# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0252
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0252?run=74
# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 40, page id 797435492:0252
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=252
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000252.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.90
# 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.

18. 27
L R C F. IV
Nam connectatur subrensa MI N, ducaturque recta NI R ad Z A
Parallela. Fit quoniam angulus Z P I non minor est recto, exit.
COMaIOT ENTErNUIS, N HI P obtuluS. ErgO reca NM major est quam
NIII. Leaque magis arcus, arcus IIH major est quam ipsd B II:
2. F. D.
Icem, quoniam ans RN F ipsi X O F par haud minor est recto.
exit RF L RN. quare MR J. HF = MH -1 R N. hOC eA
MEL MR. L R B. Flt auirem (ex archimedais a NuMPEIS) MR
J. REN E arC. M N. ergomagis eAtM F L arc. MH..
VI. Perucilis esthaec propolitio in tancentium demonstrasionibus
expediendis. Ftenim hinc cousectatur, SI arcus M N indetinite par
vusponatur; ejusce loco alcerutram tansentis particulam M F, vel
NI II cuto substitui.
Speciminis hic loco methodum prononam generalem eycloidum om-
nium, es consimili modo descriptarus curvarum tansentes determi-
nandi, hinc pecit a demonstratione munitam.
Recta A E sibi parallele deportata quamcurique curram ad casdem
partes convexam aut caram, A P X perambulet uniformi motu (sci-
licetue xquales currx partes aequalibus crantisat remporibus) codem
que limul tempore punctum aliquod ab A per A T etiam uniformirer
feratur; ab hoc puncto caliter MOTO PFOSIGNCLIIE CUrVa AMZ,
cujus ad datum quodcunque punctum M carisentem oportet determi-
nare. OF hoc Hac, ducatur recta MP ad a Y parallela, curram
AP X secanS in P; Perque P ducatuE recta P F CUEVaM A P X COn-
tinsens; huic vero per M ducatur parallela M H; inque hac lumatur
punctum quodpiami R, 8 ducatur R S ad PM parallela; tum HaF
UE CuEra A P od rectamm PM (hoc eA ut unus motus uniformis ad
alterUI) ita M R ad RS; _E CONNECtATUFMS. AXC CUEVAI A M Z
continget. Sumatur enim in hac curra punctum quodvis Z, per quod
ducatur recta ZX ad M P parallela, secans curram A P Z in X.
ejulque rangentem in E; _ huic parallelam MR in HI; ipsamque
demum. Mt SinR. Sit autem primo punctum Z TupFa M versIS A.
unde recta P F = IATCPX. ad eoque PA. PF C ATCP A. PX::
PML, PN  XZ:: PM. EH = XL:: PM, LHI- FXC
PM. Z HI. GuarE PErTMUEaLIM Crit P A. PMI C PP. Z II. est
autem P A. PM :: MRL.. RS:: MH. RH:: PF. HIR. ergo
PB. TTK. L PF. Z TI. quarE HIK =  Z HI. est aurem punctum
EI extra curram AZ MI, ob F Z = XZ =IPM = FH. ergo
palum est punctum R exra curram AL. M exiltere. Sit vero secunde
punetum