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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
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dLeccate.
Cylindro, esse ut 2 ad 3; se inde coenosei posset quam ha-
beani omnes eorum diamerri ad diametros horuin, in
ventum foret quod quaeritur. nempe Ciroulum illa, hae Qua-
dratum diametri constiruunt. Reducto ita problemate
Geometrico ad pure arithmeticum.
Flsic icitur inquisitioni, istins anni 165Y fine,  ini-
tio sequentis 1652, me applicui; ea plane methodo quam
indicat hic Tractatus: opinatus vel inde constare aliquan
de posse quomode quadrandus esset circulus, vel forte ne
quidem quadrandums esse, vel saltem aliquid hinc emersut
rum esse quod opera esset pretium.
Aegressus isitur sum primo (ut a semplicioribus incho
em) series simplices, pute quantitatum arithmetice pro-
portionalium, vel in earum ratione duplicata, triplicata,
exc. deinde es subduplicata, subtriplicata, 5 c.. atque ex
his composita, puta, subduplicatae triplicata, ec. aut eti-
am qualitercnnq: multiplicata, vel juxta denomcinationem
rationalem aut etiam irrationalem. In quibus omnibus
res plane quidem ex voto ex supra spem successit. Unde
Theorema tandem generale emersit, Prop. 64. traditum.
Sed e guadraturam semul reperi non modo Parabolae nova
methodo praestandam, (ed e Paraboloidum omnium, eo
rumq: complementorum, quod nemo antea, quod sciam,
aecressus erat, nedum assecutus. Adeoque hinc statim Ce-
ometriam auetam persenst; cum enim antea ex figuris
curvilineis sola fere parabola gnadraturam nacta erat,
jam paraboloidum omnium infinita genera una quidem
e generali methodo unica proposerio quadranda doceat.
Et quidem si unius Parabolae quadratura Archimedem
tantum nobilitaverit, (ubi omnes deinceps Mathomatiei
ex eo tempore substiterunt tanguam ad Eerculis colum-
nas, eratum illud orbi Mathematico faturum satis prae-
sensi, si etiam ejus modi ficurarum infinita eenera qua-
dranda doceum. Sed es Conoidum item e eyramidoi-
dum