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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
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breniore quain Archimedea et non minus geometrica; utor
quoque inpropositionibus maris ob ziis methodo Caualleria
na, quae etiam nullo necotio reducitur ad Archimedeam vel
nostram. Duod si geometra, post dilisentem huius methodi
applicationem secundum figurae proprietates, nullum inveniat
problematis exitum; recurrendum est ad seriem convercen-
tem, cuius terminatio sit ipsa fgura incognita vel alia act
eam in ratione data; ob hanc enim rationem; conatus sum
aliarum fisurarum proportiones reducere ad proportionem in-
ter ficuras planas; in his enim exiscimo faciliorem esse serie-
rum convergentium doctrinam: non tamen au deo affirmare
seriem converrentem semper posse in veniri; suspicor enim hane
methodum esse insufficientem ad omnes proportiones non ana-
lrticas inveniendas: 2icunque nostrum tractatulum de
vera circuli ex hyperbolae quadratura volumus esse 2lti-
mumnoserae methodi refusium, nam serierum conxersentium.
doctrina est generalis, quae efisurae proprietatibus semel inuen-
ta solutionem possibilem exhibebit; ex proinde objectionibus
contranoscram doctrinam hic satisfaciamus.
Primo obiicitur contraritulum; nempe tractatum meum
male appellari veram circuli ex hryperbolae quadrarura, cum
pocius sit conatus demonstrandi illam esse impossibilem; re-
spondeo, si esset impossibilis, nulla daretur proporeio inter
circulum et diametri quadratum, et ideo fal sa esset 5 defini-
tiolib. 5. Fuclidis; si aurem sit possibilis, monstrandus est
nostrae error, si nostra vera non sit. Alii sic obiiciunt: haec qua-
dratura nulla est, quoniam non assisnatur proporcio inter cir
culum