Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 51v
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: 0.78.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 52r); this page is its left half.
The machine reads it as
- In sectione Conica
- Si recta per ceninum chordam secet, quam ubet
- chordam ei paralletam bisecabit
- Bisece Be reltum per verfilem in R
- XV y yg - 2YXFXX
- BYqu = 21X f. B41 +1) ex (4L p= Bd, ex AR y
- 4 BYgo = BRqu.
- B(), (X). XV, 19)
- B(X) Y - 218 + Y73
- p FF = 3] - Y FY- L1 + G)Y
- Cy+ (X)Y = 1 (21 4 27Y) 4 (2rE + G
- IR = tu 2....
- SP) = FGF) + WI) + FV
- ----
- S (R) = ZFy + L (X)(1 = (Y + (X) V
- Ergo LMV) = 2 FY + K Y WIR)
- _sis = F) + XY X
- per Ax). n8) en PX
- = WV,
- WR = 2 XY C et = cBF: BX WB): P) = r H : NY
- CW = CB + BWa B1 BW = iBX + L BY CW = CB + = (X)+ = BY
- 11 . V..
- V() - L GX) AE, DY.
- Tangit YT. sectionem onicam et angulo TYP recto ducta
- Y P occurrataxi in P dico essi XP = BR + BX Bt
- Seu X ad BR ut CX ad CB seu XP CCX BR: BC
- Si non tangit, ero curvam paeter Y in alio puncto secal ut E.
- sungatur a. ex puncto E, in axem agaturrorpalis hF, n est in quam ex
- Pagatur per noimalis YD juagotur TE. ob trinogula YDE sie 2t YXP
- simuilia etit Ergo YDser XF: DE = YX : XP dunsus
- FEqu = XYqu = FEFXY, FE - XY = 2XY + DE, DE
- urius FEqu XIqul: F. D PF. F.B - PX. XB = BR. 3C
- IR. FB et BF = PX +XF FB = BXL XY
- PF, FB = PK. BK + PX. FX + XF. BX ZXF. XP
- Ergo BF. FB - PX. XB = FF PX. FX + XF. BX f XT. AF
- qu
- EqtaX
- 2XYYDE, DE. Erg DE: DX PX +BY TX F,.NY u
- sit et hyp. DE. DX Et fit 2XVF DE, DE:, PX. A F _A + uF
- Erg. DE: XF = (PX + BX +XF,:, 2X Y + DE) BR: BC
- sed ex hyp. DE: XF seu XP: XY = (CK : XY) BR: BC
- et fit Px + BF jam PX + B XF 2BX + 2XF et fit
- 2BY+ 2F2XF ∞ PB + 2BX FXF, et
- seu pX + BX + XF: 2X Y + DE = CX: XY
- sed px - 2BC + BX ergo sit 2BC + 2DR + XF = CK: XY
- ut Ergo fit 2BC + 2BX + XF _ Cx: 2XY + DE = CK : XY
- sid 2BC + 2BX = 2 CX et fi 2CX + XF. 2XY+DE = CX: XY
- Ero (t XF: DE = CX: XY = ( ea hyp) qu = qu DE q differeusa quatratdum tE at. X 1s
- XY : s XP = XY: CX. BR: BC
- X Cxqu : XYqu. = BR .BC seu BC = XY
- qu:
- BX BR
- 3R BR + BL. 6
- XP = 269.B X + B
- eR gulBE BA (qu P2. B2)
- Xqu. BR XY 1u erit
- n
- XNou BC 2BC4 11 Ladiam
- U
- DEim (XY +FE) est etiam XY (+XFqu
- (X qu BXBC+ DY, qu, Bx (2B C+BX = Bx ju BA (EXB FB2Z. B
- BFE BAqu +, BX. XF + XFqu B4 pa = 2BX. XB
- ergo DE ad DY seuXF ut 2B+ +XF ad 2ZXY + DE
- Sid ex constructione ob trianus angulum pYG rectum est Y
- est Y D se XF ad DE ut YX DE ad DYs XF ut
- ut 2 Y ad p DEFEqu = XYqu = 2BA in (BX +XF)
- + eE et _ (2XB + BK + VC) BR in BRIXF
- =2CB_ F B)
- BR. XF BAB.
- BC
- BL. BBC 2BX) BC + BX, BpL, nr ta N XF. BX M DL ApAC O~ 2 + B (2BR in DX) (=
- D XEBC n
- fit 3C =BX = BR (2BC + BX)
- l. BX= oc 2bR 1. . Di d Gu. BCigu aM
- + 2BR in XF
- +BX BA C) (BY YF ∞B) Nene M et + F. XF
- et
- vede
- sit X= 2XYL De
- ME 2BR+BB
- xY XF. BR
- hine in Ellipsi faret satus rectum
- majus dxc later recto una
- maxus i ayc maje quod non licet
- Bgu, : BRqu - BC qu
- natur 2BKN Eut sse quantilaes afirmativa
- uia unu er Tilhus
- X
- (2Y X) = 2+ dx
- EY d XX -
- 2Xdx F dxdx
- 2rap + X ax = 2yd
- dq- + x
- si fiat X p - Y + ZX
- targense
- natur
- esse tangens sed
- irere curvae in
- ilio puncto E, dmatur ad uncum normulis EF
- et in hanc ax Y normalis ED quia
- e
Cite
Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 51v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0102?run=74