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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 11
# Folio 14r, page id 00068056:0027
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dderve d, rse = rdise +dr io
ex 1per2F (31
Erqo d, r= (rdo + drix -) rav + rvaras
se
d, S (= d, Bi2 -  2 v. 2- ) )dv
Sit (sax s rso quaeritur Y, fiet hdx rd+ dr v. seu
 hVdx cardo +radr. sit deLdco: a fiet vhdx - Yfco + 2Ba dr
seu _ 2hdxdco :do - rdco = dv, seu Ehdx: deo - =r_  dr: du
2V0
prer sit hdx: deo = Z et - + = 8, et ex 9 fiet dr: deo  Z + 8Y. jam
alibi invenimus in casu aequationis. H. si sit logu  sdco, fore r W ( Z. 10: a
Ergo per 12 erit log. WV= - = co + β,: a seu dW: W = (-  deo =) ( (per 7.) - = adv: V. Ergo
ex aeg. B fiet _ r = W Shdx: W ia posito B dv: W0 2. : sav. B
Ergo denque  fiet ( shaxs W Shax.u Y, pusito sduvin a istr
quod calulo comprobemus nempe differentiando aequ. 18, fiet hdx Iv ( hdx: u) + Thariu d W. i
ergo W S debet esse quantitas constans qua seu d W0 ip =o Quod et verum esse
sie patet d, W so = So dio + Wdv: 25  0. Ergo duv: W = - do: 2v. Res
pro cuculo r aa - xx fiet h = 1 v = aa - xx H. ) Saa -XX dx = W S faa- XX. posito
ergo succedit.
esse  du : W = - dv. 20 se nL   lg. W = loge - : log. B. E. gu 1 = 
Vaa-X
aequatio identica, nan fit Saa x dx = (ax tuaa.  itaque et aequ ++
seu generalis est inutilis, na fit d 1: Y. ergo aeque 8 fib identica
Frustra sc. aequadem quadratoriam vvocavimus ad Fangentialem, et hanc rursus ad quadratoriam
redit enim ut video quadratoria prior
interim didicumus solvi posse squ vetida  do  dx =. hdx- d Y seu de = Z+ Gr
si quia datur dr- _Ax  aV Y cum reducatur ad di = Z + gY, posito Z et e dari ex 
potermus et fontie X vd. dr = Z + dor seu de   vdr +
dr = E + gY datur sit sed quid si rr = Z+ gY sit r = co
fiet 1 dco = Z + 8 teo
C d= Z +9 r= f9 + 8Z fit 8 -L(. r
  r=  e 1. e sit +   = Za 8 seu dip-   Z9 p. seu de - Y2- g
quae datur sit dY: 4 = deo fiet de = num. cdZ _ -8
dy: dx = lamys + ngy, :, 9+rg + sgus etc sit yc . ficblus =
Ergo fit- do: nodu = R + m  love, s+ rve quu et adevque
O8:))-
v b
v
c
dy: dx = t bx + b + cy + ete +  fG = +gG., : l + mG+ etC+ p V= +95.
Sit B y = i fit = dv = bB + C vC  et + fV + g, v2 e t2
ndx L0  tmp
possumus, et pro X fucere yze, et sit ax = X ly + ydz et dx i du = Z + yd2 = f D: C)
et du d = et 9 d- 0Z: O =y dz: dy seu dy: d3 = 0y 3 Z. ita necessario
omnes termitai numtraloris habent
Centemus Aliter sit y X = xy fiet du = Xdv + vax , :dx = C: D. fit dv:dx = 0 - dv, : DX. sed
ita quaesim non asinetu ax
ydy= 8tg +m dy- t+mytngu dus =myrngu: gtry. A quaeritur
aequalio salisfaciens: a +bys + cgys + eh etc. et a sit constans vel unitas quod semper
pt intelligi frat da et per reguum per regulum da 9= rbl dar + db. g = 1bm +  Ahabetur b
dbY + dc  = ibn +2Cm et per regulam nostram habetur C. et de r + deq = 2 cn +3em habetur e
et db et deg= de. Y = 3em seu de = 3en: Y quo inserto in praecedente, fit: der + 3 en g.Y =
2 enF 3em. seu rrde = 3CnY, :, 3YM - 3 R9 = e Unde et habetur de, quos vatores
Citistituendo in aeq. der = 3en habebitur aequat in datis, quae linutat quae situm. Ergo
restituamus da a, et sit du = l+ my,: gtrus. sit q. a + by + cyy +C G3 et =C
a daq = 1bl. Ergo HH. g Y + db g  1bm + 2Cl. fit db = v t q g bmu seu da = b. 1l: 9
et b. Ulriq + db. 9 = 1b m + 2cl. fit db = - b. ilt. 44 + b. 1m: 9 + c. al: 9. quo valore substitutet in aequave sequenti, fit