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

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8567

IX Adnotabimus tantùm quòd ex _Problematis_ hujuſce natura con-
ftructioneque propoſita ſatìs attendenti conſtabit (utique ſicut in _H@-_
_potheſibus_ antehac tractatis uberiùs eſt declaratum) duorum tantùm
ad eaſdem axis partes incidentium reflexosad unum ſeſe punctum de-
cuſſare. nam aliorum unius (qui ſubinde poteſt dari) vel alterius re-
flexi per ejuſmodi punctum tranſeuntes ad alteris partibus incidentes
pertinebunt. ‖ Ex his quadantenus eluceſcit datis puncti radiantis,
oculíque poſitione deſignari poteſt linea quævis, in qua dicti puncti
ſpecies apparebit; incumbit proximè punctum in ea præciſum deter-
minare, ad quo eadem conſiſtit. eo ſpectat hoc Theoremation.

X. Ab eodem quocunque puncto A manantes duo radii AN, AR
11Fig. 95, 96. in circuli reflectentis peripheria præter illum arcum NR (qui inci-
dentiæ punctis interjacent) intercipiant arcum PS; eorum verò re-
flexi intercipiant arcum π σ; erit arcus π σ æqualis Summæ vel diffe-
rentiæ dupli arcûs NR, & arcûs PS. Nam (1) in prima figura;
eſt PS + SR + RN = PN = N π = π σ + σ R - RN; er-
gò, pares hinc indè SR, & σ R ſubducendo, erit PS + RN =
π σ - RN. proindéque PS + 2 RN = π σ. (2). in altera figura;
erit PS + SR - RN = PN = N π = RN + R σ - σ π. qua-
rè rurſus æquales auferendo SR, R σ manebit PS - RN = RN
- σ π unde tranſponendo erit σ π = 2 RN - PS.

XI. Etiam hoc _Lemmation_ adſcribemus: Biſecetur recta NP in E;
22Fig. 94.& ubivis ſumatur punctum A; erit EA = {PA ±: NA. /2. } Nam
EA = {P N/2} ±: AN = {PN ±: 2 AN / 2} = {PA ±: AN. /2}

XII. Exhinc, ut propoſitum citiùs attingamus, Suppoſito radios
33Fig. 95, 96. A N, AR (quoad caſum præſentem) ſibi quàm proximos incidere,
punctum deſignabimus ad quod ipſorum reflexi N π, R σ concurrunt;
dicimus utique ſi dicti reflexi concurrant ad Z; bifectis ſubtenſis NP,
N π in E, & F; fore FZ. ZN: : EA. NA. ‖ Nam quoniam
arcus NR, PS ex hypotheſi ſunt indefinitè parvi (ſeu minimi) ſe ha-
bebunt ut ſuæ ſubtenſæ; nec non idem de arcubus NR, π σ dici poteſt.
igitur arc. PS. RN : : PS. RN: : PA. RA. (hoc eſt ob RA,
NA nihil, ex eadem hypotheſi, differentes): : PA. NA. ergò,
bis componendo, erit PS + 2 RN. RN: : PA + 2 NA. NA.

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