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

Si fieri poteſt, cadat pars NFM; ità ſcilicet ut curva AFB cur-
vam AEB interſecet punctis M, N; his autem interjecta concipiatur
indeterminatè ordinata EFG; ſint verò lineæ LXK, RYQ tales,
utductis rectis EO, FP ad ipſas ES, FT perpendicularibus, protra-
ctâque rectâ EG, ut hæc dictas lineas LK, QR ſecet punctis X, Y;
ſit GX = GO, & GY = GP. Jam ex oſtenſis patet eſſe _ſpatium_
IHKL = {HMq - INq/2} = ſpat. IHQR; adeóq; ſpat. IHKL, IHQR
æquari. Verùm ob GE. GO (GX): : SG; GE. & lt; SG. GF & lt; TG. GF: :
GF. GP (GY) & lt; GE. GY; eſt GX & gt; GY; adeòque (cùm
hoc ubique ſimiliter contingat) ſpatium IHKL majus ſpatio IHQR;
quod repugnat oſtenſo. itaque liquet Propoſitum.

V. _Circulum_ AFB, cujus _Centrum_ C, tangant duæ rectæ BT, E S
22Fig. 136. _Diametro_ CA occurrentes punctis T, S; & ad CA perpendiculares
ſint rectæ BD, EP; ſit autem AD major quàm AP; erit TD. AD
& gt; SP. AP.

Nam eſt CT. CA: : CA. CD. Ideoque CT - CA. CA -
CD: : CT. CA; hoc eſt TA. AD: : CT. CA. Simili ratione conſtabit
eſſe SA. AP: : CS. CA. Eſt autem CT. CA & gt; CS. CA.
quare TA, AD & gt; SA. AP. vel componendo TD. AD & gt; SP.
AP.