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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 36v, page id 00068160:0072
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ita cet gereraliter tam  in ratione temporum incrementa sunt in composita ratione raovorum enpro
radiorum et paracentricorum, et progressuum cyrcusa dump
Ergo sumbis aequalibus temporum incrementis in
protio
projectorum, erunt radius paracentrici reciproce ut progressus
A(C)
mobilis circulares.  sunt autem progressus circulares in
e
1LC)
composita ratione radiorumX
e
CH irculatio
CP(C). Ero ips nem. demrum in gemeners. sit aquabilis
alies a
sit molus projecti gravis in sua atbita
Ergo aequalibus
circulationum in ratione duplicata reciproca radiorum
AB aequales ipsis pC, et sipsae BE pro portionales areis
C itaque ssiGeri Nassumto pro motus initio
itaque si A2 = p _ habebimus lineam BEE temporum seu arearum
per A ducantur AF parallela ipsis BE, et porro ducantur EF
vel areis
AF, radios fore AB vel FE angulos circulationum insumatur AQ
aequal in AF sumatur AG. aequalis ipsi A 2 et per Z ducatur9 H
parallela ipsi AB et per curvam tangens  ET curvam langens
in E, occurrat Axi AB in T et ipsi A H in H. sumatur in y
ipsa yB aequalis AT et jungatur TR perpendicularis ad ZH.
erunt cet ipsae RH ut radiorum incrementa LC seu ut promessus
progressus autem circulares cum sint reciproce ut
radii itaq, et circulationes reciproce ut radiorum
incimenta
anhoumseu
quadrata itaque si ducatur  linem ZmM talis ut is FM
sint ad A7 reciproce ut quadratum AZ est ad quadhatum FE
erunt ordinatae FM ut circulationum seu angulorum incrementa
et spatia 7 A F M 7 ut ansuli integri ypC
Nams istis novi repertis adjungamus quod supra
ut
ets
monessus C
en alia scheda repetivimus conatus paracentricos 3CK
esse in duplicata ratione progressuam in orbita  ZC3C
PC
composiba cum directa secantium tiou
aroca radiotum Vi quos habent circuli
angulorum contactas side curvedinum
radios et curvara
omnia ad Calculum
osulantest. Itaque nunc demum.
de vocemus sit p Radius paracentricus pC sit X
angulus circulatio seu angulus sit y et LC erit dx,
et (C) erit ad et incrementum circulationis seu angulus CBCC)
erit  dy. (sumtus pro elemento circus circuli dati radia et est autem
L(C) sC progressus circularis L(C)F dy ti pC pasiet L(9 - dyX: a
et area incrementum L() in X eut dyx quad = at. quia
repraesentat tempus jatue seu + = (dyx.   et porro
Ut autem exprimantur
integra tempora, sumatur recta ex A puncto  certo
a
s
sumtis temporum incrementis in mota projectitio gravis alicujus
vel levis centrum certum respicientio, erunt anguli
 circa centrum
ex centro emisso paracentricorum.
restilinei
Elementum curvae 2C3C = Sdx dyq sunt autem elementa
cuure in composita ratione temgpotum merencaloum tempocatemum dt ot
2() = 1 -
C. any
PC l
ergo FEMC
0