Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

ctum. His utcunque majoris evidentiæ cauſâ, prælibatis, ad corolla-
ria quæ diximus expromenda nos conferemus è veſtigio.

II. Imprimis autem (poſthac quidem in decurſu, quoad plures ſibi
parallelos, aut ab eodem puncto divergentes (velin idem convergen-
tes) & huic vel illi ſingulari, quæ tractanda veniet, ſuperficiei inciden-
tes (radios, ſingularia quotvis inflexos deſignandi compendia, radia-
tionibus organicè examinandis profutura, tradituri) generales nunc
aliquos incidenti cuivis propoſito competentem inflexum aſſignandi
modos proponemus; quorum adhiberi poſſit, qui rei natæ videbitur
accommodatior. Pro reflectione. Incidat radius AB ad B; Et per
B ducatur QB reflectenti perpendicularis; & fiat ang. _a_ BQ = ang. ABQ, vel per B ducta ſit EF reflectentem tangens; & fiat ang. a BF = ang. ABE; liquetque factum eſſe, modo utrovis, quod
requirebatur, Pro refractione vero; ducatur QB refringenti per-
pendicularis, & ſuper diametrum (in hac liberè ſumptam) QB de-
ſcribatur ſemicirculus, incidentem AB ſecans in R; tum adjunctâ
QR, factóque I. R : : QR. T (terminis autem I, R hìc & dehinc
perpetuò proportio refractiones metiens indignitatur) circulo QRB
adaptetur QS ipſam T exæquans; erit connexa SB protracta nempe)
incidentis AB refracta. ? Vel: perincidentiæ punctum B ducatur EF
refringentem contingens; & in hac utcunque ſumpta BK ſit circuli
diameter, incidentem AB ſecantis ad R; & fiat I. R: : BR. T; & adaptetur BS = T; erit SB _a_ ipſius AB refractus: Vel demum: In ipſa AB ſumptâ utcunque diametro RB, ſuper hac deſcriptus cir-
culus ſecet perpendicularem QB ad Q; vel tangentem EF in K; fiátque I. R : : BK. T. & adaptetur QS = T; erit rurſus SB _a_ inci-
dentis AB refractus. quorum ratio è poſitis inflectionum legibus ad-
modum eſt manifeſta. verba piget impendere.

11.1.

Fig. 16.
Fig. 17, 18,
19.

III. Radii cujuſvis incidentis inflexus inflexi viciſſim incidens
evadet.

Hoc plerique, diverſè paullò prolatum, accipiunt, aut poſtulant. è præmiſtis autem facillimè colligitur. Idque potius methodi gratiâ
(ſicut & nonnulla quæ ſequentur) quàm quia res meretur, oſtende-
mus. Proreflectione; Radius AB ſpeculo EF impingens reflectatur
in B _a_; dico radium B _a_ permutatim in BA reflecti. Nam quoniam
AB incidens reflectitur in B _a_, erit ang. _a_ BF æ qualis angulo ABE. Poſito jam _a_ B incidere, etiam angulus quem facit ejus reflexus cum
BE æquabitur angulo _a_ BF; proinde non alius erit ab ipſo ABE
quare BA ipſius _a_ B reflexus erit.

11.1.

_Albaz_. VII. 4.
_Herig. Catop_.
_Axiom._ 2.
Fig. 1, 16.
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