Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 301r
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. 300v); this page is its right half.
The machine reads it as
- X a et
- X 1 b 4c
- X 1 13bC X ps gX ster
- et erit X bZC - ser v+c.
- adeoque sublata jam X habebium aequationem:
- b’a + cta = ser p 50 gb + Nq c - 3 abc - 2bc
- (Sive NN +59b N X- B) b
- separitur haec aequatio in duas, excerpendo: -NrrN 4b.
- fiet sT) qb et residua aquatio erit:
- bar ca +hab C + 3bC A 4 b 9c
- vel b2 + 3c B + 3c b +c
- sive C + 3b C pb c + b3
- faciamus Cp H- b fier:
- Repeterdu est calculus dumlsionis novissimae:
- X H b +C. X b3 + 3b0X agX + a
- siet 6+c bC + 3bC, - agb) - aGc = ar 10
- Sarmus excerpamus: 2t E be- aqb 10. fiet bg ag- 3c
- et bp aq3- 9ae 9 27 ag 17, 3 agu rar
- Unde aequntio ponendo fpi 3C. fier: r f 2 + 4f - a
- sive pro f ponenb , fier: 9’ + - a d - ra videamus
- aan haec aequatio sit tractabilis. Nimirum debet esse
- P iq reditur ergo ad detenul nationem ordinariaum.
- superest alia divulsio: b+ C, aq b +c. sive devidendo utrobique
- per b +c. fier: b + c - bc B ad. quae est aquatio ad circulum
- b+ - bc superest alia aequatio: 3bc +3bc p, at
- adeoque b7 a 4Dbc - C H a = 3C B
- + -be +) et b 5 aer +3C=0 1a93
- oiquiaum et loco Ra ponamus RC
- eror novi
- rodibit X3H 42bC sed satius erit fere retmere ordinationem et exposteriore aequationefier+ b +C RC dc + bc ec
- secundum b. ponendo b, d - a
- rumtando c. in a quoniam C. nullum habet huc usui g
- debet esse (a) - 2ag +q’ a
- 3ar gaera
- adeoque 18r +6X 97) 94
- ei 9r + 6r 9 + f92q - 9r
- sive 3rt + 97 s 29 - 9r
- 1
- quae determinatio adhuc arctior, quam
- dr Scipionis ferrei–
- quid si aliter divellamus, ponamusque: X 4b-3 abc - 36 0.
- fiet b5) N4 3ca. et b27 N g2 - 27 C8 9e 2nq
- ut aequatio residuae erit:
- Ga 27aCZ 3Ca
- erit en ea +ba, et Cn 2 a + 23ab + Va
- et fiot novissima aequatio b2+ L,
- = 2 ab - ba 2 a + 2ba
- RE b + 2 a + 28 a b + b a - - 2abR, - b aR - 2’ aR 0
- e ordinud. b (+ 226 b + 2 a- ea R
- N qu 174) (9 2 4 - 3X qu C- 3 ra C2 p bi 9 y et
- +27a C6) ( qu . 1) quae est aequatio quadrato quadratica
- carens termino penultimo.
- pro s ponamya 5 scribatur a. et pro c fiat a
- e vaa
- C + = 24C = 27 ar e = 18 a 70 aequatro-
- quadrato quadratica secundo termino carens, reducibilis ad Tubicam
- =6a h= (+ 94) h - 17 2r a e r 7
- sue H2 - 6a H - 62 a h - 17. 1 a6r p 0. F sis Hg ta
- fier. 8 (+3, 19 +3ag +8 a
- im ea 5 qi
- 63 9 012, 2a
- b (+ 22a b (+428
- E s
- 42 an) + C. MF 456 EaX)
- -2 a + ZaR + QR aR- ae
- R + a - a R
- jam ( Q a + ba et Xp, b + c.
- Ergo X, EaK b = 2aR +, Za R 4 2GR Sak - a
- R3 + aR - a R
- do quam dividendo per c jam inventam,
- habebimus radicem quaesitam,
- Ermutum est. resumatur: 3bc + 3bE H RC.
- Ergo b + bc H RC. componutmr haec aequatio
- cum altem b+ c (b
- 1 2E fiet bp et Ra + Aa a
- jam loco b + et p 2C. Pcribendo valores diliendo omniasti
- fier ea Ea + Aa - a; + e e + RC fier aequala
- 2 (ea Bd( a) r2a 1 D2a + Ra
- s et redit aequatud ab miho data
- Eeplicando
- b2 a bc at. b aer - beb
- N ag-c + bC. Ergo b a r aqerC
- a gr. et fier aequito bx + eb - a qr
- b e et ag - c n X ar - (6b0, et b7 ar agete
- et B ⊓ a - 2 argC + 2ar C, +aC = 2a9ct +
- Can usta racinma
- aa
- iea
- quo posito orit autem aequatio autem quadra
- loquadatica superior semperctadirem halebit realem,
- 3aq p. 29
- in eximpito ubi B9. H12
- 00 Tanim ultiu pcii
- trichle cerrumipent
Cite
Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 301r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0601?run=74