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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 79, page id 797435492:0303
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=303
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
# Lines: 46 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.
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L R C F.
X.
lineamque V P F tanGaL recta F T. irem lineaM V R E Fangat recta
FS. Fst ergOSD (a) = 2 TD. aEquiD E XDT (b) =VDEL.
4) 5. Tect.
1Z0.
erBODE XSD = C2VDEZ =) FDg. unde constat angulum (b) Cor. prac.
DFSrectum esse. quod Provolitum erat.
Adjungam es illis cognata haeC.
XIII. Sic curra quaevis AC F.Z, punctumque quoddam D (a quo
projectx D A, DC, DE, 55 6. ab initio D A continuo decresCanE) F1s. II2-
cum altera (IE Curra D R E, priorem interlecans in P, naturaque Ca-
lis, ut a D utcunque project a recta D R C (QuIX CUIEVAM A F L. PeCeF
In C, CUrYAI D R E iN R) sit perpetuO rectangulum CX DR, _ de-
signaca quadam linea R aequale spatio ADC; tum ductâ D I ad
DF perpendiculari, sIE DY = 2 R; e connectatur YF; hXC
curram D R F. ConingCE.
Nam Cumpto quoris in Curra D K F punCtOR, ducatuE rectADRC.
_ TumPEA DL == DR, duCatuE L R ad D T parallela (secans ipsam
DC in Z). TUM PeF F duCatuF F X ad D P perpendicularis (hXC
VeTO CXTTA CUTVaM A F Z, ad partes Z cadet, quia decrescune proje-
Atx vertus Z; unde P X versuS A intra curram F C A cadet; Cate-
nus Taltem, quatenus huic Proposiro latistaciet). Sit jam primo pun-
ctum C supea F, versus inirium A, ∞ obTD. DF:: RL. L F;
adeoque R L. XD F = T D X L F (∞) = 2 RX LF (a) L 2CDF
= 2 DFZ = EX XD E. CrBORL C EXC LY. EA aurem
punCtU Y exETa CUEVa, quiA DZE DL =DR; ergo magis
punetum R elE exEra CuEVaI.
Sic rurlus punctum C intra punctum Fi. versus Z; ceque rursus.
uei prius, R L XD R = e GDE =I ETrIAnS. FDX = FX XDF.
Cet) eroo punctum R ruxsus extra curram existie. Liguidum est igi-
quod ducta lic DKC; _ HaC D C. DR:: R. P; SuMaturqUe
DI == 2 P; _ connectatur TC; cum ducatur R S ad C Y paralle.
la; reCtA RS CUIVaM D R E tanSeF.
Nam conciviarur curra DOC, per C transiens, talis, ut recta
quacunque DON a D projecta (quae curram DOO secet in O,
CurVam L H F in M, CUIEVaM A G F in N) SIC semper DOX P X.
qualis spatio AD N; erit ideo D MI XR = DO X P; ac proinde
DM. DO:: F. R. unde linea DK E, DOG analOBX CTWNE. Ve
E18, 113.
(a) Hyp.
unde A F, == F. X =  L Y. Fs aNTEM reCTA L Y eXTFA CUITVAI PR.
FOTA, (RAMA CFIAM CXEFA AFCUM L R CUXVX R F. circumduetum tora ja-
tur rectam TF R curram D R E tansere.
Duod si punctum aliud in CurrA DR P deliBRCtUT, PUTA R; pex
xitir