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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 157r, page id 00068198:0313
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Resumamus quasi
AR, RM essent datae, ut et co unde
caetera determinantur
AR, Z AM, V.. Evolvatur
olvatur curva HR esit erit HM = SidzZ+ dodo. et erit MR
seu MP seu  = R- Srdzar + dedo
dz: de  X - Z:- y - v
AB, X. BC, y
fietqu
rugus XX + ZZ - 2XZ + yy + vv -2yv = 2p ep + 26c + coc
unde _ X- Z dx -dz + y -v dy-du= (  1p + co deo nam dip hic ralculum
pro, hac vice non intrat, dissimatatur autem aequatio () ex primens
ab
via
relationem inter Z et v. seu  unde (6to) habetur L dvidu - Z. av. a
unde ex a et 6 fit m X. Z: Y V = Z: a; v: a2 unde per aeq. 5. 3, 7 tolli possunt
q et v, et habebitur aeq. Bpn qua solum X et y
CA sit de fit de de + deo dco  dy dy+ dxdx
jam
it
q ad CA, ut MP seu 2 ad MC se ad  mp + PC est autem ~ pC
(AC) et A(C) est deo Ergo  PC essco est fiat pque ad CA seu ad de, ut
est  ad 17 co et fiet p3 = de I: 1+ co et (p9 seu (dcr est
40) 2Vic
curva evolutione descripto  sit PQ= de fietque de= 2ptee de
ot fiel + WFCd de a + deo deo = dy dus + dxax
Pi
pono dy: dx dari per X, y, a,
ex quadraturis per peraeg. 1.
poum co  V datur ex relatione intet Z et V, saltam
proabi Ex assumta relatio ae inter
(Z et v, itemque inter 3 et o determinantur omnia
literae sunt Yf Z, Y, co, X, y, dZ, d, di, do, de dus, dz.
e datur per aeq. 1. ex dq et d
X et y per aegque 2 et 3. Ergo ex aeg. 4 tolli possunt
X, y, et manebunt ex et dy;  sed eadem dx et du dentur in aq. 1. datur
et aequ. (12) in qua dy: dx = X; y; a, in qua tollendo dx et du ex 59. 4
et et aequ. 11. inventa, habetur aequatio, in qua supererunt dz dv, Z, v,  do) dx
Resumamus  sit du: dx X: y;ar
Ex aequ. 2 et 3 fiat
X -  = ya v 1ZdZ+v aV, a = (ex 3)  PFC - y -v
2
Ergo
fist y-v qua HAEtoto: de et L.Z= pra p+co, do: Savataraz
Ergo ex aeq. 4
et  X- 7. 214) 2 + co, dZ: dpdv +d
 evanescente ubiue ∞ + co, fiat, de t d dx adqu + dv (dy - dv)
et
seddvt
frel
s
 de
du compendio tdvde+aZZ sit  d d’et un vu et pret
neede a + d d - du dx: du (= dy
dy dy 28 deo dco det dep + 2deo d_ 3 - 2 deo dep az dx  dep 7 - 2 di dis dZ dx + d2aZ dx dx. 
=) (per 1) (Y+ ad e) + deo deo = axdx adeoque fier
(+
∞deo deo d pdip + 2 da du. 3- 2 deo d idz dx + dgr - 2 dip d dZ dx + dy dz dxdx + dudr xdo
(19
aequ. (2+ C  E)  avdo + dcodco dudv. (- dx dx dv d. ∞)
dedi dx dx
njiam de deo de ly +dco d43, det deodo dodo vocemus dust sit dodu + dep du-
adeo du, dep per compendium vocemus
(1)
 sit deo + di duts, fiet  d, filtu dindip - 2dn dip dZdx + dzdu axdx tla: dvam
= (22) A(X t dy) ato + de dco d-ax dx avav
dudo
unde fit date x dedu depax - 2du di du lx + de L q = (d pi dz - a vidger. y1) et rtbillio
+(co dC) dv et fit dx dep = den dz  du (+cod2)  - d p - 2deo dep)
seu  dx = de . . . . ... + der dz,: d. Ergo per 17. fiet
ne .. . .. . 
Gedd tot
d
a
ve
dy 
 et
do
fierbaner
Ergo ex 12 per 23, 24 13
(aco a + du e- dedm.. . . . . . (25
dio d2a2
-dvavdepd
(4C.)  +Z; (pted a
Rursus sed aliunde de est elementum curvae evolutione
d
du3 + dv de dZ drdo s. . . . . + dedz de + d ptr an
descriptae. Nam Fp =.  RN seu Z + Gp et GP = mq  M = RF et fiet
Fp = ZF Sy- RF sit RF ad RB, B ut MB ad MC seu ut  ad 15+ co fit  et RB = X - ZZ tco, 
oit
ubi de lalet in s.. . . . .
Ergo +P 7 +do et proinde erit
ubte aa dix aui ad a eg iadest veniad dit. atei
1Z
di
ergo RF = 1 + 0
e.de 1  seu AF=
dz
Ta