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

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III. _Superſiciem planam media dirimentem (aquam ſiplacet ac aërem)_
11Fig. 182. repræſentet recta PQ, & aquæ inſit recta FP ad PQ perpen-
dicularis. ſiat autem FP. XP : : R. I; erit X P imago abſoluta rectæ
FP; continet illa ſcilicet omnes locos punctorum, quæ in FP, oculo
apparentes in ipſa FP ſito. verùm ſi ponatur oculus uſpiam extra FP,
velut ad O, ei tota FP citra XP apparebit. tranſeat videlicet ali-
cujus radii FM refractus per O, & protrahatur OM, ut occurrat ipſi
FP in K. eſt ergò (ſecundum præmonſtrata) punctum Kinter X, &
P. itidem (è prius oſtenſis) puncti F imago quæ in refracto OMK,
ad oculum O relata, inter K, & M cadit, veluti puta ad φ. ſimili ratione
cujuſvis alterius in ipſa FP accepti puncti, ceu R, imago (cogita ρ)
citra rectam XP, verſus oculum, jacet. totius itaque rectæ FP imago
talis eſt, qualem curva linea φρ P refert. quòd ſi P F infinitè protra-
hatur, ejus totius imago P ρρ verſus aſymptoton OBA, ad PF paralle-
lam, accedens excurrit.

IV. _Delineatur autem curva P ρ φ hoc modo._ ab O ducatur utcun-
que recta OMK ſecans rectam PQ in M; & (poſito fore S = √ Rq
- Iq) ſit PH = {Sq x PM cub/Iq x FPq}; atque per H ducatur H φ ad PR
parallela, ipſi OK occurrens in φ; erit φ in dicta linea; nempe, ſi
OMK ipſius M F refractus concipiatur, erit punctum φ ipſius F ima-
go. eodem modo reliqua lineæ P ρ ρ puncta deſignantur.

V. Quinetiam adſumptâ rectâ FG ad PQ parallelâ, ductâque
22Fig. 182. GQ ad FP (vel ABO): parallelâ; item per X ductà X α Y ad PQ
parallelâ, erit quidem recta X α Y rectæ FAG imago abſoluta;
verùm ejus imago ad oculum O relata citra rectam XY tota jacet, eám-
que curva φαγ repræſentat, admodum jamjam præſcriptum puncta-
tim delineabilis. itaque compoſitæ lineæ PFGQ, circa axem OBA
rotatæ, imago fornicem referet arcuatam. id quod experiri vos velim
vaſculi cylindrici aquâ repleti ſuperficiem inſpectando.

VI. Quòd ſirecta viſibilis FG ad PQ inclinata ſit, cum ea conve-
33Fig. 183. niens in V; & connectatur XV, erit rurſus XY ipſius FG imago ab-
ſoluta; relatam verò curva φαγ repræſentat.

VII. Quòd ſi viciſſim _oculus O in aqua ponatur conſtitutus,_ &
44Fig. 184. ab indèreſpiciatur recta P F in aëre poſita, fiátque rurſus PF. PX :

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