Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

buit, ſolertia quadantenus eluceſcere videatur, ſeu ratio quædam aſſig-
nari poſſit, cur oculi fundus _Sphær@idicam_ (aut ab hac non multum
abludentem) nacta ſit ſiguram. quia nimirum illa planorum objecto-
rum modicè diſtantium (quibus in diſtinctiùs apprehendendis po-
tiſſimus verſatur uſus) excipiendis ſimulachris eſt accommodatiſſima. Sed hoc παρεισθδκῶς.

V. In reliquis reſractionum caſibus paria fermè contingunt, quos
ideò tacitus præterlabi poſſem; at minuendo veſtro labori, ſeu quò
clariùs & promptiùs de iis conſtet, non gravabor & illos vobis ob
oculos ponere: nempe

Rarioris medii circulo MBN objiciatur recta FAG, cui normalis
CA; sitque punctum Z puncti cujuſvis F, in FG ſumpti, imago
abſoluta; & ZX ad CA perpendicularis; ac CA. CR: : I. R; & RA. CB: : RC. CE; & ipſi RE connexæ occurrat XZ pro-
tracta ad H; eritque rurſus XH = CZ.

25.1.

Fig. 199.

Nam eſt CA. CR: : (FC x MZ. FM x CZ: :) FC x CZ
- FC x CM. FC x CZ- CM x CZ. quare CR x FC x CZ
- CR x FC x CM = CA x FC x CZ - CA x CM x CZ = CA x FC x CZ - FC x CM x CX. ac indè CR x CZ-
CR x CM = CA x CZ - CM x CX. tranſponendóque CR x
CZ - CA x CZ = CR x CM - CX x CM; hoc eſt RX. CZ: : AR. CM: : RC. CE: : RX. XH. quapropter eſt CZ = XH.

VI. Hinc dilucidè rurſus apparet rectæ FA Gimaginem abſolu-
tam (vel ad oculum in centro C ſitum relatam) ſi RC & gt; CE, _el-_
_lipticam_ fore; ſin RC = CE, fore _parabolicam_ (quarum ſectio-
num pars anterior ETE ad convexam circuli refringentis partem
MBN pertinet, poſterior YEEY ad cavam LDL). Quòd ſi
fuerit RC & lt; RE, _ejus image hyperbolica erit_; & quidem _hyperbolæ_
YTY pars ſuperior ETE ad circuli partem NBN referenda eſt; pars autem inferior YEEY unà cum tota hyperbola ζ V ζ ad partes
concavas LDL pertinebit. nempe ſi fuerint rectæ CK æquales ipſi
CE, tota hyperbola ζ V ζ interceptam punctis K rectæ FG portio-
nem referet, ejúſque quod hinc indè protenſum ſupereſt ab ipſa YEEY
repræſentabitur.

25.1.

Fig. 200.

VII. Porrò, quoad omnes hoſce caſus animadvertere licet poſſe
ſectionem eandem conicam innumeris rectis lineis ad diverſos circulos

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