Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 92r
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: 0.70.
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The machine reads it as
- ciats
- proponitur Y((X+ ab, XXFa) ax, = aydx formula summanda quadratura rationali
- +L X: a = 1O+ SD, : SG, fat XX:aa = 0+D f210D: V. et proinde
- Ax = 12dB: 36∞ - 10d8: 18 +18AD : sD - 1D1G: 183 : 28.d ponatur
- valor ipsius y extrahibilis, re redacta ad bimam tantum in endem formula sub esdem vinculo
- irrationalitatem, fiet et fiat Ay = aG + f16D,: 8, fietque t + D =t per
- usa et te
- L
- etbr
- fet gy = at +bQF 2d 10D, aZ + bB + 2440D,: 44 = ad 4 + ACD + 2af2 1CD: YG
- H
- n Ah + bc Q8 + aetrZ + 4 aa
- a9
- abc
- t+
- C +24
- NOD ~ aa 9+ fOD +2afe 10)
- ut jam conci identificentur irrationates siet se = 2at, + eg. Etque ut etiam
- identificentur rationales sut aat h + bc TL + act, 5B, ff = aassqu+ 0D, adeoque
- ff, aatit + bc 84 + a et = 4 atitu + 4a et q aec ZY + f OD. sit quaaf = ag
- l
- qu
- sit, aegts fagH0D + aghZ+ auegqF + (aaee -bc f) B Y = 0 sit avec bst dh
- (D. 1)
- quaOD
- Et puit
- ii a eq
- +4
- et + 9th - dts OD = 0 est autem D= u et DD-
- 24 at
- bil
- F aat
- et adextractionem ordinando ∞8 + eg et + eego
- sat
- seu Q+
- 2
- Z- (eegg - 9aah9) Gt + 2hatt 0
- att gaathL
- Auath
- e9+ A(eegu-taang) th + ahy stOD), 2at
- HEF Reddamus quod in vinculo est, tale, ut varians quantitas in ec non manet, quod
- duplia modo fieri potest, vel reddendo formulam sub vinculo extrahitotemel
- re salva variabilitate, vel redient
- am constantem, priorem modum
- est velor
- il
- ota tentabimus explicetur D per t-O; fint B egh rec fiet OD = Ot- 00, e
- formula ex in qua variantes sunt avirulo liberandae est ((eega-anahus ht + Anqeti
- ic
- E et ponendo eeAaat = aaque sit a
- Eah
- d Ach + tO - 4uH00)- egF
- ill aaq
- id quod in vincule est identifietur hunc Gh + 2mO + mm BC
- seu
- Eatin
- 1
- 2= 1
- a
- aaque
- et s
- = mn = = 4h
- pa
- na A aaque
- aaque
- ratL
- et fiet 2n= aaH
- a rpa
- fiet ff = - 1, sen Hf - -
- eaque
- et fro ah, et anqe ponendo valoies siet lanee ff- bc f - -59+ 4a tr = (expli-
- antetenalic E Cundo g eth) , Caec taa ace ff + Aaana ed- 4aab 55 fuo f +aa = 0
- fieti Aaa = H = 0=9
- e seu H = aa ex : bc = gaa et ee = 4bc ude b -c =0 quod non ficet
- 5
- Ergo a non licet reddere quod sub vinculo est reddere extrahibile
- salve vrationalitate variabili, sed oportebit reddere aequale constanti
- Nempe in aaqttu + anfftO anffOd sit C = , ot +na, : 00
- et fit 0000gagtqe + 4. 00. 1)h titr. + 400. uHat - 4. 10 00 t Zh. go uisff at
- at tollatur titu fiet
- 60300 aaque + 4. 00 10 f - 4 10. hfs = 0
- = 4. V1. 1 hffaa
- t ut tollatur ati firt 4.00. 1hH = 8. 10. H hff = 0. seu 10 = 00 +2
- i
- ex aequatione tollente ttu fiet oera sis seH
- seu
- ago at, seu s = aa eah
- E+ 2HaY gh rat
- f. gae9-agaut,: gaa ec -8bcf
- saceg dum ah= (ee Aua) - eett (- qua ee + bc f = H. Gu (b- c)
- se abe et sied = ff qu (b- c). Dhaee - bcff) et
- et 78bcf-8 ade = aa qu (b =C) adebque
- L (a (bC) + 8aa qu (bfC): DbC
- 00. 00 aaqe +2. 00. 00 ffh - 00. 00 ffh seu aaq. + ffh = 0 seu
- a) it +Hah = 0 seu a eeg- quh + faeh = 0 s
- eg-
- seu
- agt 20 seumee at, seu aaee = aaee- beff
- et fieret, bcff =0. quod non licet. Ergo nec haec via succedit
- esset 0D = ht
- 6O + (2 -1) OD+
- Haequidemm succedunt
- 2
- seu r0D =0O+D) +20γ(i vereF
- Ergiro) = dela-a trr = 4BD sin O 2 (72 + ((or -41))
- a
- scorta tnt 5: d constant et G: B, onstai
- bs 2 qpot XC
- en
- 10c
- +
- et
- C
- a
- E
- e i
- 10 ++
- EEx
- i
- u
- e
- te
- e
- AC
- 6
- er
- v
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 92r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0183?run=74