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._
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.
_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._
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.
figura æquetur _ſigurœ_ ADBMNOPRA; nec non cui _inſcripta figura_
_æquetur figuræ_ HGFEZDH; palàm eſt _ſpatium_ iſtud S _ſegmento_
ADB exæquari.
Poterunt autem hæc ad _alios circumſcriptionis ac inſcriptionis modos_
accomodari. ſuffecerit innuiſſe.
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
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