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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
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L E C, T. XV.
Ominimo methodum hanc leviculam adhibendo pleralque superti-
cierum quarumris inflectentium hujus generis affectiones (illas nempe
qua maenitudinum apparentes quantitares, poliriones, dictantias,
tiouras respiciunt) compluriumque Phanomencor caulas ipse statim o-
pera levi deprehendes; quibus in exprelsius deducendis libri plures ad
tantam molem extumescere vel possunt, vel solent; ut mihi lalteri
opus non suc hujulmodi plura conserere. veruntamen ne pars haec
nimium deficiat, ex quoniam nonnulla succurrunt anim adverlione non
indigna, de magnicudinum etiam apparentiis, tam Dioprricis quam
Caroptricis, specialia quaedam proponam; ea vero commodius se-
quencem praeltolabuntur Lectionem.
Hluic interimi, ne abnormiter curta sc, aliquarenus explendae Pro-
blemation hoc adnectam:
Exponatur oculo, cujus centrum O, loncinguum objectum FG,
ab oculi, circulique refringentis axe A BO bisectum; datusque sit
anculus simpliciter (oculo nempo nudo) apparens FOG. item assie-
netur punctum P, quod imago sit puncti A a circulo refringente facta:
datus sit denno ex refractione apparens angulus POO; propositum est F18. 175.
circulum istum refrincentem de foribere (vel determinare).
Analysis. Factum esto; CiEnempe circulus B N, qualis requiritur
Cujus lIEcentrum C, vertex B; _ qui rectam OP in N secet. duca-
cur C Y ad OF parallela, rectaeque OP occurrens in Y, _ COn
nectatur C N. cum itaque ( NY retractus radii ad FO, vel CY
paralleli, erit C Y. YHI:: R. I. eroo rario C Y ad Y W datur: 8
cum praeterea angulus Y (dato FOP aequalis) detur, etiam (in eri-
angulo CT N) angulus C N Y innorescer. itaque trianculum C OY
speciedatur; unde rario C O ad CH (vel CB) datur est aurem
CB. CZ:: I R. R. ergoratio CB ad C Z datur. icdque ratio
CO adC Z quoque darur: unde ratio CO adO Z datur. veriim
OL datur; exso eriam CO datur. hinc demum _ ipsa C B datur.
Componitur autem in hunc modum: In O Purcunque capiatur
O8, 8 Hat 05, 90:: R. I. _ connectatur 05C. ducaturque
Z R Sad Yo parallela. tum Aat OZ. LT:: I R. K (unde cori-
ponendo OY. ZT:: I R) icem V = VZTXLS: _ X
NO29= V q; tI X. OZ:: OZ.Y. denique Z. Y:; OZ.
OC (unde erit X 9. OZ 9::  ~.OC; hoc est OZg. =- V9.
Or9::OZ. OC; hoc est 02. 9- Z. Tx 2. 5. OL9:: OL.
OC). per C vero ducatur C NY ad Z. S parallela, secansO P in N.
denique cerero C. per M ducatur circulus B H; is propotico latis.
lacie.
Tac