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Then also the Sine of the angle DAE is to the Sine of NAF as BC is to AN. But the ratio of BC to AN was the same as that of the velocities of light in the substance which is towards AE and in that which is towards AF; therefore also the Sine of the angle DAE will be to the Sine of the angle NAF the same as the said velocities of light.
Whence it is easy to recognize this chief property of refraction, namely that the Sine of the angle DAE has always the same ratio to the Sine of the angle NAF, whatever be the inclination of the ray DA: and that this ratio is the same as that of the velocity of the waves in the transparent substance which is towards AE to their velocity in the transparent substance towards AF. For, considering AB as the radius of a circle, the Sine of the angle BAC is BC, and the Sine of the angle ABN is AN. But the angle BAC is equal to DAE, since each of them added to CAE makes a right angle.
And the angle ABN is equal to NAF, since each of them with BAN makes a right angle.
The man of unquiet nerves or of exacting lungs would do well to leave that arena to the hard-heads and cool-bloods who can pursue their aim and secure their interests: undisturbed either by the fractional rat-a-tat-tat of the auctioneer's "Twenty-seven af naf naf naf, who'll give me thirty?" or by the banter and comicalities which a humor-loving auctioneer will interject between these bird-notes, without changing his key, or arresting his sale a moment.
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