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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 42, page id 797435492:0254
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 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.
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F18. 3Y
E18. 32.
l. B C F. V
Ducatur enim quavis HO; haec tangenti prius occurret, pura ad
R. liguet H R majorem esse quam HM; multoq; magis ese HO
C HIM,
ZI. Etinc Circulus Centro H per M deseriptus curvam concin-
Set.
ZII. Eriam inverse, si HI M minima sic omnium qua ab LI 2d
curram duci pollune, exit H M curra perpendicularis.
Nam quoniam HI M minima ponitur, circulus cenero II, incerrallo
quoris HIS, majori quam HIM, curram secabit, de proinde rangentem
MT, hanc pnca in K. ergo quum (ITH RC HIM, non erie angu-
lus HRM rectus. iden de punctis omnibus in recta T M evidens est.
erso tangenei perpendicularis non alibi quam in punctum M cadit.
XIII. Ouineriam si recta HIM minima sic omnium quae ab HI
duci possunt, eiq; perpendicularis sic recta TM; haC Curram can-
BCt.
Nam tangat alia, (Si fieri Porest) ZM; erit ipitur X MI ad EX M
perpendicularis. Ondepares erunt anguliHM X, HMF, torum
e ParS O: F. A.
ZIV. Dico porro minimX HIMI propiorem HI N remotiore HO
minorem este.
Nam ducatur subtensa M HI; haec producta curram tran(gredietur,
ex iplam IIO secabit, pata in R. _ quoriam AnguluS AIM R obeu-
sus est (major illonempe, quem tansens cum HM constiruit ad M)
eric LI. VR masis obtulus, adeoq; recta HIRL HIHIOCmaSISHIOL HHI.
ZV. Hinc perspicuum est Circulum quemvis Centro H deseri-
prum, uno rancum ad ea Idem puncti M partes puncto curra occurrere;
nec omnino pluries isitur, quam in duobus punctis.
ZVI. Perpendiculari H M parallelae, sint rectae IN, RO; Ha-
rum propior INremotiore R O rectins incidet.
Nam per NI, O ducantur ipli currae perpendiculares R NI, FO, H∞
cum ipsa AM intra curram conrenient, puta ad R, Sc P; sibi vero
iplis in.
Liguet jam elle ang. FOR = anS, FP HE anS. PRO = an
NREI = anS E N J. Cimm ers o sic ans. F. O R raajor aveulo F.N)
liguet propolicm.
XLXXVII