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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 20, page id 797435492:0228
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li R C F. II.
sividarur BC in parres requales, e connectantur latera V D,
V F
non erune Suverticies B VD, DV P, FV C aequales inter se, sed
inscrurabili plerumque ratione; juxta varias ansulorum inclusorum.
ex lacerum inxequalium differentias, insequales; id quod hactenus
illos divexavit _ Tor(it, qui dimeriendae coni scaleni (uperficier ineu–
buerunt. I Fex his consectatur quod poslie hujusmodi circumlario
tacta quadancenus concipi motu quoque cali linex rectae genetricis.
ita ut ejus singula quae que puncta parallelas lata limiles directrici linex
lineas describane, modo tamen concipiatur linea genetrix ubique pro-
portionaliter aut contrahi, vel dilatari secundum omnes sui partes.
Ouomodo nempe (i recta V B ita sensim diduci concipiatur, ut pun-
etum B coram lineam B C perambulet, erium punctum C paraslelo
ad B C mocu delata, lineam C HI ip(I B C. similem describet. Oui-
nimo si consimili pacto curra B C, directo quoad lineam rectam B V
motu licuque semper ad seiplam parallelo concipiatur promoveri, (IC
ut ejus linsula quaque puncta lineas rectas deseribane, lecum omnes
in punctum V concurrentes, hoc est ica uc ipsa per torum suuni pro-
erellum juxta suas omnes partes analogice coneratatur, ad verticem
ulque V: Producentur ex hujusmodimoribus Superticies conicx pror-
sus eadem cum jam proxime cractatis. Verum hujusmodi motus ima
dinarii sune, ee quales rerum nacura respuir. Explicandae tamen
hujusodi Superficierum naturx deservire porsune, e supponi Paltem
ut per divinam potentiam effectibiles. I Ad haec, A linea directrix
in motu proxime memoraro supponatur undique clausa, sic ut fsuram
quamiris comprehendat, Superticies curra progenira cum hac Agura.
ceu base, corpus solidum includet pvramidale, vel conicum (stricte
vel laxe pro dicta figurae natura Tumptum) cujus generalia Cympto
mata Paris e dictis elucescunt. Nempe quod a parallelis ad hujusce
Folidi basin planis abscindentur similes ad verricem superficies, similé(-
que bales incercipientur, et similia corpora Solida progionentur.
Verbodicam, quae de Conis generatim Euclides, Apollonius, aliique
tradiderunt, ea conicis hoc modo factis, servata debita analosia,
convenient, _ simili ferme modo demonstrabuntur convenire. (I
Ve-
rum ulitatissimus apud Mathemarieos corpora progignendi modus est
is qui peculiari nomine Rotario dicitur, _c sic suppolito lineam quam-
vis, aut quamlibet superticiem planam cirea rectam lineam Axam.
eanquam axem, rerolri. Ouomodo ex motu Semiperipheris circu-
laris circa diametrum producitur Spharica Superficies, ex motu se.
nicirculi iplius circa eundem Spbara derornatur; ex motu linex recte
circa lineam ipsi parallelam Superficies Cylindrica; ex motu parallelo-
Grammirectansuli circa lacus unum ipse Cylindrus rectus; ex MOTU CrUXIS
unius