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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 2
# Folio 32r, page id 00068202:0063
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si corpus cogente qi centripeta quacunue moveatur ulcunque
ontque eorum velocitates
in aliquo aaequalium altitudinm casu aequales
velvertates ecrum
in vibus casibus erunl aequades (+ nempe non mulatur descensus etsis
vis impressa cogat a line recta decedere +)
st sit maxima a centro distantia ad quam corpus
Hinc si quantitas
de quovis puncto
trajectoriae ea quam abi EF belocitate sursum projectum ascendere
possit sitque quantilas A distaa corporis a centro in alio quovis
orbis puncto, et vis centri pela semper sit ut ipsius A dignitas quaelibet
p-) cujus index n - 1. esq numerus n multe mminutus vel vertas
corporis in bi allitudine A erit ut In P = nA atque adcodatur
differentia virium quibus corpus in orbe quiescente et corpus
aliud in eodem ortie revolgente a qualiter moveri possunt est in
sruplicata rave cois altitudtinis iiverse
 Hactenus cum centra virium centripelarum sunt in
planis orbium. et tamen et centrum essi extra planum
oibis, ut cura grave movetur cn plano inclinato
posito quod vis entripeta proportionalis sit distaa corporis
a rentio corpore oia in planis quibusnimus revolventia describent
Ellipset et revotuves cemporibus aequalibus peragent quaeque
noventur in lineis rectis ut tro cilibus discurreneo, sungulas eundi
releundi periodos iisdem temporibus absolvent
sa rota globo extansecus (intrinsecus) ad angulos rectas
insistat et revolvendo progrediatur, ncirculo maximo longitudo
lineiris curviliner sccucaveidat ) quod punctum quodvis in rotor
perimetro datum ex quo globum fetigit confecit erit ad duplicatum
sinum versum areus dimidii quoque lobum hunc doturs hoc tempore
inter eunde tetigit, ut summa (differentia) globi et Tota
diametrorum glbbi et rotae ad semmdiametium globi (+datur ergo
omnium harum curvarum in rectum extensio +) (+BB eadem curra etrum
gometrire deviniri possunt; ob datam proportionem areuum +)
Hinc pulcherrime deducit modum describendi cyclvidem evoluve
alterius hoce modo: e Glo cycloitalis dicatud intin globum qua
descubitur a q ca concavo, extra qua a convexo seu a rota
exterius incidente jam sic: Intra globum ZVS centro C. descriptum
detur cycloidalis QAS bisecta in R et punctis sins extremisque ets superficier
globi hinc inde occurreris Agatur CR bisecans ZS in O et producatur ea
ut sit (A ad (O ut CO ad CR centro C. intervallo A describatur globus
exterjor Bd et intra hunc Globum rota cujus diameter sit AO defcribantur
duae semicuc vides AQ, AS quae globum interiore tangant in Z et S. et Globo
exteriori occrrant in A a puncto illo A filo Ap F longitudinem AR aequante
pendeat corpus T et ita inter semicyclvides AQ, AS, oscilletur ipsum pondus I
prateren si vis centripeta cendens ubius
pudique ad globi centrum (sit in locis singulis ut distaa locia centro et hac
describet cylloidem datam
sola viagente corpus T oscilletur in perimetro incloidis modo descripto
oscillationum lennque maequalium aequalia erunt tempota
si vires a madhina in pendulum ad molum conservandum impressae
ita cum vi gravitalis Enoni possint, et tota vis deorsum semper sit ut linea
olation eunt
cncip cons nd sinum 7
cemnes ilochione.