Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

Ducatur enim quævis HO; hæc tangenti priùs occurret, puta ad
R. liquet HR majorem eſſe quàm HM; multóq; magìs eſſe HO
& gt; HM,

XI. Hinc _Circulus Centro_ H per M deſcriptus _curvam_ contin-
get.

XII. Etiam inversè, ſi HM minima ſit omnium quæ ab H ad
curvam duci poſſunt, erit HM curvæ perpendicularis.

Nam quoniam HM minima ponitur, circulus centro H, intervallo
quovis HS, majori quàm HM, curvam ſecabit, & proinde tangentem
MT, hanc puta in R. ergò quum ſit HR & gt; HM, non erit angu-
lus HRM rectus. idem de punctis omnibus in recta TM evidens eſt. ergò tangenti perpendicularis non alibi quàm in punctum M cadit.

XIII. Quinetiam ſi recta HM minima ſit omnium quæ ab H
duci poſſunt, eíq; perpendicularis ſit recta TM; hæc curvam tan-
get.

31.1.

Fig. 31.

Nam tangat alia, (ſi fieri poteſt) XM; erit igitur XM ad HM
perpendicularis. Unde pares erunt anguli HMX, HMT; totum
& pars Q: E. A.

XIV. Dico porrò minimæ HM propiorem HN remotiore HO
minorem eſſe.

31.1.

Fig. 32.

Nam ducatur ſubtenſa MN; hæc producta curvam tranſgredietur,
& ipſam HO ſecabit, puta in R. & quoniam Angulus HMR obtu-
ſus eſt (major illo nempe, quem tangens cum HM conſtituit ad M)
erit HNR magìs obtuſus; adeôq; recta HR & gt; HN & magis HO & gt; HN.

XV. Hinc perſpicuum eſt Circulum quemvis Centro H deſcri-
ptum, uno tantùm ad eaſdem puncti M partes puncto curvæ occurrere; nec omnino pluries igitur, quàm in duobus punctis.

XVI. Perpendiculari HM parallelæ, ſint rectæ IN, KO; ha-
rum propior IN remotiore KO rectiùs incidet.

31.1.

Fig. 33.

Nam per N, O ducantur ipſi curvæ perpendiculares EN, FO; hæ
cum ipſa HM intra curvam convenient, puta ad R, & P; ſibi verò
ipſis in Q.

Liquet jam eſſe ang. FOK = ang, FPH & gt; ang. PRQ = ang. NRH = ang ENJ. Cùm ergò ſit ang. FOK major angulo ENJ,
liquet propoſitum.

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