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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 123, page id 797435492:0199
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L B C F. XVIII.
buie, solertia quadanrenus elucescere rideatur, seu ratio quaedam astie
nari possic, cur oculi fundus Sphaero dieam (aut ali hac non mulcuim
abludentem) nacta sic figuram. quia nimirum illa planorum objecto.
rum modice distancium (quibus in distinctius apprehendendis po.
tissimus versatur ulus) excipiendis simulachris est accommodatiltima.
Sed hoc ra seosto5..
V. In reliquis refractionum casibus paria FerME CONLInGUNE, quos
ideo tacitus praeterlabi possem; at minuendo restro labori, seu quo
clarius e promptius de iis constet, non grarabor _ illos robis ob
oculos ponere: nempe
Rarioris medii circulo M B N objiciacur recta F A C, cuinormalis Fig. 299.
CA; sicque punctum Z. puncti cujulris F, in PC sumpri, imago
absoluta; _ Z X ad C A perpendicularis: ac C A. CR: : I. R;
_R A. CB:: RC. C F; BE iPLI R F COMIIEXX OCCUTRAE ZZ prO-
tracta ad FI; exitque ruxlus X HI =C L.
Nam eA C A. C R:: (E C XMZ. FM K CZ::) FC XCZ
F C X C,M. FC X CZ -CM X C Z. QuarEC R X FC XC Z
CR X FC X CM = C AXFCXCL = CAXCMXCZ
=CAZECKCZ = FCXCMXCX. ac inde CR XCZ.
CRXCM = CA XCZ =CM X C X. transponendoque C R X
C7 = C AXCZ = CRXCM = CXRCM; hoc est RX.
C2:: AR. CM:: RC. CP:: RX. XH. quaproprer est C Z
XFI.
VI. Hlinc dilucide rursus apparet rectae F A C imaginem abColu.
tam (vel ad oculum in centro C licum relatam) (I R CE CF, el
sipticam Fore; sin RC = C F, Fore parabolicam (quarum lcctio-
num pars anterior E. P E ad convexam circuli retringentis parrem FIB. 200.
MBHI percinct, posterior Y FF Y ad caram L DL). Ouod s
fuerie R C = QR F, ejusimago hyperbolicaerit; e quidem hyperbola
YTY pars superior P T F ad circuli partem NB I reterenda est;
pars aurem interior Y F P Y una cum cora hyperbola 5V C ad partes
concaras L DL perrinebic. nempe (i Tuerint rectx CR aequales ipsi
CE, tota hyperbola CV e incerceptam punctis R rectae FC porrio-
nemreteret, ejusque quod hine inde procentum superest ab ipla YL F 
repraesentabitur.
VII. Porro, quoad omnes hoice cdius alaureeet poite
sectionem eandem conicam innumeris rectis lineis ad dirersos circulos
R 2
C0B.