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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)
# Folio 114, page id 1047377675:0130
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114
naTurX, ve (ducta recta F. C tangenEe curvam BIED in quoli
bec puncto F. _ ductis parallelis FF BC) rectA FBACaqua
lis e parallela rectae CF: manifectum est ex huius7 rectam
CF seuBF eNe criplam rectae P O, cumque hoc semper Aac,
evidens cA Fguram HIBDE eNcrriplam Hgure FIODFs acque
ex huius eY AgUTATIBDE eA xqualis Agura TIEDR; de prO-
inde Egura FIFDK eR ad Rguram FTODF in ratione Z ad 13
dividit ergo curra HIFD quadrancem circuliin ratione 328
2. quod demonstrare oportuit.
Ouod si rario CIad F I eNer quineuplicata racionis Cl ad
OI curra HE D quadrancem circuli diuideree in rarione 8
dd 3; E aurem sepeuplicata inratione 7 ad5; d lic in pene-
res liratio C Iad FI he multiplicaca rationis GT ad OI in ra
tione cuinscunque numeri imparis adrnicarem, curra HIFL
dirider quadrantem circuli in racione ciusdem numeri im
paris adnumerum imporem proximeminorem, qua omna
demonstrantur sicuc hoc cheorema. Lodem prortusmodo
demonstracur no solum illa Vallihi incerpolicio qua spacium
cissoidale mensurat inlibro de creloide, sed eciam omnes
Fortalis aliae quae imoginaripossune, suppolica primae incer-
Pohica tigura mensura. Guod Ciracio C lad E. lGc mulripl1
cacarationis CTadO I in ratione numeri cuiuscunque paris
adrnicatems Facile daretur Agurae IEFIED quadratura opC
huius 5q. uc docer Vallihus in sua Arichmerica intinicorum;
e ideo innorescie in recta DR centrum aequilibrii hgurae
DEFK opChuius 37. Hlinc cciam evidens cst DEF eandem
semper habere racionem ad D E.O quam habet I F HI K ad
DE FIO, quod summopere nocandum, nam (praecer mulca
alia pulcherrima problemata) si secetur conois parabolica
plano ad anem porallelo, ex daca eiuldem ab axc diltancia
dabirur huius ope urrumlibes conoidis scemencum.
Sa
Dat
N