{\mathrm{x}\mathrm{x}}$ pro initio quotientis. Et sic de cæteris.

Cæterùm invento hoc termino, si \is/ contingat esse negativæ potestatis, æquationem
per eandem potestatem indefinitæ speciei potestatem deprimo, \eo ut/ non opus sit inter
solvendum deprimere, et \insuper/ ut regula de superfluis termin [illeg] |i|s elidendis \mox tradenda/ aptè possit
adhiberi. Sic proposito $8{\mathrm{z}}^6{\mathrm{y}}^3+\mathrm{a}{\mathrm{z}}^6\mathrm{y}\mathrm{y}-27{\mathrm{a}}^9=0$, cujus quotiens exordiri
debet a $\frac{3{\mathrm{a}}^3}{2\mathrm{z}\mathrm{z}}$, deprimo per $\mathrm{z}\mathrm{z}$, ut fiat $8{\mathrm{z}}^4{\mathrm{y}}^3+\mathrm{a}{\mathrm{z}}^4\mathrm{y}\mathrm{y}-27{\mathrm{a}}^9{\mathrm{z}}^{-2}=0$,
antequam solutionem [illeg] |i|neo.

Subsequentes q [illeg] |uo|tientum termini eâdem methodo
ex æquationibus secundarijs inter operandum prodeun
tibus eruuntur, sed \ut plurimum/ leviori tamen curâ. Res enim
peragi solet dividendo depressi\ssi/mum e terminis cum
indefinit [illeg] |è| \parva/ specie ($\mathrm{x}$, $\mathrm{x}\mathrm{x}$, ${\mathrm{x}}^3$ &c) absqꝫ specie radicali
($\mathrm{p}$, $\mathrm{q}$, $\mathrm{r}$ &c) affectis, per quantitatem quâcum species
illa radicalis unius tantùm dimensionis abqꝫ alterâ
indefinitâ specie afficitur, et exitum scribendo in quoti-
ente. Sic in exemplo sequente termini quotientis
$\frac{\mathrm{x}}{4}$, $\frac{\mathrm{x}\mathrm{x}}{64\mathrm{a}}$, [illeg] $\frac{131{\mathrm{x}}^3}{512\mathrm{a}\mathrm{a}}$ &c eliciuntur dividendo $\mathrm{a}\mathrm{a}\mathrm{x}$, $\frac{1}{16}\mathrm{a}\mathrm{x}\mathrm{x}$ [,]
$\frac{131}{128}{\mathrm{x}}^3$ &c per $4\mathrm{a}\mathrm{a}$.

Cæterùm