Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

arc {NR & + -; : πσ/2} = NX; item eſt {NZ & + -; : Z π/2} = GZ. eri@ ergòarc
NR. NX : : NZ. GZ. quapropter erit (juxta præcedentem)
NZ. GZ = NG. NE + CE. CG.

19.1.

Fig. 124.

VIII. Porrò liquet punctum Z eſſe locum imaginis, quem expe-
timus, oculo conſpicuæ in recta N π conſtituto; utpote circa quod
viciniorum ipſi NP radiorum refracti ipſam N π interſecant; qua de
re multoties egimus, ut pigeat eò plura βαττλγ{εĩ}ν.

IX. Facilè verò, Secundum _Theorema pramiſſum_, deſignatur
punctum Z. Ducatur nempe CG ad refractum NK perpendicula-
ris; & ad connexam CN ducatur perpendicularis GV; & per V
ducatur VZ ad CK parallela, ſecans ipſam NK in Z. factum erit. Nam, connexâ GE, liquet angulos GEC, GNC(circumducti
nempe per N, E, G, C circuli ſubtenfæ GE inſiſtentes ambos) æqua-
ri; hoc eſt angulos GEC, VGCæquari. quapropter (utrique
rectum adjiciendo) toti NEG, ZGVæquantur. item alterni
GNE, VZGæquantur. ergò triangula GN E, VZGſimilia ſunt,
unde NG. NE : : ZV. ZG. itaque. CE. CG + NG. NE =
CE. CG + ZV. ZG. verùm (ob refractionem) eſt NK. KC
: : I. R : : CE. CG; hoc eſt NZ. ZV : : CE. CG. eſt igitur
CE. CG + NG. NE = NZ. ZV + ZV. ZG; hoc eſt CE. CG + NG. NE = NZ. ZG. ergò punctum Z conditionem
obtinet, imaginis loco congruentem, è mox oſtenſis. adeò liquet
propoſitum.

19.1.

Fig. 125.

X. Quin ſubnotamus rectam NK ad punctum Z ità dividi, ut ſit
NZ. ZK : : NGq. CGq. Etenim eſt NZ. ZK : : NV. VC
: : NVq. VGq : : NGq. CGq.

XI. Subjiciam & hoc è dictis conſectarium _Theorema:_

Fiat √ 3 Rq. √ Iq - Rq : : CB. CQ; ductáque QN ad
CB perpendicularis circumferentiæ occurrat ad N; radii verò MN
ad CB paralleli refractus ſit NK, circuli peripheriæ denuò occur-
rens in Z; dico punctum Z eſſe imaginem, qualem mox definivimus,
oculo conſpicuam in ipſa NK ſito.

19.1.

Fig. 126.

Nam (ductis CE ad MN, & CG ad NZ perpendicularibus,
ac junctâ CN) ob 3 Rq. Iq - Rq : : CNq. NEq. hoc eſt
3 CGq. CEq - CGq : : CN q. NE q; erit dividendo 4 CG q

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