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

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4123 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
11Fig. 16.
Fig. 17, 18,
19. 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.

III. Radii cujuſvis incidentis inflexus inflexi viciſſim incidens
evadet.

Hoc plerique, diverſè paullò prolatum, accipiunt, aut poſtulant.
22_Albaz_. VII. 4.
_Herig. Catop_.
_Axiom._ 2. 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
33Fig. 1, 16. 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.

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Scan	Original
101	83
102	84
103	85
104	86
105	87
106	88
107	89
108	90
109	91
110	92
111	93
112	94
113	95
114	96
115	97
116	98
117	99
118	100
119	101
120	102
121	103
122	104
123	105
124	106
125	107
126	108
127	109
128	110
129	111
130	112

Scan	Original
101	83
102	84
103	85
104	86
105	87
106	88
107	89
108	90
109	91
110	92
111	93
112	94
113	95
114	96
115	97
116	98
117	99
118	100
119	101
120	102
121	103
122	104
123	105
124	106
125	107
126	108
127	109
128	110
129	111
130	112

Scan	Original
101	83
102	84
103	85
104	86
105	87
106	88
107	89
108	90
109	91
110	92
111	93
112	94
113	95
114	96
115	97
116	98
117	99
118	100
119	101
120	102
121	103
122	104
123	105
124	106
125	107
126	108
127	109
128	110
129	111
130	112