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# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
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PHZSICA TRACTATVS L
PROP. CCLXV.
Ouando lunatur idem arcus sem-
per est eadem quantitas linea curuae,
licet sit obstusior, vel acutior, pro
maiore vel minore tensione: IlaeC
propolitio ex supradictis neceltario
lequitur; nempe eadem est quan-
ticas curua e recta; v. 9. Cxlindrus
Ei8. 39. AC, curuacuS in FICF, est ciusdem
quanricaris; Cuppono enim, ex
censione arcus. Sequi cancum ten-
sionem; vel dilararionem sub-
cilioris materiae que in poris cr-
lindri continetur: hinc extremi-
3. 33
LaTeS HIE, co accedunt propius ad
axem, vel Cagiccam BF, quo ma-
sis lunatur arcus: Flinc praedictus
cxlindrus AC, in nullam curuam
lunari porest, cuius extremirates
ALLINSAnE reCtaS AH, OF, paral-
lelas CF; alioguin cylindrus luna-
cus longior esser sciplo recto; v. 5.
HCF ellet longior ACC, quod
CA conrra hypochelun: Plinc pol-
Cune delcribi intinicae curuae, qua-
rum contactus lic in C, aXC COI -
muni EC, et brachiis aequalibus;
quarum obcusiores, minOrem FeN=
sionem, acuriores rero maiorem
Cuxponune: hinc acuriores longius
recedunt a rectis ALI, CF; Ob-
ruliores minus: quomodo vero
possic duci linea cerminans verim-
que omnes illaS curuaS, nOn eA
huins loci dilcurere.
COROL
Primo ex his colligo, cylin-
drum C C affixum immobiliter in
C. duobus modis posse lunari,
primo s aequalirer rensio, vel in-
arcum circuli; nempe in circulo
omnis tangens in eodem Ccilicee
circulo, aequalem angulum con-
tingentiae Facie; nec habet ruum
Ceomeneum, rel rnus accus circu-
li, maiorem curuitarem, quam
alius, re perspicuum cst: si veco
curnatio, omnibus illius punctis
Secundum, hoc est (I vis censionis,
dictribuatur; Secundo (i inae qua-
vel curuitaris, inxqualicer cylindio
CO distribuarur, hoc etiam duo-
bus modis heri porest; primo, si
tensio, vel curuicas diverlorum
Punctorum GIC, ve dictancia ab ex-
Fremo puncto C; V. 8. tenlio pun-
ai O, ad centionem puncti (, ve
O5, ad R; secundo s pradicta
diueclorum punctorum rensio (IE,
re quadratum praedictae distantia;
V. 8. centio puncti , sir ad ten-
sionem puncti IE, ve quadeacum
OO. ad quadrarum RC.
Secundo, incer omnes hguras
curuas, vnus circulus aequabilem
habet, in coca periphaeria curuica:
tems celiquae veco inequalems
Parabola vero inaequalem habet.
maximam, Ccilicer in verrice, cd
tamen minorem in aliis legmentis,
quo longius à praedicto verrice re-
cedume: hinc ad verricem parabo-
lae maximus est angulus contin-
senriae; nempe tangens parabolam
in vectice, tacic angulum rectum,
cum lacere coni; ac quo lonoiiis
a vertice tangir, eo propius adt la-
tus coni, tangens ip(a accedir; cu-
ius contactus nullum Facie angu-
lum. cum Cuperticie coni; igicur
curuitas parabolae ed magis immin
nuicur, quo a praedicto verrice
lonsiusrecedir: Porro haec curui-
cas imminuieur non secundum di-
stancias, led distanciarum quadra-
ca; Sc enim v. 8. Cylindrus CB, Fi8. 39.
direr: (I pRimO MOdO, CUTUATUE In IER INCUTVETUI, re ris rensionis,
1C