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

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310117 ADLK. item patet _ſegmentum_ ADB unà cum _rectangulo_ ADZR
majus eſſe _figurâ circumſcriptâ_ (etenim _rectangulum_ ADZR_rectan-_
_gulis_ RH, PG, OF, NE, MZ æ quatur, proindéque majus eſt _irili-_
_neis_ AXR, XXP, XXO, XXN, XBM). ergò _ſegmentum_ ADB
11Fig. 176, unà cum _rectangulo_ ADLK multo majus eſt _figurâ circumſcriptâ_;
hoc eſt, _ſpatium_ S majus eſt _figurâ circumſcriptâ_, contra _Hypotbeſin._

VII. Item, ſi ponatur _figura inſcripta_ HXGXFXEXZDH minor
_ſpatio quodam_ S; dico _ſegmentum_ ADB non eſſe majus quàm S.

Nam ſi majus eſſe velis, eſto rurſum _exceſſus par rectangulo_ ADLK;
quod utique (ſicut prius) majus erit _rectangulo_ ADZR. Eſt autem
_ſegmentum_ ADB, dempto _rectangulo_ ADZR, minus figurâ inſcriptâ.
ergò ſegmentum ADB, dempro rectangulo ADLK, multo minus fit
inſcriptâ; hoc eſt _ſpatium_ S minus eſt inſcriptâ figurâ, contra
_Hypotbeſin._

VIII. Hinc, ſi _ſp@tium_ quodcunque fuerit, (puta S) cui circumſcripta
figura æquetur _ſigurœ_ ADBMNOPRA; nec non cui _inſcripta figura_
_æquetur figuræ_ HGFEZDH; palàm eſt _ſpatium_ iſtud S _ſegmento_
ADB exæquari.

Nam (utì mox oſtenſum) hoc illo majus eſſe nequit, aut mi-
nus.

Poterunt autem hæc ad _alios circumſcriptionis ac inſcriptionis modos_
accomodari. ſuffecerit innuiſſe.

Conicorum Superſicies dimetiendi Metbodus.

S It _curva_ quæpiam AMB, cujus _Axis_ AD, & in hoc ſignatum
22Fig. 177. punctum C; ad ipſum vero ordinata recta BD. à puncto quo-
piam M in curva ſumpto ducatur recta ME curvam tangens, & à C
demittatur CGad ME perpendicularis; ſit item determinata recta
CV ad planam DAB recta, & connectatur VG(erit VG _ipſi_ MG
perpendicularis; nam ſi ducatur CHad GM parallela, liquet CH
plano GVG rectam eſſe, adeoque GMeidem recta erit) Porrò ſit
linea RStalis, ut ductâ rectâ MIX ad AD parallelâ (quæ ſecet

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