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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 77, page id 797435492:0301
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L E C T. X.
LER Pele contingunt. (C) QUaRE CUrVXDTF, R F R se quoque con (1) 2. Led
rins ent. (∞) ergo denique recta F S curram DIF continget.
VIII. Ouod ( rectae D F quamvis aliam constanter candem ad ar-
cus A Fi racionem obrinuerine, itidem delignari porest recta curram
DIFransenS, exhac, e seprima octara Lectionis; erit urique tan-
sens ilta huic L.S Parallela.
IX. Tlinc nedum spiralis circularis, act innumerabilium simili ratione
prosenitarum aliarum currarum. Fangentes deterinantur.
VHL.
Ho SinE Curra GuX PIAMI A EHI, reCta A D (in qua determinatum F18. 108.
punctum D.) rectâ DH politione daca; sic item curra AO B calis,
ut in hac assumpro quocunque puncto (, e per hoc ac D projecti
recta DC F (quae curram A E II secet in F) ductaque G F ad DHI
Paratlela habeant A F, A P altignatam rationem X ad Y; tangat au-
tem recta E Icurram A E. HI; recta desisnetur oportet, qux curram
ACB ad O tangaL.
Fiat recta P V aequalis arcui P A; e concipiatur curra OCO ta
lis, uc projecta quacunque recta DOL (qua curram OGO secet
punctoO, rectam F T in L.) ductaque O ad GF parallela, (IF
VL. A. Q:: X. Y; estque curra CO (e supra monstraris) Hy-
perbola; hanc tansat recta 6S; etiam recta CS curram A G B
continget.
Nam concipiatur altera curra. N O N talis, ut cum hane secer recta:
arbitraria D L IN N, CUrVaM A F HIIn K, rectam TF in L; ductaq.
sic NH ad C. F parallela, (IEVL =)  LI. AR:: Z. X; manise.
cum est. curram NC N utramque curram AC B, _ O C7O tanse.
re. Isecet enim recta. DL curram A F B in L, ducaturque lP ad:
CF parallela; quum ergo sIE V L -)- L. R. AR:: X. Y:: AR.
AP, _C SIE VL. ). LR L AR; CrIEARC. APS vel DR -3
DP: adeoque D N- = DI; unde punctum N intra curvam ACB.
Temper cadet; ac proinde curra NGN Curram ACB Tan.
set; limilique plane discursu curra NONI curram OC.O concin-
BCF. ). Itaque currX AG B, OOO Pele (xequipollenter) tangunt.
Duare cum recta C,S curram OC Oransar; eadem curram A. G. B
quoque continget: Q. F. F.
Sicurra A P. HI sic circuli quadrans, cujus centrum D; erit curra
A C B Ouadratrix communis. Ejus isicur Tangens (una cum omni-
um simili racione genicarum cans ertibus) hoc pacto delixnatur,
Fhujusmodi.