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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 7
# Folio 24r, page id 00068102:0003
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si quaeratur linea CC talis ut tangentes ejus CF
lineae datae EFF occurrentes sint magnitudine
datae verbigratia ex datis AB, vel aliis ex
pe puncto fixo determineta ratione assumtis
potent linea C7 CC describi, ducendo folum
per F lineam EF, filum FC cn affixuu pondus
plano incumbens C ita, ut inter ducendum filur
debito modo, pro magnitudinis latione, decrescat
data relatione ater AB et Henivenire
lineam C(C) hhoc per axtificium fili ducenti cum
pondere nunexo ic effici potest, si conus
vel aliud quod libet solidum poretur rotatu gemtum
seu cujus sectiones basi parallele sunt circuli axi
suo per A trauseunte sit percendiculare ad hujus
pagina planum, et ita descendat Axis per a
a ut diametri arculorum in paginam inciden
tium et contractio
data relati Ergo datque relatione inter AT et TC
vel inter AD et DC describi potest inlinea
C
AB sit X BC, y AT sit T, et
et paret esse 1+X:  C:
ame 4 2tX + X 4 G
Bu
vade
TC sit C
xdy.
t+X: y: dx: dys
Ergo ydx +dy+xdy. seu Fydx xdy.
ji
et cc 1 +2tX + X + y. sit jam relatio inter y. X. et d
a
si jam tollendo duo ex his tubus per  et C. sollatur
simul tertium, erit res resata ad relatiotem inter e
et c
 sed possumu obtinere ad huc novam aequatione
s.
loco per differentialem ipsius aeq. 4, et fet cdc- Tdt+ tux xdx
+xdx +ydyue. et ita  poterimus ex orqu 5 tollere
. ∞. ayiax per +. C. ae idc. si modo producta aequatu
fiat tractabilior
seu reducibilis ad relationem inter
uum
sit BP- ex AB seu X fet y: p:. dx: dy
et C
sit jam relatio inter X. y. xdy: dx. si non ponatur
aquatio servare leges homogeneorum, secundum y et du
s
verbi gatir a+ V+ dety Y est qdu L0 patet simul tolli
polle  et daxidiet restare solum p et X. Eistque hocq
a