And that this is true, not onely in one, but in every Ray that goes to the
constitution of the Primary Iris; nay, in every Ray, that suffers only two
refractions, and one reflection, by the surface of the round body, we shall
presently see most evident, if we repeat the _Cartesian Scheme_, mentioned
in the tenth _Section_ of the eighth _Chapter_ of his _Meteors_, where
EFKNP in the third Figure[9] is one of the Rays of the Primary Iris, twice
refracted at F and N, and once reflected at K by the surface of the
Water-ball. For, first it is evident, that KF and KN are equal, because KN
being the reflected part of KF they have both the same inclination on the
surface K that is the angles FKT, and NKV made by the two Rays and the
Tangent of K are equal, which is evident by the Laws of reflection; whence
it will follow also, that KN has the same inclination on the surface N, or
the Tangent of it XN that the Ray KF has to the surface F, or the Tangent
of it FY, whence it must necessarily follow, that the refractions at F and
N are equal, that is, KFE and KNP are equal. Now, that the surface N is by
the reflection at K made parallel to the surface at F, is evident from the
principles of reflection; for reflection being nothing but an inverting of
the Rays, if we re-invert the Ray KNP, and make the same inclinations below
the line TKV that it has above, it will be most evident, that KH the
inverse of KN will be the continuation of the line FK, and that LHI the
inverse of OX is parallel to FY.
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