Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 11r
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.80.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 12v); this page is its right half.
The machine reads it as
- x compendio a S erit XX +. ab = aa suN F. ab X
- n Xx + ab = 9a _ S + aC 74. et
- a N + adi H
- et XX +ab, XX raC R.
- si esset at a2 = - 5Z foret 5 Z rationalis
- et ∞t (, OOVV, 40 OD+60DF, +46 Lor.t
- de e si ess fura vel etiam sC+
- si f4 - aabe,
- Et mira retare plantum qu rahonalis. sed pam
- ffXX + 2f9X + gg
- sed si fiat 2a . f2, + bt = - f2, B-c
- 2
- seu 25= - (b +c)h seu t Z tC
- productum eut ratinale aequandum quadrato
- rationali, in quo tres C t, et 2
- Post vania tentata pro quadratura ira
- tionali conica ad rationatem reducenda, sed per
- partes diversae rationalilatis seu ita ul quadratura
- irrationalis reducatur ad duas singulatim rationdes
- sed incommensurabiles inter se, hic modus
- aforet ratio
- nalis etiam Ns + 2+ firet rationales.
- foret etim se
- ad prodest
- destuatur in eo COro, et ponatur 2
- nd hsses u mou uri
- Quaeritur (dx (xx Fbb, XX FAC)
- Fiat
- et fiet
- = aa qu (b+ cY - 4 aabc.
- fL a(b + C) = a (b +C seu ff- a (b + C)
- noconicis ubi sunt negatiou antaccattollere
- opus. A i siligi vestien iptiue e0qe ductus in
- aequatuqe quartae parti quadrati
- a coefficiente ipsius C). Hoc videtur in potesta te
- n 4
- seu i
- si f+ ae + a(b+c) + aabc = 0
- 0B, et si simul 2 et h
- ponantur constantes plurimum
- contrehetur calculus, omnibus
- variantibus a majore latere
- redactis ad CDD. sed ita
- quo polcumi posso aarba
- t e 2 esse constantis, etiam d vel
- fiat constans) non posset pars ene
- rationale prius habens solum C aequ
- 9899 quia
- cum in hoc anus solum terminus altine
- posteriori 3804+
- assurgat non pote possuat in e
- tolli duo temini supremi ut deprimatur
- 1
- licot tolere ocnnintim
- Si
- Ier sermod tisui
- 45y
- reducetur, le
- et 8 s. .
- b+ c)k
- i malist
- ad 24, et 2p voliti ad
- an 4
- et gu
- 42 a
- CD+Z panetarias designari
- xformulas ratiopales integras simplices secun
- duim unam variantem, verb. gr. D= motar;a
- 5dD +a a 427
- dnls rednbrtr 4
- +2af7
- +2t10
- ab cD + abtih
- XX + ab
- +2a b_1O7
- D + G +2G VOY
- +f5O7 + aa 2 2 + 2 a f2 VC
- XXF _ Aac eD + aCtt +2a6F, 1O)
- X X + aC
- CD + hZ +2G 16)
- et preductum ex xx + ab in XX +aC,
- erit
- scopulo
- aaaistac h
- F0B fab. 5BDC eCC
- a4 4) ac. L. trh
- ffonicabis 05
- C_CBM t Eaaff0∞44+44 X aa r lc
- aab FOCVF FabC Onttt aabct
- (4 aa 5s quabe t hp a 4n.
- 1. 7 55() af2 (OD + 4sC D Jaabet r0
- Eth
- pff (3D)G ab2 BICD + 1 ab L aF2t YCY
- Jaa +H
- 2haa tq S2achC
- ex
- EBF) La3
- biquadrat. (se) D +F
- Tepsetur an duins valinit prodncti in hoc producti ex
- XX + ab, in XX tac valote per fractionem
- expresso. Numerator sit extrahibilis quadha
- vice, quemadmodum denominator: et eam
- in rem cideatur an identificari possit qadrato
- a Latere aa 6 10 + aa 8 tdZ
- a
- 8502+ 2418 + 24405210)
- irrationali Et videntur plures esse literqe quam es
- S, b ut patet. Si nuba
- Et timul nam X fieret constans
- permissum nan (d, ,
- ACo (Coco + V) = 4c YZZ Co Hton hctut Nec aubae t Hes
- s alterntra ipsarum
- ac
- fk. (3P + aa 2. 2 = 24f210)
- B.
- i
- iventificando partem rationalem rntionali, et itrationalem
- (0+ l = Z C Z = Co + 4C3( +6 cocoH
- Ergo 10 + (c0
- 177 -2 ci co4
- l
- Notundum hic perte
- - min a m v +n
- pro
- et
- et f= (a b + aC) sed hoc non procedit in eamon
- quanlittes
- Sed Glneral iter unica solum equatones
- constantem
- 10D+ a Alnotus planetarias I
- Notandum hic per non
- XX
- Erit XX
- constans et fret de Oy + nistans = quadrato 60
- quod iidetur possibile. sunt enim sufficientes
- ABN
- uttolatur f alba C) s + L aaqu (b+c)
- arbitrarii
- rgo ne
- D
- Alteratia ex ipsis, videtur posse poni aequalis nihilo
- verbi gratiatu. Quod si licet calculus redigetur p ad minus
- quam mediatatem. Hoc posito sequitur exidentipibatione
- irrationalium partium, aliquam exhis d,E
- constante ad 2t, seu reduci ad ged non evet esse
- esse in ratione
- alioqui el
- vadratura rationalis simplicior, quam haberiposse aliunde consta
- AOD deveret dividi per 2
- Inempe
- lea
- du ad
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 11r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0021?run=74