Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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141123 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
11Fig. 199. 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.

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
22Fig. 200. 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.

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

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