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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 1
# Folio 13r, page id 00067956:0025
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HGK
si super curva HGH  immota, velut basi revolvatur congrua et
2) C,) patet situm earum esse amphidextrum respectu langentis
 (C) 2(C)
communis GR, patet etiam trochoridem tali provolutione desciptam
nullo negolio posse haberi. Sit enim haec descriptio a puncti constantus (C
et ileud
motu, cui responde puncto (C) respondet fixum c eodem modo
C fixumtens
litura respectu tangentis GR quo se eas immotum, ad eam situm
situm est, ergo silantum dR normalis ad GK
e
Ergo SF + CF
et
Ergo si tantum Cm
ducatur normalis ad GR, et producatur ad HC) donec fiat M. (C) aequ
CM, habebitur il) locus in curva quae sita. Haius tangens 1c7
foret parallela.
porro icT, normalis ad GiC erit curvae cetangens
ut ex trochoidum natura constat
ux
ponamus C incidere in A
 GFV. AB X  B(C), y
F Y
BF, E.
GC sen g-G.C
ob triangula similia RFG, et RM C; fiet RC: CM i: RG: GF datur
ergo CM = A RC, GF: RG ergo datur C (C) = 2RC, GF: RG. porro
ob triangula  AM C (adeoque RFG,) et 1(C) BC similia erit angulus
c 1(C)B = angulo GRF. Ergo fit 1CB. C 1(C):: RF: GR. Ergo
C. B = C. (C). RF: GR. seu 2RC GF. RF = GR = 1C B. seu
y =  2. F- Z. V. Y : vDtEr
Ergo XX+YY =
CB: C. 1C =: GF: GR seu X~ e e
Z VVI WV+rI
 2RC. GF=: GR seu X
XX + yy = (C. 1C)E =) 2. F.Z. vV:, vet
se CB = C, 1C. GC = GR
t
Xx tgy =  V 2vC caperest una ad huc
aequatio
E supersunt duae adhuc aequa
b
tiones, una relationis
X + yC = Y- Z XV + y = Y-
eG = Rm + nG.  inter Z et v altera valoris ipsius Y, seu ipsius
d.v. de =r porro superest adhuc aequatio pro 1C. Y tangente
Nempe ipsa GrC normatis ad curvam producatur, dum ipsi FC ai eccurrat
CM in C ∞C =- G (() in C9. Ergo (g = GM. C. 1(C). G. 1() CG
ipsius curvae (C) 1(C)
in p.
st. A
X
= G
et
LG + Fp = F p. CZ. F
seu (GF9) + F p FG1 Fp
1
G9
da
Ge GZ + (GP seu) GF + F N, CZ Fp. FG ut fiet
GZ scu GF, BF p = pp C∞ 1FG + G8 2FP Cq. GG
vt
ex G ad B iC) agatur normalis, ipsi
FpCg. G) FC occurrens in N. cum G G. 1C) sit
normalis ad curvam ( (6) (C) erit GN: N.C):: B. 1(C) : B, 
15
GFGCFZ FG C9 seli ex est autem GN = 2+X et _. (C) = y. v et fiet: Z+X: y. B = y.: t.: ty. 
t autem Gi C)= GC, ergo fit ec e2ty (GN+ N 1e) (it X2X ∞- 2vy
seu X+y 1Vy-