Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 121v
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: 0.77.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 122r); this page is its left half.
The machine reads it as
- Invemri tres numeros, quorum differentiae quadrati, e differentiae quadra
- torum, etiam
- quadrati.
- Inveniamus primum tres numeros quorum differentiae quadrati
- a
- b. C..
- aub.
- a -b a - c, b- c X + dX +
- Inveniamus primum tres numeros quorum different quadrati
- Ergo primum a e X +, dX + d. Ergo a A X + 2dx + d + bl
- Ergo X + 2dX + d + bl Y = el N Z + 2eZ + C, poneudoque ZX ef
- fiet _X + f s
- 1et
- +2e +ref
- +Vor
- comparanda cum X + 2d X + d
- ideo d sut
- bl et d f 2fl +
- ideoque nes i fl + C +bl + cl sive e + bl + et seu
- 2
- HI
- ntmerus quadiatus
- bl- cl. tartumque Ergo et, pro arbiteae sumatur, et duo quilibe
- alii numeri, negati, ipsi quadrato aequales,
- vim
- cuio non comparanda sed ot ascribenda, non enum sunt duaeaequationes, sed
- una, fiet
- ilem
- 2dX x + WX +s
- Rursus bl- el 57 X + 2gX + g
- vel mntatus siguis
- v
- n
- +X
- n
- tec eno + ref
- uid.
- -2f X ++ 2ef. 2d sy s
- -re
- +2d
- +29
- +C -20d- 2 + +ef
- + +d +2dq + e
- (9 = d2
- +C
- + et
- c
- v
- qu
- +f2 es - 2df - 2gf
- S
- + et-red - 2 eg
- + d +2gd.
- Rectius numerum literarum contrahemus, omisso df, fietque uno non est omittendu
- X +2dx +d +bl - cl 5, X + ref + e
- Ergo X a- f - e + d rgF 2f + 4 ef +2C, +29 = adf - 2gf a2gd
- =2d0 - 2ge
- ponendoque e af h, fiet X - h + 2d +g5) S2h + 29 - 2dh - 2gh + 29d
- nde t sufficere ab initio dici: X
- sive X + 2d X + d
- sive
- +29
- -2C
- + qu
- et
- 1
- +2dX + de+ bl - cl BX + 2CX + e
- 0
- +X +29X +g
- sive X +2d X + d f2d9F2de ( +d rdgrude
- +29
- ne
- +92 - 2ge
- gv 4922ge
- +fer dc +
- sive X + fd rg sive X + fd H. fe B S 3d + a Ygd + 2de - 2cg + 2gr
- +2dX + d
- + 29
- +gu 5 x + e.
- erus Ergo d d +9 1 d +g. sive
- 12
- + 29.. + qu 1I X2 + 2ex + e 9 B d + g + 2d9. Ergo 2d95
- vel X + 2dX + 3V
- + 2d9
- X + d + g 1
- + 2d9: fiet X + d +g( SX +2ex+
- poncudoque idg B2h x + rehrt h, fiet:
- tione arbitraria, fiet d +gF, 2dg + 2hX +-h
- ac proinde
- vel e ad + sg + B9 + G. Unesi, d cedut adgh
- item X ( e - bl + cl - d
- 2d - 2 e
- +2d9
- X + C + h. et pro e substituto ejus valore ex aequa
- X Y, 2dh + 2gh - 2d9 + h
- 2h
- 2 h
- = c + d + g
- Unde C3 - ble + de - de + de - bl d + cld + d + Cg- blg +clg - dg 5
- ( = 2d e + 2d9 + 2d g
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 121v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0244?run=74