Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

CN Π, angulo CNP æquari. z 2. Accepto quovis in NM puncto
(puta M) centro C per M deſcribatur circulus MQH; item centro
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.

15.1.

Fig. 63.

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, eſſe

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