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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 61r, page id 00068200:0123
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q. XX + 272a X aequ+aa p ex fc xF
elle bb quobb
ag
seu ZZaa 2aa27 x aequ. = a bb f2G9bb X f 2 caqbb X + c 9b b xx
X explicetur rationaliter per V, et Z per co V.
ita ut fiat eo quantitas rationalis per V. erit etiam
7 quantitas rationalis per v., et cum de sit etiam quantitas
rationalis per v. Habebimus rationaliter 7dx.
per V et dv. Exempli gratia sit: X aequ ( + f. f + mB+ nove
et Zaequ. d V + h co + 1 et
termini: 74. v Co. vco. vCo. Vco. V. 13. Vc. VCd. V. Co. veo tionpeter
eropeharum quatuor t arbihariarum destrui poterunt imo possumus explicare X per
termini cot Y coh. cot. assumatur aequatio:
aequ
a saa rax + a xx + C)2) 2ax + a xY
2aX + a XC
quod si detur quadratura ejusdem numeratoris divisi
solum per 2a + a X. v et ejusdem divisi solum
per X. haberetur figura data
Teutemus Methodum ligussrmund reducendi curvas
irrationales ad quadraturam rationalium. Sit:
 axx+bXy + Cy + dx + C aequ. 0 quae est aequatio ad curvam
rationalem est enim y aqu a XX- dx = e. Cum ergo detur
summa omnium tx dubitur et summa omnium Xtus. sit
b X + d
jam alia aequalio 1Z +mys +n aequ x. Quia ergo datur
Xdus et cujus ope ex aequ. 1 X latur X, fict:
porr
rationaliter.
aa + Cx
a lZZ + 2 alm 7y + 2 al nZ + ammyy + 2amny + ann
y
=bmyy + bny
+ C y
+ dm y + du
quae aequatio est ad aequationem ad rationales
tc
revocabilis, nam haberi potest summa omnium Zdus
quia haberi potest summa omnium X dq ermysdus et naue
ex quibus  summa omnium (Z dus componitur per aequ. 3.
il
Et quidem pro omnibus institui posse videtur calculas generalis hijusmodi
hui Assumatur aequatio a + by +c X + d XY + C XX + f xxY + qX+ hXy et C aequ. 0
quae est lationalis generalissim a decundqum scribatur alia etiam hatio nalis generalissim
neu: M + HZ + y pV + qVZ+ Y yy +5 99 + +y+ vYZ erc aequ. x nd
quae aequatio etiam est generatissima rationalis, serundum Z. nam ita det priorifit
t loco a b. c. defgenti ek, scripserimus m. n. p. g. r. S. + V. erc. et
loco y posuerimus Z, et loco X posmerimus Y. jam in locum ipsius X in aequ. 
substituatur ejus dator ex aequ 2. habebitur aequo 3 inter  Y et Z quae
dut dato milibe poterit companari data aequationi 4. ergo data aequalio
troberit reduci ad rationalem, nam per aequati habetur rationalite
summa yax. Ergo et summa xd
V et co. et Z per V ex co.
ut tandem frat aequatio
in qua  h cohabeatur
ration alter V, Ergus et
ationalite
Z labebitur p per V.
 hub et X
punc per v. ergo dx pure
per V. Ergo Zdx 
per v et do. supr
 si X sit quadratus
item 2a + a x quadratus
item
Exx
an
 quadral
pabitur quaesitum itaque frat
X aequ yy, et 2a + a x erit
2a +ayy aequand quadrato:
(si  sit + sequent
a yy f2yV Sa + vi
Ergo y aequo
2a - nv
aqu. 0)20 sa
aqu 3aa- 4ave+v
1X
se