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

Table of contents

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[31.] Lect. IV.
Page: 222 (29)
[32.] Lect. VII.
Page: 249 (56)
[33.] Lect. VIII.
Page: 256 (63)
[34.] Lect. IX.
Page: 263 (70)
[35.] Lect. X.
Page: 268 (75)
[36.] Exemp. I.
Page: 274 (81)
[37.] _Exemp_. II.
Page: 275 (82)
[38.] _Exemp_. III
Page: 275 (82)
[39.] Exemp. IV.
Page: 276 (83)
[40.] Eæemp. V.
Page: 277 (84)
[41.] Lect. XI.
Page: 278 (85)
[42.] APPENDICUL A.
Page: 287 (94)
[43.] Lect. XII.
Page: 298 (105)
[44.] APPENDICULA 1.
Page: 303 (110)
[45.] Præparatio Communis.
Page: 303 (110)
[46.] APPENDICULA 2.
Page: 308 (115)
[47.] Conicorum Superſicies dimetiendi Metbodus.
Page: 310 (117)
[48.] Exemplum.
Page: 311 (118)
[49.] Prop. 1.
Page: 312 (119)
[50.] Prop. 2.
Page: 312 (119)
[51.] Prop. 3.
Page: 313 (120)
[52.] Prop. 4.
Page: 313 (120)
[53.] APPENDICULA 3.
Page: 314 (121)
[54.] Problema I.
Page: 314 (121)
[55.] Exemp. I.
Page: 314 (121)
[56.] Exemp. II.
Page: 315 (122)
[57.] Probl. II.
Page: 315 (122)
[58.] Exemp. I.
Page: 315 (122)
[59.] _Exemp_. II.
Page: 316 (123)
[60.] _Probl_. III.
Page: 316 (123)
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page |< < (117) of 393 > >|
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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