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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 85v, page id 00068124:0170
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pla
cos et darys socionos
coratae quantitatos,
augontz y duminuanth tangue
. 2 et ppoluy meromontu N docro
de puncus lornis sic nolat V, X ij, Z et hery
Lua 2aV d fluxro quantitatis V et i fluoeco ipsius
denontos practd Y sardae, flusciones dary sue notat.
Eu veronos F y. _ et V aa = 3e X et hary fluaiones st 5 X et
6 = 3
Jere ( doepositis mothodus sua in pepositione ha Problomatita bundat
20b. 1.
Tatâ aequaliond fluontos quotrunque quantitaros mverent invoniro feuacionos.
Solutio.
MultooltoB quilbot aequationit oru soparati q induos singulos dignitatus, quantitatus ocysfluentiu
quae in 1ro 1lo glmontz et m singnes multiplicaorbus mulol3 Calus unys dignitatis in op fluociond, et aggrogali
phodutoru oeu sub propris signis componet aequationo nora, quae rolavom fluscionus involvot.
Explcatio
Sput abE. d. ve quantitates dolratae ot un matabilos; et proponats aequatio quaevis quantitatas
flnontos Z, y, X De involvons puta X - X 44 + a a 2 - 6 =0 Maltiphoent lori prnno por
induos dignitatus ipsis X in iposis contontarus rospoctive, et in qualibot multipliao pro une Caloro d
dignitatis (hoc D ero X unes dimonsconis) soubalz X et summa productorus dut 3 Xex ieua. 
fiat in i et producolh = 2X 41. Gdo fiat in 2, et produrob3 + aa 2 Summa productorys oiu
aequolu nihilo et Rabobiths aequao 3 X X = X 44-X gy + aa 2 =0. 8100 qd haer ont aequa rolacom
fluoeronus invoevens.
Domonstratio.
Sit  e quantitas infincte parva et sint o2, Oi, oX, synchrona momonta sou meromonta
momontanda quantitatus fenontus Z Y B X: et quantitatos prosenno compouis momonto por accosdam
meomontoy momontandon ouadont 2 + 02, y + oi, X + oe quce n aequad grma pro 2 4 et
Xe scrypce, dant lanc aequadoin X =3X x 0X + 3 X 00 s X = 3 X 03 = X 44 - X 0yu = 2X oiu
=2X ooiy + X00y i + x 0 ii + aa Z + aa02 - 6 =0. Subduc aequaoom  pruna et 26suduy divisus p
0 dut 3X 2 = 3X X OX + X 00 - yy - 2∞yi - 2 X oyi + Xoiu + è ooyi + aa 2 =0. Soros
mueliplicalos por e tangue insimo parvos doeo, et manobit aequao 3X  - X un - 2 X 41 + aa Z = 0. g. 3. d
Punali mothodo aequao X = X 4n + aa rax - qu - 6 = 0. oradit 3 X  e nu - 2 Xe qu + aa YaX
1 =0. Ubi si fluxionem rax= un demumaro rotis pone rak - in = =. et p consoquons ax-yu
= 2 et Proposctio dabit a  - 244 = 222, id d a  - 24n = Z sou 21 a X - 4y = rax - yy et
indo aequalio pramo moonta fit 3X X - XyY = 2 Xyy + ad X - 2 avy
a X - 2yy
et dado mothodo pergere lirot ad fluocionos. 2dut ac tortias. P on al3 aequalio 2 1 = 2 + at = 0 et
== 0.
varyu
Propositio undo dabit Z qd + 3Z 147 - 4Z2 = 0, et haes aequa por oporaom roporita dradotZ yd
+ 62i y2 +3299 +62412 4223 -12 22 22-0 et su doncops.
ut appliots haec mothodus ad quad ratura Curvarus. nontones pro flurciono absriso umforim
posita, unitato assuunt, et ordmata ponit pro peuocond arvae; domdorotaom unor alheise a  aequat
ne quavis assumplâ definit, et indo colligondo oavrys fluxciones oennet aequadom nova qua rola inter
abscissam