Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

Pro refractione vero: Incidat radius AB medio EF in B; & iſthic
refringatur in B _a_ dico permutatim radium _a_ B regredientem in BA
refringi. Nam per occurſum B ducatur QBP media dirimenti EF
perpendicularis; & in hac utcunque ſumpto puncto P ducatur PG
ad AB protractam perpendicularis, ut & PH ad B _a_; & produca-
tur _a_ BS. Eſt ergo PG ſinus rectus anguli incidentiæ ABQ ad
radium BP; & PH ſinus anguli refracti QBS ad eundem radium
BP. Cùm ìtaque ratio PG ad PH refractionem metiatur è ſuperiori
medio factam in inferius; etiam viciſſim rectarum PH, PG propor-
tio refractionem determinabit ab inferiori medio factam in ſuperius. Unde ſi radius _a_ B jam ponatur incidens; cùm ſint PH, PG recti ſi-
nus anguli incidentiæ PBH, & anguli PBG, liquidum eſt ipſam HB
in BA refringi.

11.1.

Fig. 20.

IV. Angulo incidentiæ majori major competit angulus inflexus. (Angulum inflexum vocito, qui à perpendiculari continetur & in-
flexo; is proinde reſpectivè dicitur angulus reflexus, vel refractus. Angulus autem inflectionis (hoc eſt reflectionis reſpectivè, vel refracti-
onis) appellatur is, qui comprehenditur ab incidente & inflexo; inci-
dentiæ verò, nè quis ſecùs accipiat, apud nos angulus eſt, quem con-
tinent incidens & perpendicularis.) Quod propoſitum ſpectat effatum,
id è poſitis principiis manifeſtè conſectatur. Etenim in reflectione
ipſi anguli reflexi angulis incidentiæ proportionales ſunt; in refracti-
one ſaltem recti ſinus angulorum refractorum ſinubus angulorum in-
cidentiæ proportionantur. Unde liquido conſtat propoſitum: quorſum
verba, quorſum Schemata multiplicem?

V. Cùm incidentes ad ſuperficiem mediam ſeſe decuſſant, iidem
ſeſe inflectionem paſſi decuſſabunt, eodem ordine ſervato, quem directè
progedientes habuiſſent (utique ſic ut perpendiculari poſt inflectionem
propior incedat qui propior antea fuit.)

Hæc propoſitio reverà non differt à præcedente; quò demirer
eam à non nemine principia noſtra uſurpante aliunde compro-
bari.

11.1.

_Herig. Diop. 8_.

VI. Angulo incidentiæ majori major convenit angul@s inflectionis. Quoad refiectionem, res extra dubium evidens eſt; angulus enim refle-
ctionis incidentiæ majori conveniens eum planè continet, qui minori
incidentiæ reſpondet. Pro refractione vero: ſit recta QBP refrin-
genti perpendicularis; incidant autem radii ABG, DBH (ſcilicet AB

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