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

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10890 aſſimilantur. unde NK. KF : : AN. NF. ſeu permutando NK.
AN : : KF. NF. erat autem priùs KF. NF : : GF. FA : : CK.
11Fig. 137. CR. eſt igitur NK. AN : : CK. CR. unde (juxta dictum Theo-
rema) conſtat factum.

XIV. Ad conſtructionem iſtam advertentes animum, hujuſmodi
facilè _Conſectaria_ deducetis:

1. Si circulus GNH_refringentem_ contingat ad H; ipſius AH
(perpendicularis utique) refractus in K terminabitur; & aliorum
incidentium refracti ad unas ipſius K partes (ultra nempe vel citra
K reſpectu centri, pro diverſitate caſuum ab ipſius A poſitione reſul-
tantium) cadent.

2. Si dictus ille circulus _refringenti_ non occurrat omninò, _Problema_
conſtructionem reſpuet; nec ullus refractus punctum K permeabit.

3. Si circulus GNH_refringenti_ coincidat (id quod facilè concipi
poteſt, & in aliquo reverà caſu contingit) omnes refracti in punctum
K confluent. ‖ Hæc & alia conſtructionem iſtam conſectantur ſoler-
ter expanſem; quorum ſaltem nonnulla haud abs re fuerit exertiùs
oſtendi; velut hoc imprimìs palmarium.

XV. Si fuerit AB. CR : : BZ. CZ; dico punctum Z eſſe limi-
tem, ultra vel citra quem nullus refractus axim interſecat; ſeu per-
pendicularis ipſius AB refractum in Z terminari.

Nam cujuſvis incidentis AN refractus axi occurrat in K, erit ideò
CK. CR : : NK. NA. ergò quum ſit CR. CZ : : AB. BZ;
erit CK. CR + CR. CZ = NK. NA + AB. BZ.

1. Eſt autem (in prima figura, ubi puncta Z, & K ſunt ad partes
22Fig. 138. centri, vel ubi refracti ad axem directè procurrentes convergunt)
BK& gt; NK, & AB& lt; AN; adeóque BK. AB & gt; NK. NA.
ergò CK. CR + CR. CZ& lt; BK. AB + AB. BZ. hoc eſt
C K. CZ& lt; BK. BZ. vel inversè permutando BK. CK& gt; BZ.
C Z. dividendóque BC. CK& gt; BC. CZ. ergò CK & lt; CZ;
adeóque punctum K ſupra Z exiſtit, verſus centrum; quod erat pro-
poſitum oſtendere.

2. In ſecundâ verò figurá ubi puncta Z, K ad alteras ſupra punctum
33Fig. 139. A partes à centro averſas cadunt) connectatur ſubtenſa BN, & du-
catur AS ad KN parallela; hæc ſecabit angulum BA N, majorem
ipſo BK N, vel BA S; & cùm angulus ABNfit obtuſus, èrit AN
& gt; AS. adeóque KN. AN& lt; KN. AS : : KB. AB. erit etiam hîc
igitur (ut ſupra)C K. CZ& lt; BK. BZ. vel permutatim CK.

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