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Updated: June 11, 2025
Since then the angle HBF is equal to PBA, and the angle BFG equal to QBC, it follows that the sine of the angle HBF will also have the same ratio to the sine of BFG, as the velocity of light in the medium A is to its velocity in the medium C. But these sines are the straight lines HF, BG, if we take BF as the semi-diameter of a circle.
Micklethwaite? asked Everard. 'I? Oh dear, no! I never got much past the Rule of Three. But Tom has forgiven me that long ago. 'I don't despair of getting you into plane trigonometry, Fanny. We will gossip about sines and co-sines before we die. It was said half-seriously, and Everard could not but burst into laughter.
Fourier has reduced these two hypotheses to calculation, and he has hence deduced mathematically the experimental law of the sines. After having resisted so radical a test, the two hypotheses were found to be completely verified, they have become laws of nature; they point out latent properties of caloric which could only be discerned by the eye of the intellect.
This is why I have distinguished this ordinary refraction from the other; and having measured it by exact observation, I found that its proportion, considered as to the Sines of the angles which the incident and refracted rays make with the perpendicular, was very precisely that of 5 to 3, as was found also by Mr.
He also thought in conic sections, squares and roots and ratios, and geometrized like Euclid. He made Kepler's laws for the planets to follow; he made velocity increase proportionally to the time in falling bodies; he made the law of the sines for light to obey when refracted; he established the classes, orders, families and genera of plants and animals, and fixed the distances between them.
Tutors came to give him lessons independently of myself, and I listened with envy and involuntary respect as he drew boldly on the blackboard with white chalk and talked about "functions," "sines," and so forth all of which seemed to me terms pertaining to unattainable wisdom.
There is no great harm in singing college songs, if it is accompanied by good work in the recitation-room." "Brothers," resumed Walter, "we will do our best to drive dull care away. Let us forget, this happy evening, that there are such things as logarithms, and sines, and tangents, and Greek tragedies. To-night our hearts shall be uplifted by sentiment and song.
I placed one of these so as to reflect the sun's light at an angle of forty-five degrees, and fixed it in such a manner that while it revolved round one of the lines as an axis, I could measure its angular motion; I found that the longest red color occurred at the inclination 10 1/4 degrees, 20 3/4 degrees, 32 degrees, and 45 degrees; of which the sines are as the numbers 1, 2, 3, and 4.
The Chinese furnish numberless other gewgaws and ornaments of little value and worth, which are esteemed among the Spaniards; besides a quantity of fine crockery of all kinds; canganes, sines, and black and blue robes; tacley, which are beads of all kinds; strings of cornelians, and other beads and precious stones of all colors; pepper and other spices; and rarities which, did I refer to them all, I would never finish, nor have sufficient paper for it.
Then one will know the length and position of the lines NH, EM, and of HE, which is the thickness of the Crystal: which lines being traced separately upon a plan, and then joining NE and NM which cuts HE at P, the proportion of the refraction will be that of EN to NP, because these lines are to one another as the sines of the angles NPH, NEP, which are equal to those which the incident ray ON and its refraction NE make with the perpendicular to the surface.
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