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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 6v, page id 00068197:0012
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(16)
inde nnsi ponamus 00D aequ 1. seu  aequ
rum quia
destruantur,
omnia destinuntur.
b aequ. 7. satis fait si et 15 satis facit si omnia
et eo casu nihil novi colligi potest ex aequ. 15. ideo
evera nihil novi colligi potest ex equ. 15. licet revera aequ. 16
etum ipsis non sit incompatibiles. Sed ipsam pro arbitrio ponere
Atque exhis
e
colligimus post aequ. 7.
otemet habitam fuustra novas differentialis adhiberi, quod et praevi
aepea,
deri poterat quia ea quae assumsimus,
nempe 49q et 7)))
 tanquam aliunde notas, ex his ipsis prioribus jam consequantur
data fuisset relatio inter AB et AP. seu inter P et X. videamus:
poramus ergo datam pex X Est autem dx: dy:. y: p X repetitur ex
c5)C
drioribus aequ. 3. 4. unde fiet f ex 2 et 4. y: px: V+G: Z-x. seu:
yq yx aequ pvapy.
cuique
quodum differentialis: Edue. Yax. xdus aego dp vdx tdpydx
daqu Namdatur de per ex ob aequ 1 per X ob, aqu. 1. seu breviqus.
Xduydx aequ 940 d da + pdus. Ergo dx. dys
(5)
ii ZEx P: y+ yudp
d yx aequ ∞p +Yp - XVC XG) seu y. Z P aequo v p- X idque nihil aliud
canficat, quam quod patet extigura nempe esse. BC: RS.. Bp. Ps. nisi
vid sub p intelligendus ejusvalor ex X. cujus de equ. 6. differentialis est
Ep dy y dp dx aequ V d da vdx dput seu Z pdy + vix aequ. vtus apdo
a per 2
nic ex G.
-P. PX:  + v aequ v+ dp.
go ex aequ 3.
y+ v. v
eu go
(81
RPAup y - p. seu 71D. v.: +x X.Z. 
ee
ss= quad ZX: V5: 7- x Aliter per 5vel 6
 p: pax yequ. va
a
e e
e
E
PG+V aego VP) vX + vZC PP: Z- P seu +V ago v. Z X: 2-p. seu
vau.
quadrando et addita aequ. 3. fiet (-  quad Z-X aeque WV quad Z-X: Z- p c ujus differen
tralis erit: fZXsis aequ. vv
(9)2
X.2p. 2
 X. Z ap +Z p: quadr. Z. p
Vv. X-Zdp +Z- p aequ cub g- p quod est notabile Fheorema generale
curaad
no volutione descriptis. Vei de
 A. Cam demonstrari possit ccirculum curvedinis secare curvam in
qualuor punctis coincidentibus, seu esse quatuor radices aequales sequeretur aequ. q
huc semel ad maximas et minimas determinari posse et  haberetur adhuc una aequa
(10
decima sclicet, nempe vo Z aap + dp- dp) aego 3 quad Z. p dp (ubi
nota dp esse dimensionis nultius seu numerum, et dap esse dimensionis minus quam nullius
seu -1. quae si procedenent, semper habetetur (urva generatrix et
nunc quidem nondum habeo quod quid contradicamu sed mesa
accuratissime
qvia tim cupposni
disentienda, inno video jam rationem cursit non procedat
circulum tangere curvam, aquando dx. dy. utriqque, et postea adhuo ad
icet cooncidentibus, et ceta revera habui jatu a radices aequales Ergo
lio 10 non procedit
ana radices aequales u
F.
i
in
retio
e
E enon audemus
e
u