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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 2
# Folio 1v, page id 00068074:0002
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sit X: a = 5dZ: Z et g. a = saV. Z d dy. de  E dv: d2
Sit aquatio sit fea sade faz. V ia dque  de et dde2o, fiet
+Z. V ddqe + dZu: v = 0 seu Sd D - 4 da ZV
sit ((V. Z d dZu  de adde=0 fiet dd dq av: Z + Sav:Z dd 2 =0
siu sav: Z= - dz dv,:, ZddZ Sit jam aequatio data
X:a + dy: dx = yy: aa seu saz: Z + dv: dZ = (3 sav: Z seu
Az. q + d2 av- dv.l. Z, :  = dv. Z2.5 dv. Z. Et ex 7 et 8. fret
H: q+ et faciendo ddz20 id enim in fallor in arbitrio est
ese, f fiet dz: Z + dav: dque = le dv: Z 2 V5 (23Z + dv: tque verum
hac aequatio non est, tractabilis, et si tos quia adest sdz:Zue. et
ad hauc tollendam, adhuc magis descendendum foret.
Sit X: a = (dz. Z et y: a = (dz: v sist dy. dx = Z: b
sit x. a + dy: dx = yg: aa fit Saz: Z + Z. B = () sdZ: B et differentiando
fit dZ. Z + vdz- Zav, ve =  2 dZ. v saz: v. Ex 2 et 5. fiet
y: d Saz. Z + Z. V. itaque tantum opus est relatione inter Z et V
1X 5 et E fit aB  v: Z + 1 - Z: vaviaque = 2Y aZ. Z + Z:B. Sed ita nihil
lucramur, quantum judicare licet; nam lollendo Aze: Z, prodit 4 aeqs
ex v, Z. du due ddo, ddque. ut in coibus, cum tollimus a.
Redeamus ad calculum praecedentis paginae, et
rem diligenter examinemus
X: a = (ddz: dZ y: a = Sddz: dv dy: dx = dz: dv.
Sddz: du du de fit adz + Sdd Z: du sdv = 0 et Sadz: du = - ddz: dan
= de: dv. Atque haec quidem communia sunt. Jam accedamus
(1)
ad aequationem datam X: a + dy: dx = yy: aa unde per 12,3.
fit fadz: dZ + dz: do = () sadz: av. Ergo ex ag. 2. fit
y: a = Sadz: dz + dz: dv. id est postulatur relatio inter dque et du
(11)
(10)
Ex aeq. 9 et 4 fit sadz: dz + dz: dv = de: dv item ex g et6
fit (ddz: dz +  d2: dv = adz: adv. Quae omnia ducuntur ex aeqp
2)
ex aequ. 4, 5, 9. Sed ex aeg. 9 differentiata, fit nova aequatio,
ddZ: dZ + dx ddz- dZ adv,: dv = 2 dd Z: dv (dZ: dx in qua sunt
Z sadz: dv, du: dZ, ddz: ddv. pro  Et pro Sddz: du substituendo
valorem ex aeq. 6. fit g ddz: dque +  ddZ: dv - dz ddv: du + 2dZ: dav dx
ubi sunt ddz: div et du: dz.
 quae est tractabilis quadra.
Sed consideremus esse
torie, et hactenus nulla est difficultas.
Sed jam m Tom aeg. 13 in qua (ddz: do, du:dZ, et ddv: ddz, comc
binemus conjungamus cum aeq. 9 in qua sadzueidqe, dz: dv et (adz: dv, et cum aeq. +
in qua ddz.: dv, de: dv, et cum aeg. 5, in qua (adz: dx et ddv: ddz, ex
his necessi est auci posse caetera. Ex aq. 13 et s fit aequ inter dv. dque, et de, r. AB
et ddv. dtZ Nempe sunt eg9. Quatuor, et li quantitates sunt quinque 
(ddz: dv, (ddZ. dZ, de: dzue, de: de, ddv: ddz ex quibus tres
quaeris tolli possunt. Ergo res reduci potest ad aeq. (15) ubi solum sint
dv: dque, et FddZ: dZ si adjungamus aegg 2, dicemus nos habere quantitates sex
y: a, (ddy: dv, SddZ: d2, dx: dZ, dz: de, dd v: ddz, et aqq. quinque, unde quatuo
quidascunque sublotis, habeluo 8a. inter y. a et star, eaque sine cis