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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 162v, page id 00068124:0328
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etsi notubile sit, si quid maxime in hac materia duas aequationes
collatitias perumque sibi consentire et plerumque unas earum sufficere
casus tamen eoeuore posset, quo foret forsan opus utraque isi sclce ut
dixi mentia per unam pure haberi possit.
suffict ergo unam y pro
incognita sumi  duos habente valores aequales et hoc ipso alteram earum, nempe
vel s. vel V, elidi, unde reliqua pure habebitur, quod sufficit ad x quoque pure
habendam: resumamus ergo aequatio est  generalis quatuor indeterminatarum u
52= v + 2vy -27 0. Ponatur 
= y
no a
r1 4 
ar
=1  V)
posita scilicet (3. infinite parva, fiet XN Y v - y. et X ∞, y v - 2ytv + y6
fietque: 5’at - v a + +2vy a  - 2y a -  Fv + 2yV - y6
vel yb - 2v  + v Y  X +2a tY ∞2va ) + vat
4
per numeros cg. Mdmta
at
7 0. maltipho
= 5 at seu 5 - p - y, C, - y - v.y 
quo valore, in equatione X H y V - y substituto
habetur X ope solius V, id est descriptio curvae quaesita a
va
243 (vel 
a
Eadem melliodo sit aequatio:
ety
posset daretur Tetrahonismus, ut alibi inveni: erit
v- y  2a
unde
a Fy
X B va - y a + Vy -y Unde eodem modo caetera investigari ne
cessario possunt  semper enim s, statim tolli potest. Facilior est calculus
opinor videamus jam aliam calculi speciem, si scilicet ipsa V -y. Simpliciler
habeatur, ut si ponamus B - y seu PM
2a3
quadrato, v- y substititudo ejus ratorem, sed hoc modo aequatio difficilis resolutu est,
adue vel inde Judicari potest, quod multi plicando certo modo per arithmeticam progressionem
sequitur absurdum et falsum, quod probe notandum et accurate exiutiendum. Interea
hinc observo ad caetera investiganda ex datis MB, satius esse mutare quaestionis
genus et aliam querere jiguram, in qua data sitit Me unde cuni sequetur quaesita;
MC
2a noestigare
a
ut atbi deprehendi. Eadem ergrmethodo summam ipsarum
ponatur ergo V= Z et a + , fcet X e v - y, ∞ a + et
2qu
ea
et X B v - y, E, a + y, D eoque valore in aequatione generali substituto, fiet:
4 a4
5= A v - y, - y - 8p y,  a XyB
1
Unde abjectis cognitis Mm. Sed ut omnia fran certiora uter excmpers facillimis
ut parabolae. Quaeritur summa omnim d, pouatur ergo v. Y 5 3. Ergo X,, ap ad
et X B V - y, C, a eoque valore in aequatione generali substituto, fiet:
 v -y, _ - y _, V- y, 4, -a 70 sive,
 - sad
-s - Y + 2y -y -y  - va + 2Y1 a - y a , 0. et onchriundo:
16 - vy +5 V 4 a 1 - va  ) + arvy e0
sed quo si ipsa V sumta pro incognita ita fecissemus:
fiere aegontio hrevissuia: 2V, + 2y5 V C
2ya
unde Calculus satis prolixus
v, +2yBV + erc..
+ 2ya
-V-a
S sive LV  et y51a eoque valore ipsus v in aequatione superore sabstitito, fiet:
d a- aytae
Xe a y, + a- a ay quaeramus jo
+ 2y0 a + ay
a2- ay y + ary
Quod nog, arto quomuot prion seqpatom consutiat, ad pronde nerepe sot, intesse quendi
in calculo paralogismum
+ 6C ra G ratey Y6tat, fier. abe v aat  a V 2 a y +6C1) a  2a
cotra
differentias ipsarum A, fiet R e
t gr tunc pro S- V 4 2V9 29 
 2a5 +y 2 - y - X, nimirum pro- v + 2vy - seu
substitui potest: 5 - 4 a
utile est;
+2
∞ unde post mnlliplicationem Aichmetic, sit: 2 v a  - 2ya, - P- Y, B, y 3 F0
restabit aequatio in qua duae tantum supererunt incognitae V et, habebiturque valor
ipsius V. absolutus, per y.
24
+2
4
prgespons Arictu.
fiet