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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 109, page id 1047377675:0125
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=125
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000125.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.86
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

25 alct; de proinde rrilineum 6OLI C( 1024 (c3  12815+ 
6256+
 287562 62563
236lc5,  idco recta AF es ad curuam, AF VE ba seu reCtAR-
3725b4
Sulum AC: NF a d ba F ca = 2024 (c3 - 7281c4 - 256lc5 TCU
187562 62563 312564
mixcilineum AC L.F, dacur isirur recta ae qualis currae AF, quae
inveniende erse. Quomodoinvenineur superticies Facta ex
rocacione curra A F circa rectom A C. cuidens elt ex huius
45. Quoniam ex huius 57 Facile est invenire centrum orari-
cacismixtilinei ACFF. quod si in aequatione reducta, ex vna
Parce invenca Fuisset non 2 scd 22 (quod semper accidie, (1.
raciOFF od C D sic mulciplicaca rationis AE ad AC in rario-
nenumeri paris ad numerum proxime minorem) invenea
EUISTCE EANEUM (UPCTFICIES GENIEA CX FOFAEIOHC CUIEVK AF
circarectam AC, repat et ex huius e3 _ 43.
P R O P. 59. F E FO R F M A.
en Tc parallelogrammum ABF F, seque curra F C: HI ealis
anacurae, ve (ducta recta quacunque C+ Parallela rectae
AB Curram F FI secanCC in C: _ rectam BF in D) rario AB
ad CC Et mulciplicaca rationis BD ad BF in rarione P ad.
dicoparallelogrammum AB FP ense ad ficuram longicudi-
ne inANIEaM IIAEFOHI DE( = P adG. producatur recta BF
in M _c ducatur curra MKHIcalis nacura, ve (duccta recta C5I
tangence curram F. C HI in quoliber puncto Cr d ductis pa-
rallelisCC, KI) recta CK lic ae qualiS _ Parallela rectae C I:
manifectum cst ex huurs7 rectam AC. ad CI vel L. C ad CK
eHe veP ad G, cumque hoc semper hac, cuidens est figuram
HIFBH CNC 3dEgUrAM HI FM HL UE P ad G, aEque ex huiUS
IF ABUTA EI FM HI est aequaliS Agura HI AF FH, e idc0
figura EIA E FH elt ad Liguram H F BH ve Q +a P, 8 Per
conuertionem racionis. H AL F HL CH ad parallelOBram
tDum