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

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135117 ſuggerens haud aſpernanda. relinquantur igitur ei cætera, mihi
ſuffecerit, quòd veriorem _phænomena{εμ}_ detegendi declarandíque me-
thodum adniſus ſim aliquatenus enucleare. pergamus ad alios caſus,
haud ità pertractatos.

XIX Objiciatur ſpeculo MBND recta FAG, rectæ CA (per
ſpeculi centrum C tranſeunti) perpendicularis; adverto, ſi fuerit ipſa
11Fig. 189. CA major quàm CZ, quadrans diametri BD, quòd rectæ FAG
ad infinitum utrinque protractæ ad totum circulum (ejus ad partes
intelligo concavas ſimul acconvexas) imago abſoluta (quinetiam ima-
go ad oculum in ipſo centro C conſtitutum relata) erit _Ellipſis_. item
ſi CA minor ſit, quàm CZ, quòd ipſius FA G imago abſoluta
(vel dicto modo relata) conſtabit ex hyperbolis oppoſitis; ſi denuò
CA ipſam CZ adæquet (vel FG per ipſum Z tranſeat) quòd ad
parabolam ejuſmodi conſiſtet imago. Sed modum tranſgrederer hæc
jam aggrediens demonſtrare. Expectent igitur. ‖

Lect. XVII.

1. ADea, quæ ſub finitam præcedentem propoſuimus demon-
ſtranda _neceſſariam, alioquin notabilem, Conicarum Sectionum_
_proprietatem_ imprimìs oſtendemus.

Sit triangulum ACE, rectum habens angulum ad C; & inde-
22Fig. 190. finitè protractis lateribus AC, AE, in AC ſumatur quod piam pun-
ctum X, ducatúrque XG ad CE parallela; inſeratur autem angulo
CXG recta CZ æqualis ipſi XG; dico punctum indeterminatum Z ad
ſectionum conicarum aliquam conſiſtere.

II. Nempe primò, ſit angulus A ſemirecto minor (vel AC & gt;
CE) erit punctum Z ad ellipſin, quæ determinatur hoc pacto: An-
guli LCP ſemirecti fiant (ad utramque rectæ CE partem) liquet
igitur rectas CP ipſi AE occurrere, puta ad puncta R, & S. ab

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