Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 68r
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: 0.75.
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The machine reads it as
- sire rmaginaliis
- incognita pujus
- De transformationibus aquationum, (adhibitis duabus incognitis ad praeparationem.
- quadrato quadraticam
- stusis in Aralysi Mesolabi aquationem propositam quam libet:
- ()
- 4 2
- x Ex, bpX t
- ita resoloit in duar X X 9y et 4y + bngy - b X + b aX p b H- B pX
- ex
- a (+)
- no
- Jam faciamus X E Z + d. et Y A e V + f
- ab
- X + rCd qe 1S a BE V 2f Y
- jam ex 2fer aequae redque +d = Z - bd p equ + af sive v⊓ 7. Z
- V
- 94 Cd 32 Cgo + 4 cd3q + d+
- bit
- = 2c3d.
- Q- Ba - b d pv. pone b p 4C, for
- a C - XCd sive a
- tantum modo ponatur b, seu 3d
- seu CH (3-el
- 13-
- 2d
- CV
- p2
- seu C+l, 2C N13 quod fit ponendo ex lvel
- si velmius lc ut a sit assrmativn sufficit
- o
- 2
- nct.
- -2∞9F..
- q ed.
- =a ed..
- - 4 cd..
- acdut
- - 2cd..
- +2 cbd.
- +2c45.
- - 203b
- - 289f
- +bd
- - 26395
- +qu
- utor hic praeformane per duas
- incognitas, quae etsi non vet alias
- superneomerarias dat tamen alias
- expressione, quam praeformatio
- per unam
- redque + d. et
- V2 - bd
- c p =4)
- Hac
- id ac quidem recte sed utilius deprehendo immutare calculum, neque secundi termini cognitam b, sumere
- ese 12 er e 8. et 1p et
- G+ c.
- eut a pro danitate, fieri enim potest, ut secundi termini cognita absit, quo casu b nihilo aequalis. praeterea
- esto c
- eum calculus sit magni momenti, utile est adhibere numeros
- tertius
- 6aa brabat juleru videndum in aequatione cubica trium formularum, ac pimum cum secundus terminus
- 18. 14
- est affin tou extrat potest radio videamus cum est negatious
- s 4 aH ba b d. 0. unde aequationes duae: be a, et da + a pe. nt da= be
- Eigo b pd
- (11)
- ponntur e n L3 + m, et ap V a + P
- 11
- P s + almy +N, a p n V + anpB + p
- Nam ex aqualine sir Amalogia. at 3 mendo bessa.
- e
- a
- ca p V, fier:
- ac ab + db
- ace
- iumet ea at e , ast
- na, b, a a, c.
- t b ad a ita
- +
- Unde ob aeq. 1., erit ly + mb 1 2 v + 2np V + p et per 2 fet: d2 v + d ps d F 2m t m - lymtil
- ande ex fer (9P (+ 1m D B uil yV = anplvys + p 1y lmy. Et valorem ipsius substitient
- 62
- in aeq. 7. puo ipo fer. C) du V + dp p t l yr = inpl vy + p l y (- 1m . 3lim y + m -ly mb
- b
- enpen F
- = mb3
- 12
- lv + nplv + P
- + mb
- l. m. n, P ipsam l omnino evanuisse
- b
- 5d
- +im
- ob + 2npor. +b, et facta multi plicatione
- tollendae fractionis causa:
- bdu B + dp (n b m b) (F mb) (undon
- Ubi notabile est ex quatuor arbitrariis,
- Unde
- b D) er dpB +b
- 1)
- b4
- pro y sabstituendo ejus valorem d +dp - m + nb y, tumfier ex cq. 6. frei
- huvr dot nibe ub
- 0) 1is
- quy
- s
- n v + 4 ne pb V + 2n s V + anpb V p
- + rupbv.) - b+ no2
- (+ in b3C nv
- a
- absdu. + dp ( +nV + pb
- +4n pb..
- + p2b2
- + 2npbr
- +prb
- frei )V (4) X + bdeZ H ab et aequabiter a radici quadrato quadratica ex
- bae + b da
- ba
- a
- Esto (14)
- facimus jam n. V + ib rpB + ban F
- quopu +
- + d g faciamus bd nV + db p, o. sive pnV
- Ergo 910. Quod est absurdum, quia qa.
- restabit n Vr
- Elia ita ex i bn +2bn pP + bEx n BE + anpbV + 6n paC2 B
- aup BP + p+B+
- 15) 1a
- Sq
- 3 = b dn . =b dp
- Ponamus . 6) p3 b d u erit XPB 1Dbd, et env bdp
- sive (9) +nV ( b6) bd. et ex 15 fier. bnV +Bp nv = anpb D + b. Video ergo rem non
- procedere hoc modo, firei enim aequato itoditas, quia a n confderane vetat mna iesgnta itiaue posita neb quia mlis s
- Ab ad a, ita aedeceade
- Tentaturan fri posit ad epressionem
- Geometricam omnium radicum crbicatum
- et de Radicibus cubicis
Cite
Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 68r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0135?run=74