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

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XVII. Si à puncto quopiam Hin perpendiculari HM aſſumpto
ducantur ad curvam rectæ HN, HO; harum propior HN, remoti-
ore HO rectiùs incidet.

Nam ducantur EN, FO curvæ perpendiculares, & IN, KO ad
11Fig. 34. ipſam HM parallelæ. Eſt igitur ang. FOK & gt; ang. ENI. Item
ang. OHM & gt; ang. NHM. hoc eſt ang. KOH & gt; ang. INH.
quare ang. FOK + KOH & gt; ang ENI + INH. hoc eſt ang.
FOH & gt; ang. ENH. Unde conſtat Propoſitum.

XVIII. Hinc patet à perpendiculari progrediendo, (ab uno
nempe puncto H) iucidentium _obliquitatem_ creſcere, donec ad illam
devenitur, quæ _curvam_ tangit, omnium obliquiſſima.

XIX. Porrò ſi introrſum jam ſumatur punctum H, & ab eo in-
22Fig. 35. cidens HM ſit omnium curvæ incidentium minima; erit HM _curvæ_
perpendicularis, ſeu tangenti MT.

Nam dicaliam MR tangenti perpendicularem eſſe. ergò HR & lt;
33_Apoll. V._ 32. HM. & magìs HO & lt; HM. quare HM non eſt minima contra
_Hypotheſin_.

XX. Item ſi recta HM ſit omnium ab H curvæ incidentium _maxima_,
44_Apoll. V._ 29. erit HM curvæ perpendicularis.

Nam Circulus Centro H per M deſcriptus extra curvam totus ca-
55Fig. 36. det. ergò ſi recta MT Circulum tangat, hæc magìs extra curvam
cadet, eámq; proinde continget. Eſt autem ang. HMT rectus. er-
gò liquet.

XXI. Hinc ſi MT ſit minimæ vel maximæ HM perpendicularis;
66_Apoll. V._ 30, 39, hæc _curvam_ tanget.

Nam ſi dicatur alia MX tangere; erit ideò ang. XMH rectus, &
par angulo TMH: Q. E. A.

XXII. Exhinc ſi recta YM non ſit curvæ perpendicularis; in ea
nulla ſumi poteſt _maxima_, vel _minima._

Nam ſi ſumi poſſet, eſſet ex eo ipſo YM curvæ perpendicularis
77_Apoll. V._ 31, 47. contra _Hypotbeſin_.

XXIII. Si HM ſit incidentium minima, & intra ipſam ſumatur
88_Apoll. V._ 30. punctum quodpiam I; erit etiam IM minima.

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