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 |< < (33) of 393 > >|
5133 ipſius perpendicularis AB (quaſi) refractus in ipſum punctum Z ter-
minatur. Porrò:
VIII. _Lemma_: ſit AB ad EF normalis, & à duobus in AB
ſumptis utcunque punctis A, I (quorum A proprius ipſi B) ad duo
puncta quæ vis M, N in ipſa EF acceptis (quorum verò M ſit ipſi B
vicinius) connectantur rectæ AM, AN ; & IM, IN; dico fore A N.
AM & gt; IN. IM.
Nam centro N per A deſcribatur circulus PA OR (rectas IM,
IN interſecans punctis O, R) & per R ducatur RT ad EF parallela,
ſecans IM in S. Et ob angulum NRT obtuſum, patet rectam RT
extra circulum totam excidere; unde SM & gt; (OM & gt;) AM.
adeóque AN. AM & gt; AN : SM : : RN. SM : : IN. IM. li-
quet igitur eſſe AN . AM & gt; IN. IM : Quod E. D. Hinc
Si duorum radiorum AM, AN (quorum hic obliquior) refracti
M _a_, N _a_ cum axe AB conveniant punctis I, K, erit in primo caſu IB
& lt; KB; in ſecundo IB & gt; KB. Etenim connexâ IN; eſt in primo
caſu, NK. MI : : NA. MA & gt; NI. MI. adeóque NK & gt; NI.
unde BK & gt; BI. aſt in ſecundo, NK. MI : : NA. MA & lt; NI.
MI quare NK & lt; NI; & indè BK & lt; BI.
11Fig. 37.
IX. _Coroll_. Refractorum in primo caſu concurſus extra angulum
AB N verſantur; in ſecundo, intra eundem. Sed hæc eadem in decur-
ſu liquidius, ac multifariàm conſtabunt.
X. Porrò, bina quoad hos caſus _Theoremata_ ſubjiciemus, uſus haud
contemnendi.
I. Si ſiat (in primo caſu) YB. AB : : I. √ Iq - Rq. ſit autem cu-
22Fig. 39. juſvis incidentis AN reſractus KN _a_; & connectatur YN: erit KB.
YN : : √ Iq - Rq. R.
Nam ob YBq. ABq : : (_a_) Iq. Iq - Rq. erit per converſi-
33_(a) Hypoib._ onem rationis YBq. YBq - ABq : : Iq. Rq : : _(b)_ KNq. ANq.
44_(b) 4 hujus_& permutando YBq. KNq : : YBq - ABq. ANq . componen-
dóque YBq + KNq. KNq : : YBq + BNq. ANq. (nempe
YBq - ABq + ANq = YBq + BNq; quoniam ANq -
ABq = BNq) Quarè runſus permutando eſt YBq + KNq.
YBq. + BNq : : KNq. ANq. dividendoque KNq - BNq.
YBq + BNq : : KNq - ANq. ANq; hoc eſt KBq. YNq
: : Iq - Rq. Rq: Q. E. D.

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