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# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folio 199r, page id DE-611-HS-3653099:0397
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reciprore in duplcata ratione dictantiarum, concludit pariter pag. 55.
coroll. 1. ergo vicissim curva in qua viret centripeta sunt in reciproca
ratione duplicata distantiaum a centio virium, illaa curvam
esse sertionem conicam; Ego vero dico non legitine collisi posse
seas convertas, licet earum veritatem singulari quodam calculo (qui
alias ad differentias secundas dedurit haud Facle separabiles) com
pertam habeam: Conclusiones igitur Hucloris vitiosae sunt for
maliter, quamois vera materialiter; demonstrare enim puut de
buiscet (quod autem non seut) unicum tantum hic genus cuva
rum posse datae legi vis centripela satiifacere, seu legem eam vi
rium soli sectioni conicae competere et nulli alii curvae; Norli enim
Lijusmodi problemata quae praesentia desinunt adin aequationes dif
fereatio differentiales plerumgus admittere diverta curvarum genera,
imo quandoque curvas trantiendentes quasdam, et alias algebraicat eidem
problemali posce salitfacere, quemadmodum alibi ortendi; quid opus ett
mullis: habenus exemplum apud ipsum Nerotonum pag. 47. prop. 9. ubi
otendit in spirali Logarithmica centium habente in ceatio virium
Creciptoca)
vim ceahriretam esse in triplicata ratione dittantiarum; potuistet
enim eodem sure ex ea concludere conversam, dicendo, unde viciscim
roce
Culi ferit pag. 49. corell. 1.) Si vis sit ait cubus dirtantiae, movebitur cor
pus in spirali logarithaica centrum haberte in centio virium; inter
ria ila ratiocinando Auctor non tantum formaliter sed et materialiter
enorari modo peccasset; nam praeter logarithaicam spiralem reperio aliud
genus curvarum, ubi similiter vis centripera eit reciproce ut cubut dirtantiae a
centio, sic inter alias quam plurimat quae satis faciunt unam praecaeteris ne
morabilem invenio Hiyperbolam spiralem, cujus nempe natura hac eit, ut
recla a centro ad curvam duitae oblineant rationem reciprocam cum angulis
u faciunt cum recta aliqua positione data per ceatium ducta: Item
Si ad recbam haac tanquam super axe describatua curva algebrarca cujus
hac aequatio 5=
rr- 2aa
iua-rr
Suntis scilicet coordinalis seer excentio virium
dico etiam hanc curvam algebraicam hoc praestare ut mobile in illa feratur
viribus centricelis dittaaliarum cubit recmproce proportionalibus. Ea ergo jam
hes curvas diversissimorum generum comuni Lanen Lac afsectione gaudeates, qua
igitur si in aliqua curva reperiatur, ex hoc solo nondum concludi potest
illam curvam esce logarithaicam spiratem potius, quam Hysperbolam spiraleno
aut alteram illam atgetraicam, aut aliam etiam quam esxtibere possem, ita