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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140122 CZ. FC : : CX. CA; adeóque CZ x CA = FC x CX). qua-
propter (elidendo FC) eſt CM x CR + CZ x CR = CZ x
CA - CM x CX; tranſponendóque CM x CR + CM x
CX = CZ x CA - CZ x CR. hoc eſt CM x RX = CZ x
AR, quare (ad analogiſmum redigendo) eſt AR. CM : : RX.
CZ. hoc eſt CR. CE : : RX. CZ. hoc eſt RX. XH : : RX.
CZ; unde XH = CZ : Quod E. D.
II. Exhinc (& ex iis quæ circa _ſectiones conicas_ nuperrimè ſunt
oſtenſa) liquido conſectatur, ſi CR major fuerit quàm CE (vel
quod eódem recidit, AR major quam CB) quòd punctorum om-
nium F in recta FA G imagines abſolutæ (quales Z) ad _ellipſin_ con-
ſiftent, cujus _Focus_ C, cujúſque penitus determinandæ modum ſatìs
facilem tunc oſtendimus. item ſi CR = CE, quòd imagines iſtæ ad
parabolam erunt; & denique, ſi CR & lt; CE, quòd eædem in hy-
perbolis oppoſitis reperientur; quarum etiam ſectionum focus com-
munis eſt punctum C, & quarum axes deſignandi modum reliquáque
circa ipſas præſertim advertenda declaravimus. (Nempe, ſi rectæ
CP cum ipſa CA ſemirectos conſtituant angulos; & hæ rectam RE
interſecent ad puncta S, indéque demittantur ad A@ perpendiculares
ST, SV, erunt T, V axis termini, rectáque CE ſemi-parameter erit)
unde patet totius rectæ FAG ad infinitum protenſæ abſolutam ima-
ginem (quin & illam, quæ ad oculum in centro O poſitum refertur)
aliquam eſſe dictarum conicarum, pro ſuo peculiari ſitu hanc vel illam
reſpectivè.
III. Adnotari porrò debet in iſto caſu, _ſectionis ellipticæ_ (quinetiam
11Fig. 198.& _parabolicæ_) TE Z partem anticam TE ad concavas circuli partes
LDL ſpectare; ſicuti poſtica EY ad convexas MB N pertinet. in
hoc autem altero tota _byperbola_ ZVZ, nec non _hyperbotæ_ ETE pars
(infra ECE) YEEY ad partem circuli convexam referri debent
(nempe ſi centro C, intervallo CE deſcriptus circulus rectam FG
ſecet punctis K, K; hyperbola ZVZ rectam interceptam KK repræ-
ſentabit, ipſiúſque FG quod reliquum eſt hinc indè protenſum pars
YEEY referet) pars autem ſuperior ETE ad cavam circuli partem
LDL ſpectat. ‖ Semper autem (cúm hîc, tum ubique) intelligatur
ad utraſque propoſiti circuli partes ejuſdem generis refractionem effici,
ſeu ejuſdem ſpeciei medio radios incidere.
IV. Ex his obiter naturæ, quam in oculi figura conſtruenda

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