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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[51.] Prop. 3.
[52.] Prop. 4.
[53.] APPENDICULA 3.
[54.] Problema I.
[55.] Exemp. I.
[56.] Exemp. II.
[57.] Probl. II.
[58.] Exemp. I.
[59.] _Exemp_. II.
[60.] _Probl_. III.
[61.] _Probl_. IV.
[62.] _Probl_. V.
[63.] _Probl_. VI.
[64.] _Probl_. VII
[65.] _Probl_. VIII.
[66.] _Probl_. IX.
[67.] _Probl_. X.
[68.] _Corol. Theor_. I.
[69.] _Theor_. II.
[70.] _Theor_. III.
[71.] _Theor_. IV.
[72.] _Theor_. V.
[73.] _Theor_. VI.
[74.] _Theor_. VII.
[75.] Lect. XIII.
[76.] Æquationum Series prima.
[77.] _Notetur autem_,
[78.] Series ſecunda.
[79.] Not.
[80.] Series tertia.
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6648 CN Π, angulo CNP æquari. z 2. Accepto quovis in NM puncto
(puta M) centro C per M deſcribatur circulus MQH;
item centro
11Fig. 63. N per M deſcribatur circulus MRH, qui priorem MQH ſecet
in H;
erit HN Π reflexus ipſius MN P. Etenim connexis CM,
CH;
& NM, NH, ex conſtructione liquet triangula CMN, CHN,
invicem æquilatera fore;
proindéque angulos CNM, CNH (&
indè relìquos MNR, HNR) æquari 3.
protenſà CNR, à quovis
in MN puncto, puta M ducatur MG ad CR perpendicularis, &

in hac producta ſumatur GH = GM;
erit conjuncta HN Π iterum
reflexus.
Nam connexis NH, NM patet angulos GNM, GNH
æquari.
verum hi modi ſufficiunt huic conficiendo perfacili negotio.
IV. Nocetur ſi fuerit HN P reflexus ipſius MN P fore N Π =
N P.
V. Diſpiciamus jam primò quid ex hujuſmodi reflectione contingat
puncto ab infinitâ quo ad ſenſum diſtantiâ radianti, ſeu parallelos
projicienti radios.
quorſum, per circuli reflectentis centrum C
protendatur indefinitè recta ABC (hoc autem in ſequentibus evitandæ
repetitioni perpetuò factum intelligatur;
quin ejuſmodi recta nomi-
netur axis;
hîc _Speculi,_ poſteà _Diapbani_) biſecetur autem Semidiame-
ter CB in Z;
& per Z tranſeat recta ZY ad CB perpendicularis,
indeſinitéque protenſa ;
tum quilibet incidat axi parallelus radius
MN P ad N;
(convexo circuli nil refert, an cavo; nam in utroque
caſu reflexus quoad directionem idem erit;
vel ejus qui in hoc, iſte qui
in illo productus erit) connexáque CN ipſam ZY interſecet in V;
ſiátque CK = CV; ducatúrque NK; erit NK ipſius MN reflex-
us (vel reflexi productus) Nam ducatur NQ ad CB perpendicu-
laris, &
connectatur CP. éſtque CZ . CK : : (CZ. CV : : )
CQ.
CN . quapropter antecedentes duplicando CN . CK : :
PN.
CN. item angulus KCN æquatur alterno CNP. ergò tri-
angula CKN, NCP ſimilia ſunt;
adeoque KN = KC. igitur è
ſuprà generatim oſtenſis patet fore KN, ipſius MN reflexum.
VI. Hinc particularis emergit methodus hujuſmodi quotcunque
reflexos quàm expeditiſſime deſignandi;
quin & ipſorum erga ſe ra-
tiones ac reſpectus;
nec non pleraque primaria _Symptomata_ facilè
diluceſcunt;
corollariis nempe ſubjectis comprehenſa.
VII. I. Patet punctum Z, Semidiametrum CB biſecans,

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