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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 10v, page id 00068072:0020
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Compropemus fiet - deo = dd vdz) Y. 2 dzde se d2d2
q dudo
lco( (aabico deosto 3+ 2sdco A; (= (1 + 5d 1)) X 4=
ec
osaa 
2dv (d1+ sico 7. aa
seu -deo = - du    + suo)) (+ 2do (it st) et habitur successus. Est
(10) (asdao acot joco
ed cd (1+ Sa)
ergo -deo = dd de d d  2 dedy duddz: deed 
et invenimus ergo -ddv: ddZ = (23) deodo - 2d2dZ, dv: d2
) dq ddv - 2 dodezue, dz c: dodvddz
atque ideo
ia postra  aggredi (ad comprobationem
uersa
novae Methodi) estroblema differentale tangentium 
olvi possi
t quia ergopesteus 2 est y. a =  aaque bidx et per aequ. + est
X. a, =
adque do
inde per aeg. 3 est dy: dx = do: dz. Ideo hos valors substitnem
= seu 3 = log X - 12) utione 
quam pea
fiet dy do = sadZ: de Cle seu d dvidy = (X. 9  xod
ye-dy
 in aequatione 5,
pu substituendo
fiet dz: do (25) (Sdd Z. dv: (ddz. d) - 5dZ do, seu fie t
dZ. du) seu dx. dy = ax seu Ay axdus), qy = x: a substrimendo quantum
opus est, et quando opas est fiet y (d Zd) , a-y = fddq: de vell (d Zd) et differentiando
ae agradus ( (. d) F 
ddo  dv) (9: a) (d2 do)
1  13) an9)) + (B a. 7) (dv daz dZ ddv: dudo)
: 1 - (y: a)
=a fadz: dx. Unde different audo fit
(. ladss se via avdur dudae - dar
 1-gia
sex Aequatio jam solvenda laugentialis est 15, nempe dxidu = ax  Xyi ays
(8) eet
sst seu velo dx dxidus, gry. a,: 1 - y. 4 = x: a, quae si differentietur, fiet
d x, y. a + dx ((D) d
dus 1- y:a
IX 9:  xa disperentiando fit
seu dy -2
seu (dx de ayyd
dx ydy, +
a 2) qu u.3
dx ( 8) 
+yia dau = 
X 5o sdeo t dx = deo, 1+ Sd: c0 et d   
du ddx dxtaZ
ady: dibus du ded: co, sed
n esberum oportet ergo erratum esse
gia fiet coscevico t sdco  cor lnsaedico
 x= r X = dy 1 B3. a,
u r 
de (p(d pen (Z (.2
a) qu. (1- 2
- seu
aydus 
asd etd =a dev: co et ddus = adodioic
seu dus dux: dx = ddus. dus, quod est verum nam
dus as agaa
et ) deo adgidus ddx: dx = deo co + cosdco: co
Differentietur XQ
differentiee
ya d
adco cadico + s o: cd)
a (31) dx
a pyia
dZ. du. scomprobatio ded it sig-aud . t do. 2) taio  corcoso
que + sceoico
quia dz. do  per 19) = co + Co silco : - a) cendeet erit az: dv)  deo + du + deo auviuo
 A- corespeociope nempe prota r. a
e
ponendo d
et fiet deo, qu (1 + Sdco: c) = du + 2 deo Sde + qu Sded quod est verum calculus ergo succedit)
=dq  -_lo, 2tsiaim ex aeq. 31 tellantus inveniamus et fiit y nempe explicite fiet est sibt
(1 29: a + yy: aa = 3ye (aX, + (y: a - gy: aa) a d d d (d8. dy)
seu fyy: ca) (+ L a  (dz: d) (2 + a d (a dv))9. a et divisis omnibus per y; a
fiet dx, - 2 + y. aB (1 - y: a) a d (aZ: dy) adeoque y iet ) (a c (d 7. d1) + 2) ex i adt car. 40) 41
ex ea dule
adeoque y: a (33) a d (dx. dy) + 2dx,:  a d (dY: dy) + dx  comprobemus fiet
- (dco: 10 = -g(l ad): _ 2 + Sdao: c0) + Idco) (, +. sdco : C0): - a (Lcd.: 4) (2 + solco: co) + deo (1 + sdco: co
 seu - sdco: co = C(-2 (= falio: cd (F 2) + sdev: C0) + sdlaoi co, :  - D (- 1) - sduoico (+ Bt Sdae : c0)
quod succedit. )jam aequ. 33 pro y: a, dx: a, dxidus substituamus valores
per dZ, du, daz: ddv, uet per aegg. 1, 2, 3, et fier sddz.d-od ef c
jam d (dZ: dv) = deddz - dz ddo: dudo
et fiet sadz. d7 = 5), doddz-dzddx + 2 d vddz,: doddz- dzddv + dvddz, seu erit
(ddz: dz =  d (d Z: dv) + 2 ddz: dv,: d ( Z: dv) + daz: dv
(ddz: d3 = 3 dvadz - d Z ddv,:, 2d vadz - dz ado sedquia haec aequatio iterum differentianda
est, ideo jam tone descendatur infra ddZ et dao, opus est adz: ddo tolli ope ipsius doo
constantis inque eum finem posset deo assumi pro arbitro per de sume pracc ddz: ddo
assumi pro arbitrio per dx az: ded et do: deo, sed quia alius posset nisi priorem ipsius
illo valorem jam cognitum assumeremus, alia prodiret quantitas cd, et per eam valor ipsum
ipsorum Z, v, X, o quam assumsimus, Redeamus ergo ad valorem dav: daz jam
ex aeg. 35. rursus quaeramus vel ex aeg. (32) inter explicata quae et
iterum quaeramue valorem ipsius dav: idZe, fit autem ((32) aequatiotalis ex plicata aequatio talis
inventum aequ. 24
3V) ( = y:a) (dv adque = d Z ddx: dv av)) seu -d dv. dlZ - (36) dv, 2y: a) - 3,: dZ (1 - y: a)
comprobemus: q o Eos, 3 +2(dco: o: Co H (1+ (d v. C3) =  A a dl Cd ud (1+ Sdco: 1)) (= 2 salo: co - 3
ad :dB) B. 
adcetiad) sit sacdic scccedit
aalo clat cor et stiono vesera . 2 Salivico 23
et pro leporea