Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

XIII. Item, dico fore NX (rectioris itidem reflexi concursûs
incidentiæque punctis interjectam partem) minorem quartâ parte
totius N Π. Etenim fiat ang. HR Π = ang. N Π R; quapropter
erit HR = H Π; adeóque 2 H Π = HR + H Π & gt; R Π & gt; N Π. item quoniam ang. RHN = 2 ang. HR Π = ang. XRH; eſt
XH = XR & gt; XN. quum itaque ſit H Π major ſemiſſe totius N Π; & XH major ſemiſſe reſidui NH; liquet totam X Π majorem eſſe
triplâ X N; ſeu totam N Π majorem eſſe quadruplâ N X: Q. E. D.

XIV. Hinc perſpicuum eſt, ſi fuerit NZ reflexi N Π quadrans,
quòd nullus alter hujuſmodi reflexus punctum Z permeabit. Etenim
alterius cujuſvis reflexus permeare dicatur; erit igitur, ſi obliquior
is fuerit, NZ & lt; {1/4} N Π; ſin rectior fuerit, erit NZ & gt; {1/4} N Π (ni-
mirum è proximè demonſtratis hæc conſequuntur) quæ repugnant
hypotheſi.

XV. Quinetiam ipſi N Π propiùs adjacentium occurſus puncto Z vi-
ciniores ſunt, hinc indè. Secent. inquam, radiorum LM, RS reflexi
L μ, R σ ipſam N Π punctis Y, X; iſtæ quidem (rectior) in Y, hic
(obliquior) in X; erit ZY & lt; ZX. Nam connectantur R Π,
L Π; & fiat ang. Π LH = ang. N Π L; ducantúrque rectæ RH,
RY. eſtque RH & gt; LH = H Π; adeóque ang. H Π; R & gt; ang. HR Π; & proinde ang. NHR & lt; 2 ang. H Π R. item YR & gt; YL
= YH; proindéque rurſus ang. NYR & lt; 2 ang. YHR. quare
multo minor eſt ang. NY R quadruplo N Π R eſt autem ang. NXR
quadruplus anguli N Π R; igitur ang. NXR & gt; ang. NYR. pona-
tur jam, ſi fieri poteſt, punctum X ipſis Y, Z interjacere. erit igitur
angulus externus NYR interno NXR major; atqui minor oſtenſus
eſt. quæ repugnant. itaque potiùs eſt ZY & lt; ZX: Q. E. D.

16.1.

Fig. 77.

Ad alteras partes haud abſimilis erit diſcurſus; parco faſtidioſæ re-
petitioni. ‖

XVI. Hinc obiter patet ad eaſdem partes incidentium reflexos ſeſe
priùs (velut ad φ) quàm ipſum N Π decuſſare.

XVII. Quinimò rurſus hinc conſtat ad eaſdem axis partes plures
duobus in uno puncto reflexos non concurrere.

XVIII. Demùm (utaliquando tandem deſtinatum attingamus ſcopum)

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer