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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[11.] Lect. III.
Page: 40 (22)
[12.] _Corol_. 1. Ang. _a_ BG. ang. _a_ BP > ang. δ BH. ang. δ BP. 2. Ang. _a_ BG. ang. PBG > ang. δ BH. PBH.
Page: 44 (26)
[13.] Lect. IV.
Page: 49 (31)
[14.] Lect.V.
Page: 56 (38)
[15.] Lect. VI.
Page: 65 (47)
[16.] Lect. VI I.
Page: 70 (52)
[17.] Lect. VIII.
Page: 76 (58)
[18.] Lect. IX.
Page: 81 (63)
[19.] Lect. X.
Page: 87 (69)
[20.] Lect. XIV.
Page: 114 (96)
[21.] Lect. XV.
Page: 122 (104)
[22.] APPENDICVLA.
Page: 126 (108)
[23.] Lect. XVI.
Page: 129 (111)
[24.] Lect. XVII.
Page: 135 (117)
[25.] Lect. XVIII.
Page: 139 (121)
[26.] ERRATA.
Page: 145 (127)
[27.] Benevolo Lectori.
Page: 192
[28.] Lectio I.
Page: 194
[29.] Lect. II.
Page: 206 (13)
[30.] Lect. III.
Page: 217 (24)
[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)
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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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