Light: All which compared together evince and rarify both this and the
last Proposition.

PROP. XV.

_In any one and the same sort of Rays, emerging in any Angle out of any
refracting Surface into one and the same Medium, the Interval of the
following Fits of easy Reflexion and Transmission are either accurately
or very nearly, as the Rectangle of the Secant of the Angle of
Refraction, and of the Secant of another Angle, whose Sine is the first
of 106 arithmetical mean Proportionals, between the Sines of Incidence
and Refraction, counted from the Sine of Refraction._

This is manifest by the 7th and 19th Observations.

PROP. XVI.

_In several sorts of Rays emerging in equal Angles out of any refracting
Surface into the same Medium, the Intervals of the following Fits of
easy Reflexion and easy Transmission are either accurately, or very
nearly, as the Cube-Roots of the Squares of the lengths of a Chord,
which found the Notes in an Eight_, sol, la, fa, sol, la, mi, fa, sol,
_with all their intermediate degrees answering to the Colours of those
Rays, according to the Analogy described in the seventh Experiment of
the second Part of the first Book._

This is manifest by the 13th and 14th Observations.

PROP. XVII.

_If Rays of any sort pass perpendicularly into several Mediums, the
Intervals of the Fits of easy Reflexion and Transmission in any one
Medium, are to those Intervals in any other, as the Sine of Incidence to
the Sine of Refraction, when the Rays pass out of the first of those two
Mediums into the second._

This is manifest by the 10th Observation.

PROP. XVIII.

_If the Rays which paint the Colour in the Confine of yellow and orange
pass perpendicularly out of any Medium into Air, the Intervals of their
Fits of easy Reflexion are the 1/89000th part of an Inch. And of the
same length are the Intervals of their Fits of easy Transmission._

This is manifest by the 6th Observation. From these Propositions it is
easy to collect the Intervals of the Fits of easy Reflexion and easy
Transmission of any sort of Rays refracted in any angle into any Medium;
and thence to know, whether the Rays shall be reflected or transmitted
at their subsequent Incidence upon any other pellucid Medium. Which
thing, being useful for understanding the next part of this Book, was
here to be set down. And for the same reason I add the two following
Propositions.

PROP. XIX.

_If any sort of Rays falling on the