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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 31r, page id 00068160:0061
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Investigatio
semidiametri circuli curvam, in proposito
puncto osculantis, si pro ordinatis ad hibeantur convergentes
ad certum punctum
ad centrum radiorum p
sit curva 16GC, e unde radii convergentes pC; quaeritur punctum
Vcentrum circuli osculantis, adeoque Cv ejus radius semidiameter, sint
elementa arcuum 1C2C, 2C3C unde ex 2C et 3C extremx per pendiculanite
eductae concurrant in V. ex 2C in 4 prc perpendicularis 2C.L
et ex V in P, C et P2C, perpendiculares ViZ, VIZ ex quibus V1Z secat
Producta) PrC in d, et V2Z secat pic in β.
patel obte e similiu In triangulo pharacteristico 261L+C
EC iL 2C, a vicetur: 1C.L, dx. iL2C dy; et 1C2C, de et PC, X
ob triangula 2C 1L1C, eV
CZV similia fit CZ, Z
sit CZ: CV: d dus: dc.
Russus ob triangula Y V2Zd
et P1Z5 similia sit  d 2Z: d1Z: VZ
PZ denique
ob triangula P1Z8 et PI L 2C similia fit 1Zd: 1L 2C son dy:. pZ: p
C.
Ergo dZ diZ Tollendo _d1Z ex analogia 2 per analogium 3. fit
L d2Z. PC: dy. P.
eX
Z. PZ seu S2Z: dys. VL
C
jam quia ed et srZ differeulinum hubent haberi possunt pro parallelis
errore inde sidifferentia enmerit infinitres, si 12d et B2Z considerentur ut
elementa arcuum centris p radiis pB, P, Z P2Z descriptorum, patet, sumi posse
d2Z pro  β1Z seu d2Z esse differentiam inter P1Z et p2Z adeoque
d27 esse = d p=
L
17)s
iu
dy. L: pC jam PZ = PC, 7 CZ. Ergo
o)
dez = d pC - dCZ jam d PC = x, et dC d cZ - d ay: de per 1
quos valores substituendo in aeq. 9. fit d PZ = dX - CV a dy: ac  dyVZ: p
WZ= VE VZ: VC:: dx: de Ergo set
per 7
jam V d VZive
et dy = XcO: a posito eo angut esse anguli etament seu alculationis circa
4
elementum, nam ta ratio a; nam 1L2C seu dus sunt in ratione composita
radiorum pC seux et argulorum 1CP2C Ergo dy: Bc = coia. Ergo denique
E
ex y 12. (3. 14 fit dx = eV d dy: de= dxxia d de et denius
ax
ju
ai a ag. nc. aqo
Ergo  CV = dX: d dy: dc + Codx: a de
jam ddue: de =