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

[31.] Lect. IV.

Page: 222 (29)

[32.] Lect. VII.

[33.] Lect. VIII.

[34.] Lect. IX.

[35.] Lect. X.

[36.] Exemp. I.

[37.] _Exemp_. II.

[38.] _Exemp_. III

[39.] Exemp. IV.

[40.] Eæemp. V.

[41.] Lect. XI.

[42.] APPENDICUL A.

[43.] Lect. XII.

[44.] APPENDICULA 1.

[45.] Præparatio Communis.

Page: 303 (110)

[46.] APPENDICULA 2.

Page: 308 (115)

[47.] Conicorum Superſicies dimetiendi Metbodus.

[48.] Exemplum.

[49.] Prop. 1.

[50.] Prop. 2.

[51.] Prop. 3.

[52.] Prop. 4.

[53.] APPENDICULA 3.

[54.] Problema I.

[55.] Exemp. I.

[56.] Exemp. II.

[57.] Probl. II.

[58.] Exemp. I.

[59.] _Exemp_. II.

[60.] _Probl_. III.

297104 AEG æquatur _Circulari ſegmento_ ADB demonſtrationem, ne longiùs
evager, obmittam.

XXXIV. Sint duo _circuli_ AIMG, AKNH ſeſe contingentes ad A;
11Fig. 154. communique diametro AHG, utcunque perpendicularis ducatur recta
DN M: habebit_ſegmentum_ AIMD ad _ſegmentum_ AKND mino-
rem rationem, quam recta DM ad rectam DN.

Nam ſit AR ad AG perpendicularis, ac ipſi AH æqualis; &
connectatur HR, cui occurrat recta MD in X; ducatúrque recta
GXS; tum ad axem AG _parametrum_ AS per N deſcripta con-
cipiatur _Ellipſis_ ALNG; hæc (utì ſatis manifeſtum) intra arcum
AKN tota cadet. Eſt autem ſegm. AIMD. ſegm. ALND: :
DM. DN. ergo ſegm. AI MD. ſegm. AKND & lt; DM. DN.

XXXV. Sit Ellipſis YFZT, cujus axes conjugati YZ, FT; ſit item
recta DC axi majori YZ parallela; & per D, F, C tranſeat circulus
22Fig + 154. DFCV centrum habens K, in ellipſis axe minore FT ſitum; dico
circuli partem DOFPC intra ellipſis partem DMFNC jacere.

Nam ſit FI ad FV perpendicularis, & in hac ſumatur FS = FV; &
connectatur VS, cui DC producta occurrat in X; & connexa TX
ipſi FI occurat in R. & cum ſit GDq = FG x GV = FG x GX;
liquet ipſam FR eſſe ellipſis, axi FT congruam, parametrum; unde
conſtat Propoſitum.

XXXVI. Sit circuli, cujus centrum L, ſegmentum DEC, & ſumpto
33Fig 155. in ejus axe GE puncto quopiam F, ſit curva DMFC talis, ut ductâ
utcunque rectâ RMS ad GE parallelâ, ſit RS. RM: : GE. GF;
erit DMFC ellipſis, hoc modo determinata: Fiat EG. FG: : GL.
GH; & per H erigatur YHZ ad DC parallela, ſitque HY par ipſi LE;
erunt HY, HF ellipſis ſemiaxes.

Demonſtratum habetur à _Greg. à S. Vincentio_, L. IV. Prop. 154.
_Corol._ Hinc ſegm. DEC. DMFC: : EG. FG.

XXXVII. Sint duæ circulorum portiones DEC, DOFC, quarum
communis ſubtenſa DC, & axis GFE; portio major DEC ad portio-
nem DOFC majorem rationem habet eâ, quam habet axis GE ad
axem GF.

Nam ſint L circuli DSEC, & K circuli DOFC centra; & fiat EG.
FG: : GL. GH; & fiat YHZ ad HF perpendicularis & ſit HY æ-
qualis ipſi LE; tum ſemiaxibus HY, HF deſcripta concipiatur ellipſis
YDMFCZ; è mox prædictis liquet ellipſin DMFC circulo DOFC
circumduci. Eſt autem circulare ſegmentum DEC ad ſegmentum el-
lipticum DMFC, ut GE ad GF; quare ſegm DEC ad ſegm circula-
re DOFC. rationem habet majorem, quàm GE ad GF: Quod. E. D.

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