Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 84r
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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The machine reads it as
- a = b
- a + AAh. + V a = + b
- ae
- X
- - gna +. rX - 5∞0
- n + Va + 1
- X + S... y.
- X
- X2 + 2 ax +6
- 3X - pX c
- X+axL.
- = b no
- Demonstratio hujus Theorematis a me
- o
- + Yd
- +
- Yad
- reperta: quod omnis radix aequatio cubica deprimibilis) XSc
- habeat radicem rationalem.
- Nam radix aequationis (ubicae
- est: + V: 9+ 1 494 - = p
- +
- 9- 3
- V)
- quod si ergo deprimibilis est, necesse
- est ex his binomiis radicem cubicam
- extrahi posse. Extracta autem
- cia
- radice fientbinomiutu a + sb
- et a - sb. uli quid quorum
- summa erit 2a quae erit radix
- X. X
- rationalis. posito a esse rationalem,
- ipsam a autem esse rationalem patet
- seriqibus
- -
- 7
- 9- L
- cubrea
- + L
- ex e eo quia in binomiis extrudts cabicis unde radio extrahenda est
- binomii exsitrahendi
- Ccubr
- P est quantitas unde radii
- extrari potest, nempe ea est. p, cujus Tadix est = P Ex tali autem binomio
- si modo radio extrahi potest, semper una pars est rationalis. Ergo ut
- in in additumento ad schotenii lom. in Geom. Cartesi
- 1
- 2
- r+
- +.
- 27
Cite
Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 84r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0167?run=73