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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 156v, page id 00068198:0312
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ex
AB
BC, y
A(R, Z
CA:. AO: VOctR:: (C9d: DD: Oc
CA ∞: AO = cd: DB
C
AD: DC = DB.
CA + _ AD + OC)= CD+ DD + DI
Meco PC -
RM. v. 
pono dari dy: dx ex X, y, a; pour et dari seu dy. dx = f.a pour et
dari relationem inter AH Z. et co, unde habetur et relatio inter 7 et 
posita dari dunensione curva H M. Investigetur relatio inter
 CA et A(C), seu quae haberi potest ope fra, adeoque et
ope fa, - f: a, X: a et y: a et ope Z et v, eo
quod si jam fiat PZ ad cA ut Mp ad AMC pate
fiet M P per: MC = Ou.  quod si jam reperiatur
C. Itaque
A(C
est autem A(C) differentialis ipsius 
V
si tabis assumatur curva . M, ut in curva da
data initio aequatione dynax habeatur dusdx se f: a
 habeatur C:) per solam DC, habebitur quaesita
quadraturatio disse tangenbialium
AB, X
l BC, y
dy: dxL f: a
et f. a 2) X: a; y: a
_ jam Me tangit HM. Egofit AB - AN seu MN, ad
BC = NM seu ad NC, ut AZ ad do seu fiet dZ: do (3tio) = X - Z3 :, y- v
MP seu p est aequale curvae evolutae K M. Hinc
AR = Z
Rn = v
PC Ar  sit c0.
A(C) est solum incrementum ipsiup AC smestdo Nempe si inter evolvendum
 punctum C moveretur in fito MC summa omnium A(C) com–
to)
poneret PC. jam per paiora patet  et dp = Ldq d3 + dodo
Jam per praecedentis paginae finem et aass) cod:
aa + su (2) Vrco edioi calculus oriltur talis, pro X, y;Z f seu atque, de
substituatur X- Z, 9. v, 4+co, adu -ddo deo et fiet
da -d2
1t dtdo = aaaa H ds aa, e  ai rdy- dx+, PF C, 1 (2)
de de to
C(5) Ldxd + dys-dv 1p+co La. Alx. 2) + Ay v) ay. do
de
de
tolli potest dy  per dx, X, y a.  Et tolli pb de per dque, tam ope 6e9. 3. gener aliter
dx -d
jam est
de de + deo deo =
ergo, in aeq. praeter de et deo, ha restat solum dq: dx
adhuc XX = 2XZ + 2) + gy - 290 + vr = Y 2Y + 21c0 + coco, fietque
tX LXdZ -  ZLX + AZdZ + ydus - ydv- vay + var  d ipdeo + codco
X (H. dZ) - Z(l X. 2Z) + y (dy- de) - v (dy du) = u (+ c0) deo
seu (x.Z) (draz) + y - n (dy d0) = (1 + cd) deo