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Updated: May 29, 2025
If the hypotheses had been exact, the results would have been correct too; but Aristarchus in fact assumed a certain angle to be 87° which is really 89° 50', and the angle subtended at the centre of the earth by the diameter of either the sun or the moon to be 2°, whereas we know from Archimedes that Aristarchus himself discovered that the latter angle is only 1/2°. The effect of Aristarchus's geometry is to find arithmetical limits to the values of what are really trigonometrical ratios of certain small angles, namely
They insisted that the coveted islands were included in their portion of the great Borgian grant. As there had hardly yet been time to make a trigonometrical survey of an unknown world, so generously divided by the pope, there was no way of settling disputed boundary questions save by apostolic blows.
The next morning we met and passed a Government Survey party, under the command of Mr. Brooks, who was engaged in a very extensive trigonometrical survey. In an hour or two after, we passed Mr. Bowman's Pernatty cattle-station; there was no one at home but a dog, and the appearance of the camels seemed to strike him dumb.
I was going to complain of the abrupt way in which he had treated me, but I had the necessities of our trigonometrical operations before my eyes, and I was silent.
On the other hand, a European gentleman, who for thirty-six years without intermission has been living in the jungle, ascending to the summits of mountains in the prosecution of the trigonometrical survey, and penetrating valleys in tracing roads and opening means of communication, one, too, who has made the habits of the wild elephant a subject of constant observation and study, has often expressed to me his astonishment that after seeing many thousands of living elephants in all possible situations, he had never yet found a single skeleton of a dead one, except of those which had fallen by the rifle.
They insisted that the coveted islands were included in their portion of the great Borgian grant. As there had hardly yet been time to make a trigonometrical survey of an unknown world, so generously divided by the pope, there was no way of settling disputed boundary questions save by apostolic blows.
His sight, however, began to fail three years later, and he died in 1840, leaving materials from which the work was completed and published in 1878 by Dr. Julius Schmidt, late director of the Athens Observatory. Much had been done in the interim. Beer and Mädler began at Berlin in 1830 their great trigonometrical survey of the lunar surface, as yet neither revised nor superseded.
In return he was always at any youngster's service in a trigonometrical problem; and he amused the midshipmen and young lieutenants with analytical tests; some of these were applicable to certain liquids dispensed by the paymaster. Under one of them the port wine assumed some very droll colors and appearances not proper to grape-juice.
Thursday, 8th December, Louden Springs. Surveying and building trigonometrical station on a light-coloured hill to the south of this. My eyes very bad; can scarcely see; can do nothing. Friday, 9th December, Louden Springs. Nearly blind; dreadful pain; can do nothing to-day; no sleep last night. Saturday, 10th December, Louden Springs.
They were 3485 feet above the most elevated point which the learned Condamine, who had hitherto ascended highest, reached in 1745, but were still 2140 feet below the loftiest summit of the mountain. They determined, by a series of strict trigonometrical observations, the height of the chief peaks of that celebrated ridge
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