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

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[Item 1.]
[2.] Imprimatur,
[3.] LECTIONES _OPTICÆ & GEOMETRICÆ:_ In quibus PHÆNOMENωN OPTICORUM Genuinæ _Rationes_ inveſtigantur, ac exponuntur: ET _Generalia_ Curvarum Linearum _Symptomata declarantur_. Auctore Isaaco Barrow, Collegii _S S. Trinitatis_ in Academia _Cantab._ Præfecto, Et _SOCIETATIS REGIÆ_ Sodale.
[4.] LONDINI, Typis _Guilielmi Godbid_, & proſtant venales apud _Robertum Scott_, in vico Little-Britain. 1674.
[5.] SPECTATISSIMIS VIRIS Roberto Raworth & Thomæ Buck ARMIGERIS;
[6.] Iſaac Barrow
[7.] Epistola ad LECTOREM.
[8.] Epiſtola; in qua Operis hujus Argumen-tum, & ſcopus brevitèr exponuntur.
[9.] Lect. I.
[10.] Lect. II.
[11.] Lect. III.
[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.
[13.] Lect. IV.
[14.] Lect.V.
[15.] Lect. VI.
[16.] Lect. VI I.
[17.] Lect. VIII.
[18.] Lect. IX.
[19.] Lect. X.
[20.] Lect. XIV.
[21.] Lect. XV.
[22.] APPENDICVLA.
[23.] Lect. XVI.
[24.] Lect. XVII.
[25.] Lect. XVIII.
[26.] ERRATA.
[27.] Benevolo Lectori.
[28.] Lectio I.
[29.] Lect. II.
[30.] Lect. III.
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311118 dinatam BDin I, & lineam RSin X) ſit MP. ME: : VG. IX;
vel, ſit linea AL talis, ut ductâ MPY ad BDparallelâ (quæ ſecet
axem ADin P, &
lineam ALin Y) ſit PE. ME: : VG. PY; erit
11Fig. 177. tunc utrumque _ſpatium_ (ſingillatim) BRS D, vel ADL duplum _ſu-_
_perfici@i conicœ_, quod ex recta per V &
curvam AMB mota progene-
ratur.
Nam ſumatur MNindefinita curvæ particula; & per N ducantur
rectæ NOKTad ipſam AD, &
NQZ ad BDparallelæ (quæ li-
neas expoſitas, ut _Schema_ monſtrat, ſecent) connectantúrque rectæ
VM, VN.
eſtque MO. MN: : MP. MF: : VG. IX. quare
MN x VG = MO x IX = IK x IX.
Item eſt NO. MN: : PE.
ME: : VG. PY. unde MN x VG = NO x PY = QP x PY.
Eſt autem MN x VG duplum trianguli MVN.
quapropter tam IK
x IX, quàm QP x PY duplum eſt _trianguli_ MVN.
pariter autem
ubique fit.
ergò conſtat Propoſitum.
Exemplum.
Sit curva AMB _byperbola æquilatera_, cujus _Centrum_ C, ſitque
22Fig. 177. CV = CA = _r._
& CP = _x_ (nam hujuſmodi _calculo_ plerunque
rem expedit peragere) tum connexâ MC;
patet eſſe EC = {_rr_/_x_};
& MCq = 2 _xx_ - _rr_ (nam PMq = _xx_ - _rr_) item eſt MCq.
CPq:
: MEq. MPq; hoc eſt MCq. CPq: : ECq. CGq. hoc
eſt 2 _xx_ - _rr_.
_xx_: : {_r_4/_xx_}. CGq = {_r_4/2 _xx_ - _rr_}. quare VGq = {_r_4/2 _xx_ - _rr_} +
_rr_ = {2 _rrxx_/2 _xx_ - _rr_} = {VAq x CPq/MCq}.
vel VG = {VA x CP/MC}. quare
VG.
VA: : (CP. MC): : MP. ME. hinc conſectatur in hoc
caſu, quum ubique ſit IX = VA, _lineam_ RS fore _rectam_;
& _rectan-_
_gulum_ BRSD _ſuperficiei conicœ_ AMBV _duplum eſſe._
Cæterùm hoc _elegans exemplum_ ſuppeditavit Generoſus, ingenio ac
eruditione præſtans, Vir (_Collegii noſtri, quod olim Sociorum Com-_
_menſalis incoluit_, ornamentum) D.
_Franciſcus Feſſopius_, Armiger;
cujus in hanc rem perquam ingenioſo mihi comiter impertito ſcripto
(ipſius injuſſu quidem, at ſpero non ingratiis) ſeu _Gemmâ_ quâdam au-
debo mea condecorare.

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