Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 22r
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: 0.72.
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The machine reads it as
- invenire tres quadratos progressionis Arithmeticae
- aa
- bb ce. Egit aa - bb = bb -cc.
- F(f: h) (b -c, a +b) = b+C, b =c
- Et ex iper2
- sit a -b= f b = c) ifiet
- seu fya +b, ih= b +C. fiet ex2, a ) F: h) (b - C) + b et
- exa fint a = th: f) (b +C) -b quos duos valores aequando
- (4)
- 4b = ffc + fh b = hhb + hhc - ftib. adeoque fiet
- +
- +hk
- quo valore ipsius C substituto in aequatione qualis E, quae
- do
- 18
- a
- et ltb. (H - tit + 2fh) b : st
- Aliter substituenda valoreum
- C in aeg. 4
- X
- ficta=
- modo
- seu utroque seu a-
- fc + hb = h
- F b, 2fh - ff +hh,:
- 2h ff thh
- b
- t Cth.h
- F +hh
- FF+hh
- b = 213
- ffthh.
- C=
- b, f- hh. + 2fh
- f+nh
- Ergo in interris, omisso communi denominatore, habemus tria
- Habermus Ergo a =
- ff +hh
- quaesitorum quadratorum OO,
- 3
- E
- = b, fh - ff + hh.
- D)
- latera
- b, ff-hh + 2Th
- D = b, ff+hh
- vel b, ff+hh = 2fh
- ubi f, h, b, sumi possunt pro arbitrio, etb potestomiti
- si h esset = f, fieret C) = bff 9 = 2bs, et
- D = 2bff
- poto esse errorem in calculo. sed statim, quod non licet,
- ∞
- ita
- enim fieret a = c. sed alia se Hert ratio brevior
- ffieret sint a-b = b +c foret fiet a +b = b-c 49
- l
- si foret a +b = b -c firut a - b = b+ c
- e
- +h
- + fhiilit P shlib 2hbCBab
- r to
- sliit sitib+ Fbst Ctiha.
- sen in a = lb hc = bG,: , firt a = hb +tbA hss + ys
- O
- LC
- 24
- su
- 1
- =2fh - f + hh fs+hh. D s lin +2st
- ffhh) +f +h 2 fh + 2fh D Hlt S + Essne +(4) stih afih t afh
- ei
- X + K
- f
- a
- (a (45
- +4fftih
- +h _ fth + 4 Bh - 4fh _- 2 ffhh)
- q
- sa
- )0-9 = 2fh rfh- 3ffhh 4fh - 4l 5 itaque res sulcedit
- N
- f.
- erectuna calculo
- d
- d0 - dD = 4fh 4F 4fk 2st 4h B
- solutio ergo haec est: invenire trt in integris
- tres quadratos progressionis Arithmeticae e erunt eorum latera
- 2fh + f- htival C- 2th D- f5 + hk
- ff +hh
- s h= 2 et f= 1 firit 3 = 4 3 =1 8 = 1+4 4 + 1- 4 male
- 2th -fF + hh
- sit h3, et 5= 1 fint 6 - 1+9 =C =14 8=9+1 = 10 D = 6+1 = 9 = - 2, sed licet D sumtre
- 49
- Crut 9, 8, D,
- est 6- 1 +9 2
- 19 10, 2 hues trs quilus niel hombe 21 3. 1 aam l 1125.
Cite
Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 22r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0043?run=73