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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 17r, page id 00068049:0033
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de pressio formularum per explicatione
Ende terminatae.
PXF 99
e formula 9 + b = fint y = pX + 993 : X + Y. fit O = bX + bt 3:, X+Y
pro tollendo termino rimo fit p2 -b si srimumet secundim simul velinus sollere siciet praeterea
Y =C - 99: b et 2 O=0, nieoque y2 -b
sit semper y = px + 44,: XtY et formul:
+9 +Bbp
+bp XX + bpYX
+ b 99X + b 9gr
+ cC XX + 2CCY X + CCYY
seu fe
gy+By + cc = O et explicudo
xraere
3 FX- EYX+ ir
seu p = 4-b+ C
uet tollatur terminus suemmus pmmus
fit p2-  b + 1 Hbb +cc
ut tollatur primus et secundus
fit: r b92 + Sbb Sacc  bg4
si compendii causa bb - 4cC Pocemus et,
fiet q p = =b + L e
(1) C x + 94
X + 299
e- b
2bb - 2B bb - 4cc - 2cc
et r- De.
Zee - 2te
B299 c8
C- b
Nam si p- b+e fii pep - bb + 2bC + bb - 4cC
seu g  = X + 299
e-b.
40) e
e b = 1. Exgre seu y=
XL 2
- b
go duo termini primi simul tolli, non possunt, quin eadem
epera ex odianta indeterminata y fiat determinata
contra propositum.
si processisset haec via, licuisset
formulas indeterminatas semper reducere ad rationales quoad
inde terminatas simplici explicatione adhibita. Et continuari
Termingea posset perpetua depressione, quod tamen non
est admittendum. Nam ex formula Nam pro formulu
y + p y3+ qyy + r y +5 = C, ponendo y
Px+ 49 feret
X4 Y
( = P: X +. X +. X ita opus esset solum formulam uXX +. x +. p 
LIX+Y
aequare oto, quia anminator jam est qtus.
Illad vider licere simul tollere terminum summum et infinum nam
sed tunc fit: x3 +. X +. X verum, ita si rursus velimus pergere tollendo
L X+Y
possumque quidem frere X = 1. Z
facere X = 10 Z + 11. 1 sed ita Prodit fomulae aequoata
12
et ila poncndo. X +. p2, . x = D. fiet D = 202 + 21Z88. sed hanc
(2) Z+12 7+ 12 
non statim est in pte aequare gtd. sumamus. 20Z + 2Z = 
et si sumamus:
203+217
R+ 12
=9
ac si 20Z + 21Z +12. 21Z esset aequandus quadrato, quod aeque
c3
+ 13. 202
difficile est ac Xha X + X) et nihil inde
lucrat sumus
idem est si in x = 3IX +32X pro X poneremus 1: Z. fieret sane
20 + 31
+32ZZ ubi 30+31Z + 312 aequari debet quadrato.
 Quodidem est ac si dicamus 30Z+ 31Z2+ 3223 debere oqumi yto
ustio
termineat
tollere possumus. Sed s quia pulla hinc rascitur de pressio ideo
si altimum provenientis ad huc semel tollere, velimus. one
peceunt tot fecmini quot ante
Sed sed si velimus uliam summ
euriam tollere, id sime fractions none possumus fit enam ul y -. 40i
fit O = +PPxX + 2p49X + 9
eg