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

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_Theor_. IV.

Quod ſi ponatur _m_ x TL = _n_ x arc BL , erit GL {_n_/} x BL {_m_/}
maximum, ſeu majus quàm γ λ {_n_/} x B λ {_m_/}.

_Theor_. V.

Si fuerit TG x GL = DG LB, erit DG LB x GL maxi-
mum, ſeu majus quàm D γ λ B x γ λ.

_Theor_. VI.

Sin TG x GL = 2 DG LB, erit GL x √ DG LB maxi-
mum, ſeu majus quàm γ λ x √ D γ λ B.

Haud difficili negotio, cum hæc demonſtrantur, tum ejuſmodi
complura deprehenduntur.

Ad illa verò ſuccinctius comprobanda deſervire poſſunt bujuſmodi
Tbeoremata.

Sint duæ curvæ AG B, DH C quarum communis axis AD ,
11Fig. 225. ſed ordinatæ inverſo ſitu increſcant ab A ad DB , decreſcant à D ad
AC ; ad ordinatæ verò communis GE H terminos, recta GS cur-
vam AG B, & recta HT curvam DH C contingant.

I. Si recta HT rectæ GS parallela ſit, erit GE H maxima or-
dinatarum in continuum jacentium ſumma.

Nam utcunque ducta OK FL P ad GE H parallela (quæ Li-
neas ſecet ut cernis) erit GH = QP & gt; KL .

Not. Verum hoc, ſi curvarum partes concavæ axi obverſæ jaceant,
aliàs GE H erit minima.

II. Si ES = ET, erit rectangulum ex EG , EH maximum:
Nam ob SE. SF : : EG. FO , & TE. TF : : EH. FP ; erit
SE x TE. SF x TF : : EG x EH. FO x FP, itaque cum ſit
SE x TE & gt; SF x TF, erit EG x EH & gt; FO x FP.

FINIS.

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