Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

ellipſin jacent. Nam punctum K inter F & Z; ac punctum φ inter
O, & K; nec non punctum L inter G, & Y; atque punctum γ in-
ter O, & L cadunt. imaginis itaque φαγ figura ad ellipticam accedit; eâ tamen aliquanto planior & compreſſior. non diſſimili ratione quo-
ad imagines ad concava factas, & quoad cæteros caſus inſtituetur
judicium. tædii plenum eſſet omnia ſingillatim percenſere. quinetiam
ê præmiſſis luculentè conſtat quo pacto linea φαγ præcisè deſcribatur,
punctatim utique. circa refractiones paria veniunt præſtanda; poſt-
quam tamen paullùm reſpiravero; nunc enim verbo quidem pauca,
rei qualitatem, ſtudiúmque demonſtrandis iſtis impenſum reſpectan-
do, ſatìs fortaſſe multa videor tradidiſſe. ‖

24.1.

Fig. 196.

25. Lect. XVIII.

I. P_Ropoſitum eſt jam nobis rectæ lineæ ex refractione prognatas. ad_
_circulum imagines aeſignare_; nempe primùm abſolutas; quorſum hoc ſpectat I [?] heorema:

In circulum (e. g. medii denſioris) refractivum MBND radiet
recta FAG; huic verò perpendicularis ſit recta CA (circuli cen-
trum C permeans) tum in recta FG ſumpto liberè puncto F ducatur
recta FC; & in hac ſit punctum Z limes (qualem anteà fiximus)
radiationis à puncto F; ſit autem ZX ad AC normalis. porrò fiat
CA. CR : : I. R; & AR. CB : : CR. CE (ponatur autem
CE ad XZ parallela) tum connexa RE cum ipſa XZ conveniat in
H. dico fore XH = CZ.

25.1.

Fig. 197.

Nam (è præmonſtratis) eſt FC x MZ. FM x CZ : : I. R: :
CA. CR. hoceſt FC x CM + FC x CZ. FC x CZ - CM
x CZ : : CA. CR. quare (ducendo in ſe extrema, mediáque)
eſt FC x CM x CR + FC x CZ x CR = FC x CZ x CA -
CM x CZ x CA = FC x CZ x CA - CM x FC x CX (quoniam ſcilicet eſt

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