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

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8163

Lect. IX.

I. Q Ualiter in obverſum Speculi circularis convexum finitè di-
ſtans punctum radiat, & ubi loci adparet oculo in recta con-
ſtituto per ipſum radians & ſpeculi centrum trajecta poſtremo con-
niſi demonſtrare; nunc idem quoad aſpectum aliàs ubicunque ſitum
aggredimur expiſcari. quò primum attinet ut rectam inveſtigemus,
in qua conſiſtet Imago; tum ut punctum ejus in iſta recta præciſum
determinemus. & primo quidem negotio ſatisfactum erit hujuſmodi
_Prob@ema_ conficiendo; quod (ſequentium quoque gratiâ) genera-
tim proponimus.

II. _Dato circulo reflectente_ (cujus centrum C) _datiſque binis pun-_
_ctis; ab horum uno recta ducatur, cujus rtflexus per alterum tran-_
_ſeat._

1. Si data puncta (puta A, X) ſint ambo in circuli peripheria,
11Fig. 86. manifeſtum eſt biſecto arcu AX in N, connexiſque ſubtenſis NA,
N X, rectas NA, NX ſibi mutuò reflexas fore; ſeu, junctâ CN,
angulum CNXangulo CNA æquari.

2. Etiam ſi datorum unum (X) in circumferentia ponatur; liquet,
22Fig. 87. connexis AX, CX, factóque angulo CXH = CXA, ſore XA,
XH alterum alterius reflexum.

3. Item ſi data puncta (A, X) æqualiter à centro diſtent; con-
33Fig. 83. nexis rectis AC, XC, biſectóque angulo XCA à recta CN circu-
lum reflectentem interſecante ad N; perſpicuum eſt conjunctas rectas
AN, XN, invicem in ſe reflecti; vel angulum CNXipſi CNA
æquari.

III. 4. Si puncta data (puta jam A, K) ambo exiſtant in recta per
reflectentis centrum tranſeunte (nempe AB KC.)

I. Fiat CK. AC: : CB. T. ac inter CB, & T ſit proportione
44Fig. 8@. media V (unde CBq. Vq: : CB. T: : CK. AC). tum centro A,
intervallo √: : ACq - Vq. deſcribatur circulus

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