Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 132r
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: 0.73.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 133v); this page is its right half.
The machine reads it as
- probl de Intervallx Num
- contumatio problermatis de intevallis in de differentiis catrium numerorum et (2)
- erirum quadratorum, quadratis
- jamque ponendo t F, 2r, fiet: - 16 alv- 8al
- ceo
- v
- Ergo 8V+ 8V t + 16a lv = 16alt , 16v + dZ At V + 16 + 2V, 8V FVF. + 877
- sed hic comminisci aliquid ut terminum haberimus non ascendentem ad quatratur, difficle
- posi explicemus a, quod nolimi; et ideo sic matim
- -
- 2022
- in aegratione supra inventa 8V55 = 16 als 165V + 8Y 4v aC
- a
- oponatur 8Vs 1, 1, egt 8 25 Ly7 sive 4Vs BHZ, et ZB2Vvs
- ponendoque V 8 et se r, quod facle est, cum numeri sint hactenus
- pro arbitrio, assumti erit Z seu c - X 2 Y8
- ca
- e
- et de caettro erit 1bals p, 165 + 4Val
- vl. 1 r 16419548 a
- Restat ultima conditio, ut scilic et differentia quadratorum primi et ultimi sit quadratus
- seu re- al t ralx sive 16 r4
- ea+ 1d
- et pu a, ponndo , fiet
- p16r+ +4a
- cet
- e
- 23
- et ut diffececitu horum quaddatieuu sit quadiatus
- b
- 1
- s
- 8 dlstro, ponendo 4l, fe
- a
- AY
- f.2b
- habebimus - 4 a l srnt F nt et ponendo P, FF= vel = 4a
- ergo efficendum et ut seu b2c
- p
- ut
- sed hic efficere diffiale est ut utrobique fiar. 8+
- ideoque rectius ab iitro 16r e m l + 4b
- tantum ergo efficiendum, ut summa horum duorum posteriorum quadratorum sit quadratus
- quod fit ponendo A Y in aequatione 167 +bl
- u
- n essn
- in, et extracta ntrobique vadice habebimus: l r. - 8r - pF 1
- Ergo - 8r - p+ e +
- o et redit prior diftrultas
- et m l ab F dbsl. p
- fretque 16 Y4 I 8p I- p (2, rectus fortasse- + a expli cuissemus
- ja
- util
- unde 167 + 4 m - 8mql + qu B m (, sive 16Y4 - ta bnq
- et ita
- b n - 4m + emg - q, sive t F+2m - g.
- Restat ut ultima conditio efficiendumque u differentia quadratorum primi et secundi
- nempe o Brevius forte et simplicius statim ab initio, in aequatione supia
- inventa 8Y - 16als ( 165 + 2Z + 4Y al mondo al, b, A
- diemus Restat ultina conutio impleatur, erit quia crraveram ponendo - 4b pro
- b - b + 26. X--
- sil ideo rd restituamus. 16r +4b muto
- V
- et ponendo 4b V, r m + 2 mG + qu, seu 285 im + 9. fiet , 16 2mq t
- . = 16 74 +2mq1 + quC
- arbitrio assumto, caetera habentur.
- Restat ultima conditio impleatur,
- nec B Ceeeo - + 2b x + 26Z - x + = 2X Z - 74
- 1I
- n
- et pn, pro p poundo +() H X ye fet ne e 12 - 21yX- 217 Z +X
- et cmutatis signis, posito antea neguta affirmatis imajora fiet:
- + 2bX + 2(27
- X. 2XV
- et pro (V, substitundo
- 6
- 12b X + 2bZ,
- et destins destruendis F. V2
- vyv, 4
- 2X LIL
- A
- -107 + 2l)X +21) ZX - 2 yst
- ega ib X abx
- X
- habebimus:
- 5d 70go 4by prgo
- eb
- () et paano eZ t C4 2X +
- pro () sulstituatur S, et pro b substituatur A + S + S cumque 1) sit pure arbitraria
- et destactis destruendes ponatur 1 b + d AL, fiet aequatio haec
- utanem
- 2d1b + 4
- A 2AIX +2ACy ideoque sau dimidra ipsius , quam X t Z erit et
- tum a 12 est quotatus, gam seprae efeciuus. Euatum et ergo quod quorebamus.
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 132r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0265?run=74