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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 27
# Folio 2r, page id 00068045:0003
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A B exist X existente su verso foret BP sinus rectus respondens fores
sit ABF se rvatis literis ut ante
ns quod pro circulis parallelis, nunc duantur recta EF vel EH parallela
id enum sufficit, erit AD x, BP aequ 2 ax- yAE vel 1BIF erit C
ergo PF erit eC F 2ax -XX B ver AK erit 8. KG erit  v.
fiei V: Z+X= Y:: C: y seu
VY aequ ez + ex + ey. cujus differentialis est:
ode de
est atem in circulo dx. dus:: Y: a -x posita X sagitta y
sinu recto ergo fet:
Est autem, ryo seu  eaequs
ve aequ
tax-
l2
a= x
agu 2aX - XX. se
a- 1 aq. 
a-Xax + X rax x vn avere
 Se eZ + CX aequ Y2ax -XX
v- C
persus y aegu
seu et ZZ + 2eCZXACCXX
y v - 2 vC + ee
aego 2ax - xx
eezZ + 2eCZX + CCxX D vv. 2vetee, aq
vV- 2Ye + ee
aego
VV- 20C4 200
C   Y
H
XX -2aX + aa aequ (- Wvaa t 2 veacit ee aatrvat rvena, dc
seu X = a aequ ea
vr - 2ve+ 2eC
seu
Spr- 2ret 2ec
quo valore O substitnto in  aequ. D. habebituo relatio
si v- e vocetio, co. fiet: eeZZ + 2eCZX + eexx aequ aa c0 et Xaeq Ca +
inter X et v.
cootee Socota
sou eezz + ree z ea +2eeza + éaa +2éa scontée eaa cocotee
eu
LNaocoree
coro + ee
aa cod
aequ
cocotee
ee zZ + 2ecZa coo + ee + 2 e’a Z Y eroreet e atre à ouree +
+ Peaa cocotee aequ aa co)
2Z + ee coco ZZ + 2eez a coco + 2 eeza ee
20a4 + eecdo aa = aa co
aego = 21a3195
=2e’aa
scocote
porro si curva cum ecta FF necessarit alicubi secet veram
I
puncto Vero perpendicularem curvae
a desevolvatur in
 etiam esse perpendicularem
curva quaesitae, vel tangentem curvae Get esse perpendicularem curvo
quaesitae
quaeratur nova hujus modi curva vac rectae EHH
loco rectae EFF.  et harum duarum curvarum quaeratur intersedo
bi scilicet concurrunt aliquae ponamus  in puncto concursus
langentem unius curvae esse 1p.F alterius curvae tangeratem esse EPi H
patet has duas tangentes coincidere respectu curvae, novae intersectionum
quam vocemus
ii.
Ergo curva intersectionum evoluta, ordine dab percure
sed noncdtum ideo demonstratur quod in ea
curva evolature olutioni incidant in puncta, ipsa GF. 24 Nam hoc si
ApIF 2PiH, et ita porro
ubi
contrugeret vere habertur curva quaesita sed hoc esse non dt alioqui Turva
e
si tamen alicubi contingat,
quaesita semper foret Algebraice in potestate,
ut curva evoluta, descripta per punctum 0b. datum sita enim rem determinam
adhuc magis inter evilvendum occuirat puncto aiquo ea propiietate qua debet
sejii
linea quaesita una ex quadra gicibus circuli