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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 18, page id 797435492:0226
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2is. 8
Dig. c
l. P C 
majore A A B B detrahatur minor circulus concentricus F P P F. F
qua genel collisitur circulorum, e sectorum circularium areas, c
circularibus peripheriis, inteoris auc parcialibus concentricis ac simili
bus, constare tornumero quor radius puneta habet; quarum proinde
calculum incundo circularis arex talis qualis dimensio quam Facillime
reveritur; id quod non est hujustemporis ulterius exponere. Ouin-
etiam supponune lineam quamris rectam, indetinire procensam, uno
manente Axo iplius puncto circa delignatam quamris in alio plano
consticuram lineam, curvam aue e rectis compolicam, revolvi, sic vE
ei nempe linex semper insictat, vel eam quali lambar, aut perstrinsat.
Sic, exempli causa, linea recta AB indetinire procensa, e in ea
finum punetum V; CE per V semper feratur linea AB juxta lineam
quamlibet B C in alio plano collocaram; ita quidem ur aliquod linex
mobilis punctum continuo linex B C intxreat; ex hujusmodi motu
producetur curra Superficies (e planis salrem compolita, quam _
generali ratione, post Archimedem, curram appellare nil vetge
quae quidem li linea directrix tota componatur e detinite magnis rectis
lineis, tiet suporficies prram dalis, e triangulis ad verricem V concur-
rentibus aggresaca; lin circularis fuerit, auc conicarum sectionum
aliqua, Superticies evadet stricte conica; sin alterius generis aliqua
conica lalcem extenso latius lignificatu dicatur; d a quibusdam di-
citur. Cujus quidem superticiei proprietas est, ex ipla generatione
marifesta, quod si per fixum punctum V plano secetur, communis
plani cum ipta sectio erit angulus rectilineus. Ntam si planum ipsam
secans per V linex directrici occurrar in punctis duobus, ut in D, F
(Occurret autem in duobus, alias Superticiem iplam non secaret) ductx
recteVD, V E eruncram in plano secante, quam in curra Super-
ficie; inplano, explani nacura; in Superticie, quia generrix eadem
recta per harum terminos rrantir, ipsilque proinde coincidit. In hu-
julmodi vero motu poliro quod linex recta à puneto fixo V (leu ver-
rice) ad directricem lineam B C ductx lunt inxquales inter le, Paris
liquet lineam. BC non à linca B delineari, vel perambulari, quia
linex inaequales (ut V B, VP, V C) sibi nequeune consruere; ade-
eque punctum. B procrediens supra, vel intra puncta B, F, C cadet.
ut nec eadem inx qualitare suppolita punctum quodris aliud in V B pura
) moru suo lineam deseribet linex directrici B C. Similem (quare
linca V B supponitur indetinire prorensa) at vero Clinea omnes, qua
ab V ad B C duci pollunt (quas Superficiei propositae lacera nuncu
Demus licet) proportionaliter secentur (id quod het à plano per hanc
Supenticiem crajecto ad planum, in quo lica est B C, Parallelo) divi-
tionum