The following propofitions concerning spherical triangles, will render them more intelligible. 1. A spherical triangle is either equilateral, isofcelar, or fcalene, according as it has the three angles all equal, or two of them equal, or all three unequal; and vice versa. 2. The greateft fide is always oppofite the greatest angle, and the smallest fide oppofite the smallest angle. 3. Any two fides, taken together, are greater than the third. 4. If the three angles of a spherical triangle be all acute, or all right, or all obtufe, angles, the three fides will be accordingly all less than 90 degrees, or equal to 90 degrees, or greater than 90 degrees, and vice verfa. 5. If from the three angles A, B, C, (fig. 14,) of a fpherical triangle, A B C, as poles, there be described upon the furface of the sphere, three arches of a great circle D E, DF, and F E, forming by their interfections another fpherical triangle D E F; each fide of the new triangle will be the fupplement of the angle at its pole; and each angle of the fame triangle will be the supplement of the fide oppofite to it in the triangle A B C. 6. In any triangle ABC, or Ab C, right angled at A, (fig. 15,) the angles at the hypothenufe are always of the fame kind as their oppofite fides. And the hypothenufe is greater or less than a quadrant, according as the fides, including the right angle, are of different kinds, or of the fame kind; that is to fay, according as these fame fides are either both obtufe, or both acute, or as one is obtuse, and the other acute, and vice versa. First, the fides including the right angle, are always of the fame kind as their oppofite angles. Secondly, the fides including the right angle, will be of the fame or different kinds, according as the hypothenufe is lefs or more than 90 degrees; but one of them at least will be of go degrees, if the hypothenufe be fo. CHAP. CHAP. XIII. OF GEOGRAPHY. SECT. I. GEOGRAPHICAL DEFINITIONS. 1. GEOGRAPHY is the knowledge of the earth, or a des scription of the terrestrial globe, particularly of the furface and known habitable parts thereof, with all its different divifions. 2. The earth is a globular body, furrounded with an atmosphere of air, by which all terreftrial bodies are confined to its furface, being attracted thereto by the laws of gravity. That the earth is of a globular form, has been demonftrated by a number of experiments, particularly by observations of the eclipses of the moon; in which it appears, that the shadow of the earth always appears circular, whichever way it is projected. Alfo, by the observation of ships at sea, which, after their departure from any coaft, gradually disappear to an obferver on land, from the bottom upwards; that is, the first part which disappears from the fight, is the keel, or lower part of the fhip; then those parts which are higher up, and so on; the top of the maft heing the part P 2 that that is last seen: this is owing to the convexity of the waters, which have the fame globular figure as the earth *. 3. The earth also has a diurnal motion on its own axis, performing one revolution in 24 hours; thereby occafioning the changes of the day and night, as will be feen in Aftronomy. 4. The circumference of the globe is supposed to be di vided into 360 parts, called degrees, and each degree fubdivided into 60 minutes, and each minute into 60 feconds, &c. Every degree contains 60 geographic miles; confequently, the circumference of the globe is 21,609 fuch miles; and the diameter 6900 miles. But as 60 geographical miles are above 69 British measure, the circuit of the globe is therefore 24,840 English miles, and the diameter almost a third, or 7900 in round numbers. 5. The globe of the earth confists of land and water: the proportion of the land to the water is not accurately known, but it is generally believed to be near one third. 6. The waters are divided into three oceans, (befides the fmaller feas:) viz.-The Atlantic, Pacific, and the Indian ocean. 1. The Atlantic or Western ocean divides Europe from America, and is 3000 miles wide. 2. The Pacific ocean divides America from Afia, and New Holland, and is 10,000 miles wide. 3. The Indian ocean lies between the East Indies and Africa, and is 3000 miles wide. The parts or The philofophers of the laft age differed greatly in their descriptions of the true spherical figure of the earth, of which there were two general opinions. The one maintained that the earth was a prolate spheroid! of this number was Caffini. The other party maintained it to be an oblate fpheroid; of this Sir Ifaac Newton was the chief, who infifted that the polar, was fhorter than the equatorial diameter by 36 miles. A party of philofophers from France was fent by the king of that country, to measure a degree on the polar circle, and alfo on the equator; the refult of their experiment turned out exactly in favour of Sir Ifaac Newton's theory. But this inequality of the shape of the earth, as well as the inequalities occafioned by the mountains, &c. make no fenfible difference in the form of the earth. branches |