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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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suli, seu trapezii inscripri (sunt enim inter se aequalia) ad
crianculum circumscriptum rationem in rectis extibere, e
ab illis rectis seriem debitam conversentem continuare, donec
conveniens fuerit approximationem adhibere. Omnia quae de
sideraripossunt de losorithmis (ex rationum compositione ope
sequentis curuae nullo nesotio inveniri possunt.
Sit linea recta DF, sitque alia recta illi normaliter insi-
Pens AB, in qua sit punctum mobile C, quod punctum C mo-
veatur earatione, ∞t, dum perpendicularis movetur versus
E 2 el D normaliter semper insistens rectae E D, interceptae
inter punctum C e recta D E sint ad ipsam C B in rationi-
bus inter se multiplicatis in ratione motus rectae perpendicula-
ris AB: 8. 8. moveatur AB in K MI D XV P; oporcet ut pun-
ctum C moneatur ea lese, xt ratio C P ad C B sie mulciplica-
carationis CMI ad C B in ratione PB ad MI B: eodem modo
ad partes D, supposito AB moveri in 1C d7 LO, Tot pun
ctum C ea lese moneatur, ut ratio CO ad C B sic multiplicata
rationis CG ad CB in ratione OB ad G B: atque e recta DF
ex duobus punctis curuae quaesitae a moru puncti C descripta
ad libitum daris; facile est curuam ipsam punctarim describe-
re, e. 5. Supposcto curuam in rectis AB, K MI, transire per
punctum C, oporcet alia huius curuae puncta invenire: diui-
datur BAL bifariam FI, sitque perpendicularis TIC media
proporrionalis inter BC, A1C; dico C esse onum ex punctis
quaesieis, est enim ratio C MI ad C B duplicata rationis C FI
ad C B, e recta MIB est dupla rectae BFI, est igitur C in +
eurua quaesita. Deinde sit recta dMaequalis rectae ALB, et
Ut