LBr. 57, 1 · Bernoulli, Joh., fol. 10r
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: 0.80.
Original at the GWLB · Page image · Annotations (IIIF) · Download text
One image of two folio pages side by side, registered by the library under both labels (also fol. 9v); this page is its right half.
The machine reads it as
- Sumtis itaque integralibus per partes duabus linelis intercluras provenit
- int. dx = X
- int. xlxde = L XxlX - axX
- Eat. pal dx = f x1 -= ap (7 + aap
- int. XL dx = pElX - Z as (p + 3.2 auxlp - 3.2
- . 4.
- 4. 4. . 4
- 12x4
- ru
- int f lap = F. Ep L = ap E + Q. aux Es - 9.32 a x x +
- (. 5. 5
- a
- 5. 5. 5. 5
- Multiplicalis his e integralibiis per correspondentes terminos lujus seriei
- bi a 1 ab 1 12 3 a bb 12 1 4263 x et positis seriebut quae sunt verti-
- cales Lorizontalibur proveniet int. fde seu spatium CFs11
- X3(∞
- 1. 2. 3 aab
- X3IX
- 1. 3.3ab
- +
- XYLX3
- X5lx4
- 12. 2. 4a bb 1. 2. 3. 4. 5a Ib3
- X1(C)
- 1. 2.3. 5. 5 a2 L3
- XIX
- 1. 2. 5. 5. 5 aab
- X
- 1. 5.5.5: 5ab3
- ex
- ∞
- ex
- ex
- 5. 5. 5. 5.5b3
- Hinc si F = b = 1, erit lx =0, proinde quaque lX, 1X, ( x = 0. spalium autem
- CFHI degenerabit in CFGA, quod itaque eoanescent bui singulit serverut ter-
- nis exceptis primis erit = 1- + - . + - ix.
- modus hic quodraturas determinand. per serie intonitas non solum succedit
- in curois percurrentbus, sed non nunquanin aciis quoque adhiberi potet
- HI. Qccaritur subtangeat curvae c = y. Sol. flc = ly, ledx = aly = adque, yledx = adis
- orgoyle. a:: dy. de:: y.s id eoque s== conrtanti; quod indicat iprat cuvvam qlin
- sitam este Cogarithmi cam, et viceversa cogarithta eam esse culvam perorrente.
- III. Detertcihanda est subtangens curva X =; sol sumatur utriurque diffecentia
- le et habebitur X’ix + Exd = leds, vel (ob cl = ∞ (5) de+ lxde ledys
- aut ad +xd= lecly; ideoque a + lf. lc:: dy. ds :: 7. s ergo s= a +7
- facile ita invenitur: quoniam yle = XlX, erit y = 2F, et yd = Xa=
- alxde + L ppallX) - L apat ideaque integr. yds = L ( - = axx
- c
- Methodus hac applicari etiam potest ad curvas percurrentes quarum aequa
- tiones pluribus quam duobus terminis condant qualis ett haec f +X = X +y
- sumlis enim separatim differentialibus cujurque tertini per modum generalem es
- hibitum, prodibit aequatio differentialis, in qua si fiat ut suma terminorum
- cum de ad sunam terminorum cum dus multiplicatorum ita y ad s, habebitur
- valor subtangentis quaesita: D iff. = de + X 1fc
- (7 - 1
- Ilxdo
- 1
- -1
- yxls1x + ay
- _= X Olpdz +dy, ideoque S a acti n ayt
- quae quantum vis composita ope logarithmicae conctrum potent, quia quaevis quantitas
- percurrens separatim sumta per illum constrim poten.
- Eadem hac metlodut eliam locum Pabet in curois percurrentibus altioii gene
- ris, omniaque quae duta sunt deoi peccurrentibus primi generis applicari possunt
- ad cjurscunque gereris percurrentet.
- Diutius quam par est, vir Celeberrime, his imoior, qua forsitan jam me
- Meliur noni: interim meac super hac materia meditationes lecum conunicare volui
- ut quourque cum Tcis conspirent videas; id unicum adhuc oddere liceat, quod
- catera qua circa Rujurmodi curvas invenienda redant, ut earum applicatae masima
- et h no, panita flesiu, caulicae et evoluta aliaque ope calculi percurrentis etiam faci
- le eppediantum
- bX + FX(Y
- e
- XFlx
- 1. 2. 4A aad
- XlF
- 1. 4. 4. 4 abb
- 1.3.36
- 4. 4. 1. 46
- qlcadratura
Cite
LBr. 57, 1 · Bernoulli, Joh., fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-958803:0019?run=74