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D'Estaing afterwards reestablished his order of battle on the port tack, forming upon the then leewardmost ship, on the line BC. Byron's action off Grenada, viewed as an isolated event, was the most disastrous in results that the British Navy had fought since Beachy Head, in 1690.
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.
A man of parts one day brought up to me an objection in the following form: Let the straight line BA be cut in two equal parts at the point C, and the part CA at the point D, and the part DA at the point E, and so on to infinity; all the halves, BC, CD, DE, etc., together make the whole BA; therefore there must be a last half, since the straight line BA finishes at A. But this last half is absurd: for since it is a line, it will be possible again to cut it in two.
Here, for example, you have Euclid writing in a perfectly prosaic way all in small type such an item as the following: "A perpendicular is let fall on a line BC so as to bisect it at the point C etc., etc.," just as if it were the most ordinary occurrence in the world.
The phenomenon is, that by taking two pieces of this crystal and applying them one over the other, or rather holding them with a space between the two, if all the sides of one are parallel to those of the other, then a ray of light, such as AB, is divided into two in the first piece, namely into BD and BC, following the two refractions, regular and irregular.
And this line being then prolonged at one side or the other will meet the straight line BL, as here at V. Let there then be erected on AB the perpendicular BC, which will represent a wave of light coming from the infinitely distant point F, since we have supposed the rays to be parallel.
And the measure of these angles is found by describing, about the point B, a circle which cuts the radii AB, BC. For the perpendiculars AD, CE, let fall from the points of intersection upon the straight line DE, which are called the Sines of the angles ABD, CBE, have a certain ratio between themselves; which ratio is always the same for all inclinations of the incident ray, at least for a given transparent body.
The point D thus found will be one of those through which the curve ought to pass; and the proof will be the same as before. And by this it will be proved that the waves which come from the point L, after having passed through the glass KAKB, will take the form of straight lines, as BC; which is the same thing as saying that the rays will become parallel.
Now according to our computation, which is given in the Treatise on the causes of the phenomena of Saturn, the distance BA between the Earth and the Sun is about twelve thousand diameters of the Earth, and hence four hundred times greater than BC the distance of the Moon, which is 30 diameters.
"Owing to my knowledge of English I was employed by the American mission to act as interpreter. One day when I was off duty I was taken by a friend to a signals unit where there were many pieces of equipment which had been 'liberated', and I was able to buy a BC 342 receiver.
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