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Updated: June 11, 2025
Here, even if not in Stonehenge, he will pause to marvel at the patient energy of the men of old who put together such colossal masses of stone. In Alemtejo, south of Cape de Sines, are several of these, usually about 6 feet in length, with a slight portico at one end.
It is no fable that a student of the higher mathematics, when his master, a practical engineer upon the Boston water-works, required his services, exclaimed, "I had no idea that you had sines and tangents out of doors." With such, "Nothing goes for sense or light That will not with old rules jump right; As if rules were not in the schools Derived from truth, but truth from rules."
I had succeeded in implicating another culprit. Not more than half the blame was now Lalage's. "The sine qua nons," the letter went on, "are marked with red crosses, the desiderata in black." "I'm glad," I said, "that she got one plural right. By the way, I wonder what the plural of that phrase really is. It can't be sines qua non, and yet sine quibus sounds pedantic."
"Having made these observations, I first computed from them the refractive power of the glass, and found it measured by the ratio of the sines 20 to 31.
This was a good shot, but he unfortunately assumed that all rays passing into a denser medium would apparently penetrate it to a depth depending only on the medium, which means that there is a constant ratio between the tangents, instead of the sines, of the inclination of the incident and refracted rays to the normal.
"I heard one of them say we were likely to make trouble for them and we ought to be chased away and scared so badly we'd never come around here again, and the others seemed to agree with him." "That sounds like a mystery," said Hal. "I don't believe Mr. Perry would talk mathematics to explain such conversation," Bud declared. "If he did, he'd probably make another pun about sines and cosines.
One sees then that as there is in the refraction of ordinary media a certain constant proportion between the sines of the angles which the incident ray and the refracted ray make with the perpendicular, so here there is such a proportion between CV and CD or IE; that is to say between the Sine of the angle which the incident ray makes with the perpendicular, and the horizontal intercept, in the Ellipse, between the refraction of this ray and the diameter CM. For the ratio of CV to CD is, as has been said, the same as that of N to the semi-diameter CG.
Let those who denounce and deplore this harsh unpeopling come and stand upon the cold, bleak summit of one of these Sutherland mountains. Let them bring their compasses, or some other instrument for measuring the angles, sines and cosines of human conditions.
It is known that Vasco was born at Sinès, but the date of his birth is uncertain; the year 1469 is that generally given, but besides the fact that if this be the correct date, Gama would have been very young not more than eight and twenty when the important command of the expedition to the Indies was confided to him, there was discovered twenty years ago, amongst the Spanish archives, a safe-conduct to Tangier granted in 1478 to two persons, Vasco da Gama and Lemos.
But he assumed besides this a constant ratio of Sines, which we have just proved by these different degrees of velocity alone: or rather, what is equivalent, he assumed not only that the velocities were different but that the light took the least time possible for its passage, and thence deduced the constant ratio of the Sines.
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