Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 199r
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: 0.75.
Original at the GWLB · Page image · Annotations (IIIF) · Download text
The machine reads it as
- vertep
- lenitatum an saltem ope
- cummasumanarum licere
- curvam conicam reddere smmabile
- mensurare
- quadea
- naato
- sit sectio Konica _ centro praedita AY. ejus
- Axis directus AX aedata. Veilex A, fangens verticis
- centrum C. ircus carvae AY, abscissa AN Xordinata XY
- sector ACA ACYA, asculatus tranversum AC+) et
- jugatum CE, a semilatus rectum Y
- qu laa
- Ex ircus
- Exarcu a verlice A incipientis AY altero extremo Y, ducatur
- tangens YT, occurrens ipsi AT tangenti verticis, in T. et A7 sit F. His
- 3
- 3
- potest
- ubi posito in Hyperbola + significat +, in Ellipsi -.
- etiam theorema sic epuntiari: sectorem ACY A esse ad 9b mo
- regtrum ex b tantum ascriptum LAFY, (id est circum scriptum
- est LAVB aAri
- trapetium seu monogonum
- in illipsi inscripitum in Hyperbola) ut 1 F , H + = B - = t ete
- a
- est ad unitatem
- aa L. It
- 2a 4X = -
- et aa H
- irgo Ce
- aa sdt
- 2a
- a +4
- a 1
- aa +. 4
- jaa
- 5a
- ag
- DaHt
- seu aa +
- aas d
- a
- + 1 3a + + = 2a
- aa 7
- a sat
- aa + f a + a + Jaa + it a
- (dt. jam
- Hinc ACYA: 9 = ac
- aa + 1t
- a+ +Y+
- 1
- a- t14 =
- aa + Ht a- tr+ acH att+
- 1+ et aaa (t - q2 a (dt + a (at
- aa + 1t a. trf a+ tsY S aa H a 2da tr4 2art
- Ergo 2a
- a.: 141, log (a - Fr +1) + lag. (a XY + 1) = a: 141, log. a H
- aa+Y+1
- porro X: g. 2tt i, naq H seu aa x pHX = 1t q se a a liL
- Porro sector AC YA in Ellips. = triunus. CXY + trilin. AXYA
- porro sector ACY
- In Hyp. = trinnus CXY = trilm. AXYA
- et aaque sat = 9+X]9 7 sydx. jam y = srX + Y XX) X- 91t
- Ergo fiat sect. ACYA = tianue CXY + trilin. AXY A
- v
- H
- aa H
- aat
- seu gy =
- 194+
- a paat +t
- 4Y gH +.
- aa + H
- 2 199 aatl + 2Yqu + 1
- 14
- Bt
- A at 4 2aat+ t
- a
- taattaa fhaat H . + oaa t)
- a + 2aaH+ F
- 29rt Hinc X: y = t: V, ut esse debet
- 2aat =
- S aaX + HL = 2gH f= a NX:, 9+
- log (a - + 41) = log (C Aaxe HLoa + (a Sag FX = a AX) - log sarq +rX
- aa L H
- seu y =
- aa L H
- a Tirg + rX +a YX) - log SErg. + rX
- logu (a4 tY +) d + gy + xy loq (a +) - log ( (a. frt1) =
- 0
- at ( = a logsa + t) nta log (a +)
- de + 20d a f6
- 4a + t id a +t
- 2
- aa +
- aa tt
- H = a4X : , 29+X, et _ _ 2td1 = (29 +X) aa dx + aaxd log (a Ferg FrX + a L Fra) -logsa vhrgeu altr
- Cy dx = + aaq aa +H
- 4+4qX + X, 29+X: (1g + X aa + H = aa 2q t aax f aay
- 1
- et at gapax
- seu 2Fdi - 2q aadxp: (2 )29+ X
- do - d (a r2rq. F rX) = fardx. 2Y9 + 1X et dcorco =, flar x. 2rg+ X 1 (+ a rdx. 2 sirg gr (4) + ar tr. 21412
- 9+X(+ Y +rX
- eX
- Ergo et: saa = H) = quodx C dxt H dx : 2a 2gX + XX
- d a sArX = fardx: 2Y + 1X
- 2p
- sqa
- Hinc 10g (avirus fnt)a SArX
- LX
- r
- Fx
- (
- ((+
- sit se co
- lEyq - 1)
- 02cq- )ab 2r9 (+ rX L rX = 2aa
- sit C = dab + Cx deo = Cdx: 2Yab +e ubi pro xponendo valorem 29Et: aa L +t, fiet
- ummata
- Ergo )Ca ydx = Co sydx _ (duo sydx
- dco = ox Cux sqa L tE,: acab L abtt +29H) sit q. b: c = 29: a, et evanest
- in hominatore Wy-H2rX +
- sed hoc est pro parte extrahibele
- T~I
- a: (a -X) = t: (1 .t,
- e
- ax.
- a: (a -X) = tF: (ax- H
- H -
- CXYV
- a: y =
- y = AX:
- a (a-X) =
- x= 2 a t:
- 1 =l-6+0b-6
- 1+b 1Fb
- in cu
- au 2d H. 3 ad + H
- F1 - b + bb- b etc
- +b - bb + b et
- log atv)
- a
- ato
- sit aoq- abstus ex abirus
- sit deo cox: fab
- et C0 = Ylab L ab X)
- seuco=ab,
- et yerat = (X, 2 2X
- eut 0g se y dx =
- d ax (Auxab, 4 2 d XX)
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 199r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0397?run=74