Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

1. Si fuerit I & gt; R; fiat I-R. R: : BC. CZ; quare compo-
nendo erit I. R: : BZ. CZ. ergò factum.

19.1.

Fig. 105.

2. Sin I & lt; R; fiat R - I. I : : BC. BZ. ergò rurſus compo-
nendo R. I: : CZ. BZ. vel inversè, I. R : : BZ. CZ.

XXV. Fiat jam CA. AB: : CZ. BZ; Dico punctum Z eſſe
metam, citra quam (reſpectu centri C) nullus reflexus axem de-
cuſſabit; hoc eſt præmiſſis inſiſtendo, fore CK & gt; CZ.

Nam ducatur NT circulum contingens ad N. erit ergo NK. NA
: : KT. AT & lt; BK. AB. quare NK. NA + AB. BZ & lt; BK. AB + AB. BZ = BK. BZ. eſt verò NK. NA : : CK. CA. & AB. BZ: : CA. CZ. ergò CK. CA + CA. CZ & lt; BK. BZ. hoc eſt CK. CZ& lt; BK. BZ. vel permutando CK. BK & lt; CZ. BZ. unde dividendo CB. BK & lt; CB. BZ. adeóque BK& gt; BZ. unde liquet propoſitum.

XXVI. Exhinc (ut in caſibus antè pertractatis) conſectatur ejuſ-
modi punctum Z eſſe locum ipſiſſimum imaginis punctum A exhiben-
tis oculo, puta O, in axe CA conſtituto; patétque quàm longè paſſim
ab Opticis; nominatim à noviſſimis _Stevino, Hobbio, Fabriog_ in eo
aſſignando loco aberratur; quorum ex ſententia verſatur is ad pun-
ctum (puta Q) tanto ſemotum à vertice B intervallo, quanto radi-
ans A ab ipſo B diſtat. id quod præterquam quòd nullâ veriſimili rati-
one nititur (imò rationi prorſus adverſatur; cùm nullus omnino
radius oculum ingrediatur tanquam à puncto Q proveniens) experi-
entiâ facilimè refutatur. Nam ſi tanquam circa punctum A accenſa
candela ſpeculo cavo GB γ exponatur, oculo velut ad O ſito longè
majori diſtans intervallo conſpicietur, quàm ipſo BQ, quod ipſam
AB exæquat. quinimò tantillo verſus centrum illum adducendo non
æquali diſtantiâ, ſed admodum majori videbitur elongari; tantâ
circiter ad ſenſum, probabilémque conjecturam; quantam proportio
requirit à nobis præſtituta. quo circà diſcurſus noſter experientiæ
ſuffragio conſtabilitur.

XXVII. Quod demum attinet ad locum imaginis reſpectu visûs
extra radiationis axem poſiti; determinatur is eodem ac in caſibus
antecedaneis modo; biſecando ſcilicet ipſas NP, N @ punctis E, F; faciendóque EA. AN: : FZ. ZN. Adnotandum ſaltem in recti-
oribus reflexis imaginem extra circulum conſiſtere; ſed in obliquio@i-
bus intra illum, nempe ſi fuerit AE & gt; AN punctum Z ultra axem

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