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"I did not leave untried," says he, "whether, by assuming a horizontal refraction according to the density of the medium, the rest would correspond to the sines of the distances from a vertical direction, but calculation proved that it was not so: and, indeed, there was no occasion to have tried it, for thus the refraction would increase according to the same law in all mediums, which is contradicted by experiment."
Lue rue = luem ruem, the last an old word for ruinam, with the case-ending lost, as frequently, and the copula omitted, as in Patres Conscripti, &c. Marmar, Marmor, or Mamor, is the reduplicated form of Mars, seen in the Sabine Mamers. Sins is for sines, as advocapit for advocabitis.
But these sines are the lines KL and GQ, if GK is taken as the radius of the circle. Then LK ought to be to GQ as 3 to 2; and in the same ratio MG to CR, NC to FS, OF to DT. Then also the sum of all the antecedents to all the consequents would be as 3 to 2. Now by prolonging the arc DO until it meets AK at X, KX is the sum of the antecedents.
"I looked just as you do now- -I felt just as you do now all in a fright and a puzzle, when I first heard of angles and sines, and cosines, and arcs and centres, and complements and tangents." "Oh mercy! mercy!" interrupted Francisco, whilst Carlo laughed, with a benevolent sense of superiority. "Why," said Carlo, "you'll find all these things are nothing when you are used to them.
"Yes, and Hoosay too, thet Presberteen man thet sines his name with er dubble D hung on ter ther een." "Jonas Melvin is er windin up his kerrare in Free Will Church. We'll hev no sich men fumblin wi ther werd ev God in our pulpit. I never did think them Presbyteens hed eny religin no way. They air full of book larnin, but havn't bin tech wit ther sparit.
"But because this computation was founded on the hypothesis of the proportionality of the sines of incidence and refraction, which though by my own experience I could not imagine to be so erroneous as to make that angle but 31', which in reality was 2 degrees 49', yet my curiosity caused me again to make my prism.
Stern believed he had an answer to this problem on the afternoon of the second day. For many hours he had hung his pendulums over the cliff, noted deflections, taken triangulations, and covered the surface of the smooth stone with X's, Y's, Z's, sines and cosines and abstruse formulae all scrawled with charcoal, his only means of writing.
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.
And Butler, in his satirical description of Sir Hudibras, ascribes to his hero more practical philosophy than he appears to have intended, and more, certainly, than is found in some modern systems of education: "In mathematics he was greater Than Tycho Brahe or Erra Pater; For he, by geometric scale, Could take the size of pots of ale; Resolve by sines and tangents straight, If bread or butter wanted weight; And wisely tell what hour o' th' day The clock does strike, by algebra."
In this form it states that a ray of light in transition between two media of different densities is refracted at their boundary surface so that the ratio of the angle which is formed by the ray in either medium with a line at right angles to the boundary surface is such that the quotient of the sines of both angles is for these media a constant factor. In symbols sin α / sin β = c.
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