Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 109r
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: 0.84.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 110v); this page is its right half.
The machine reads it as
- X+dx- = aequ.
- 23 Mortii via revocandi ailias differentrales
- 1682
- adquadraturas. Et evitatio exaltavis
- ad comparendas aquaves requisitae
- in curva datur relatio inter AP et A∞. quaeritur
- relatio inter AB et AD. sit AP, Z. et AB, v.
- et AB, X. et AD, y. t BP. HC GW, dx. WL, dy.
- ob Triangula similia GWL, CBP, co DC, erit:
- BP: BC :: WL: GW, sive BP: y: : dy: dx, et BPerit y oly
- eodem modo DD: DC:: GW: WL sive DV: X:: dx: du ax
- et DU erit XdX. Est autem AP aequ. AB + BP, erit
- dy
- (1)
- ergo Z aequ X + 3 az similiters aequ. AD + DC erit
- ergo v aequ. y + X dx. denique ob triangula
- y
- i
- AP et GWL similia est APO: AP:: GW: WL. sive
- v: Z 3: dx. dy. vel dx aequ. v. quem
- y
- v+do v
- valorem inserendo in aequationibus 1 et ~ fiet:
- Zaequ X + 32 ex aequ. 1. seu Zaequ. vX et
- +)
- v-y
- vaequ. y + XB ex aequ. 2. seu v aqu. ZV vel
- =X
- exaequ. 6. fiet: ex quae aequationes rcoincidunt
- nempe 4 et 5, , cum 6. et 7. fit enim utroque modo:
- vZ aequ vx +Zy. Unde differentialis aequatio
- 9
- erit: Zdv + v dque aequ. vdx + xdo + Z dy +ydz
- sit jam data relatio inter Z et v ex problemate
- L(101
- v verbi gratia sit: aZ aequ no quem valorem
- psius Z inserendo in aequ. 8. fiet: taqu ax +vy
- y+vax (XD. xdo) v aequ VX F vvy. seu v0 aequax ty. cuius
- a (2)
- Ergo L x aqdixdo differentialis: 2V dv aequ. adx + vdus + y dx. Et quia
- vv.
- +X + X + d
- conpalier
- +xvIex
- +(HIXdo
- sit +s
- epsit
- et () sit t
- ex qualibet ordinaria derivari possunt duae differentiales
- fiet scribamus loco aequ. 1,
- (14)
- 13)
- vaequ ax +y. fiet:
- do aequ a x axtaedx + dy
- jam ex aequ. 12
- 1
- Vvnaxtvy
- do aequ. adx + vdus ex aequ. 14 est dv aequ. vvdus +avax
- 20- y
- (15)
- quos duos valores aequando, erit:
- (17)
- v0+ ax
- tat; is avvax (+ VLy) - aa xdx-axvdu aequ. Q dus (2avod
- constanter
- durnando
- ut simplex
- Lwvydy tavydx
- ho un ponamus valorem ex aequi 11. fiet;
- majore (2(3aex dx tavy dx (aa x t a xvdu aeqiavrau ravelus
- X a
- seu X+dx
- se
- M (17)
- taax dy tavyd
- Faxyayue. Vyy chyavydi
- detraratur avi das vuo ayt aaxt axvduque Ebvodus a vvix .y vedu avydx
- vy y ovdy
- +
- op qua aequatione 17. facta explicatione et destructis destruendis redit
- aequatio II. itaque inutiles sunt duae differentiales. Omnia ergo redennt
- ad aquationes 2et 1. n
- nempe
- 1oq vertatur
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 109r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0219?run=74