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 |< < (81) of 393 > >|
27481 rectam AP ſecare ad T; ut ipſius jam rectæ PT quantitatem exqui-
11Fig. 115. ram; curvæ arcum MN indefinitè parvum ſtatuo; tum duco rectas
NQ ad MP, & NR ad AP parallelas; nomino MP = _m_; PT
= _t_; MR = _a_; NR = _e_; reliquáſque rectas, ex ſpeciali curvæ
natura determinatas, utiles propoſito, nominibus deſigno; ipſas au-
tem MR, NR (& mediantibus illis ipſas MP, PT) per _æquationem_
è Calculo deprehenſam inter ſe comparo; regulas interim has obſer-
vans. 1. Inter computandum omnes abjicio terminos, in quibus
ipſarum _a_, vel _e_ poteſtas habetur, vel in quibus ipſæ ducuntur in ſe
(etenim iſti termini nihil valebunt).
2. Poſt _æquationem constitutam_, omnes abjicio terminos, literis
conftantes quantitates notas, ſeu determinatas deſignantibus; aut in
quibus non habentur _a_, vel _e_. (etenim illi termini ſemper, ad unam
æquationis partem adducti, nihilum adæquabunt).
3. Pro _a_ ipſam _m_; (vel MP) pro _e_ ipſam _t_ (vel PT) ſubſtituo.
Hinc demùm ipſius PT quantitas dignoſcetur.
Quòd ſi calculum ingrediatur curvæ cujuſpiam indefinita particula;
ſubſtituatur ejus loco tangentis particula ritè ſumpta; vel ei quævis
(ob indefinitam curvæ parvitatem) æquipollens recta.
Hæc autem è ſubnexis Exemplis clariùs eluceſcent.
Exemp. I.
Angulus ABH rectus ſit; & ſit curva AMO talis, ut per A du-
ctâ utcunque rectâ AK, quæ rectam BH ſecet in K, curvam AMO
22Fig. 116. in M, ſit ſemper ſubtenſa AM æqualis abſciſſæ BK; hujus curvæ ad
M tangens eſt deſignanda.
Fiant quæ ſuprà præſcripta ſunt, & (ductâ ANL) nominetur
AB = _r_; & AP = _q_; unde AQ = _q_ - _e_; item QN = _m_ -
_a_. ergò eſt _qq_ + _ee_ - 2 _qe_ + _mm_ + _aa_ - 2 _ma_ = (AQq
+ QNq = ANq = ) BLq; hoc eſt (rejectis, uti monitum eſt,
rejiciendis) _qq_ - 2 _qe_ + _mm_ - 2 _ma_ = BLq. Porrò eſt
AQ. QN: : AB. BL; hoc eſt _q_ - _e. m_ - _a_: : _r._ BL =
{_rm_ - _ra_. /_q_ - _e_} quare {_rrmm_ + _rraa_ - 2 _rrma_/_qq_ + _ee_ - 2 _qe_. } = BLq; ſeu
(rejectis ſuperfluis) {_rrmm_ - 2 _rrma_/_qq_ - 2 _qe@_} = BLq = _qq_ - 2 _qe_ +
_mm_ - 2 _ma_. vel _rrmm_ - 2 _rrma_ = _q_4 - 2 _q_3_e_ + _qqmm_ - 2 _qqma_ - 2 _q_3_e_ +
4 _qqee_ - 2 _qmme_ + 4 _qmae_; hoc eſt (abjectis iis, quæ

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