Ptolemy - Ptolemy's Tetrabiblos - Appendix 1 lyrics

APPENDIX NO. I ALMAGEST; BOOK VIII, CHAP. IV THE various constellations of the fixed stars having now been duly described, their aspects remain to be investigated. Independently of the steadfast and immutable aspects which the said stars preserve among themselves, either rectilinearly, or triangularly, or by other similar forms, 1 they have also certain aspects considered as referring exclusively to the planets and the Sun and Moon, or parts of the zodiac; certain others to the earth only; and others, again, to the earth, the planets and the Sun and Moon, or parts of the zodiac, combined. With regard to the planets only, and parts of the zodiac, aspects are properly considered as made to them by the fixed stars, when the said planets and fixed stars may be posited on one and the same of those circles which are drawn through the poles of the zodiac; or, also, if they be posited on different circles, provided a trinal or s**tile distance between them may be preserved; that is to say, a distance equal to a right angle and a third part more, or a distance equal to two-thirds of a right angle; and provided, also, that the fixed stars be on such parts of the circle as are liable to be transited by any one of the planets. These parts are situated within the latitude of the zodiac, which circumscribes the planetary motions. And as far as the five planets are concerned, the aspects of the fixed stars depend upon the visible mutual conjunctions, or configurations, made in the forms above prescribed; but, with respect to the Sun and Moon, they depend on occultations, conjunctions, and succedent risings of the stars. Occultation is when a star becomes invisible by being carried under the rays of the luminary; conjunction, when it is placed under the luminary's centre; and succedent rising, when it begins to reappear on issuing out beyond the rays. In regard to the earth only, the aspects of the fixed stars are four in number, and are known by the common term of angles: to speak, however, more particularly, they are the oriental horizon, the meridian or mid-heaven above the earth, the occidental horizon, and the meridian or mid-heaven below the earth. And in that part of the earth where the equator is in the zenith, the whole of the fixed stars are found to rise and set, and to be above as well as below the earth, once in each revolution; because the situation of the poles of the equator, being in this manner on the plane of the horizon, thereby prevents the constant visibility or invisibility of any one of the parallel circles. But in other parts of the earth, where the pole of the equator is in the zenith, the fixed stars can never set nor rise; because the equator itself is then on the plane of the horizon, and circumscribes the two hemispheres (which it thus creates, one above and the other below the earth) in such a manner, that in one revolution every star must twice transit the meridian, some of them above, others below the earth. In other declinations, however, between these extreme positions of the equator, as just mentioned, there are certain of the circles always visible, and others never visible; consequently, the stars intercepted between the first of such circles and the poles can neither rise not set, but must, in the course of one revolution, twice transit the meridian; above the earth, if the said stars be on a circle always visible; but below the earth, if on a circle never visible. The other stars, however, situated on the greater parallels, both rise and set, and are found in each revolution once on the meridian above the earth, and once on that below the earth. In all these cases, the time occupied in proceeding round from any angle to the same again, must be everywhere equal in its duration, for it is marked by one sensible revolution; and the time occupied in pa**ing from either meridian*l angle to the angle diametrically opposite, is also everywhere equal; because it is marked by the half of one revolution. So, also, the pa**age from either horizontal angle to its opposite angle is again effected in the same equal portion of time, wherever the equator may be in the zenith, for it is then likewise marked by the half of an entire revolution; because on such a position of the equator, all the parallels are then divided, as well by the horizon as by the meridian, into two equal parts. But in all other declinations, the time of pa**age of a semi-circle above the earth is not equal to that of its pa**age below the earth, except only in the case of the equinoctial circle itself, which, in an oblique sphere, is the only one divided by the horizon into two equal parts, all others (its parallels) being bisected into dissimilar and unequal arcs. It follows, accordingly, that the time contained in the space between rising or setting, and either meridian, must be equal to the time between the same meridian and rising and setting; because the meridian divides equally such portions of the parallels as are above or under the earth. But in proceeding in an oblique sphere, from rising or setting to either meridian, the time occupied must be unequal; and in a right sphere, equal, because the entire portions above the earth are, in a right sphere only, equal to those below the earth; whence, for instance, in a right sphere, whatever stars may be together on the meridian must also all rise and set together, until their progress becomes perceptible by the poles of the zodiac; while, on the other hand, in an oblique sphere, whatever stars may be together on the meridian can neither all rise together nor set together; for the more southern stars must always rise later than those which are more northern, and set earlier. The aspects made by the fixed stars, in regard to the planets or parts of the zodiac, and the earth combined, are considered, in a general manner, by the rising, or meridian*l position, or setting of the same fixed stars in conjunction with any planet or part of the zodiac; but their aspects are properly distinguishable, by means of the Sun, in the nine following modes:-- 1. The first is called matutine subsolar, when the star is found together with the Sun in the oriental horizon. Of this aspect, one species is called the oriental, invisible, and succedent rising; when the star, at the commencement of its occultation, rises immediately after the Sun: another is called the precise oriental co-rising; when the star is found in partile conjunction with the Sun in the oriental horizon: another is the oriental, precedent, and visible rising; when the star, beginning to appear, rises before the Sun. 2. The second aspect is termed matutine location in the mid-heaven; when the star is found on the meridian, either above or below the earth, while the Sun is on the oriental horizon. And of this aspect, one species is called a succedent and oriental location in the mid-heaven, invisible; when, immediately after the Sun's rising, the star shall be found on the meridian: another is the precise oriental location in the mid-heaven; when, exactly as the Sun rises, the star is at the same time on the meridian; another is the oriental precedent location in the mid-heaven; when the star first shall come to the meridian above the earth, and the Sun may then immediately rise. 3. The third, called matutine setting, is when the Sun may be actually in the oriental horizon, but the star in the occidental. One of the forms of this aspect is called the oriental, succedent setting, invisible; when the star sets immediately after the Sun's rising: another is the precise oriental co-setting, when the star sets at the moment of the Sun's rising: another is the oriental, precedent, and visible setting, when the Sun does not rise until immediately after the setting of the star. 4. The fourth aspect is named meridian*l subsolar, and takes place when the Sun is actually on the meridian, but the star on the oriental horizon. Of this, one is diurnal and invisible; when the star rises while the Sun is posited on the meridian above the earth: another is nocturnal and visible; when the star rises while the Sun is placed on the meridian below the earth. 5. The fifth is called meridian*l location in the mid-heaven; when the Sun, as well as the star, may be at the same time on the meridian. Of this aspect, two sorts are diurnal and invisible; when the star is on the meridian above the earth, together with the Sun, or on that below the earth, diametrically opposite to the Sun. Two also are nocturnal, and of these, one is invisible; when the star is on the meridian under the earth, together with the Sun: the other, however, is visible; when the star is on the meridian above the earth, diametrically opposite to the Sun. 6. The sixth is meridian*l setting; when the star is found on the occidental horizon, while the Sun is on the meridian. Of this, one species is diurnal and invisible; when the star sets while the Sun is above the earth on the meridian: the other is nocturnal and visible; when the star sets while the Sun is on the meridian below the earth. 7. The seventh aspect is called vespertine subsolar; when the star is found on the oriental horizon, while the Sun is posited on the occidental horizon. One form of this aspect is the vespertine succedent rising, visible; when the star rises immediately after sunset: another is the precise vespertine co-rising; when the star rises and the Sun sets at one and the same time: another is the precedent, vespertine rising, invisible; when the star rises immediately before the Sun sets. 8. The eighth is named vespertine location in the mid-heaven; when the star is on the meridian, either above or below the earth, while the Sun is placed on the occidental horizon. Of this aspect, one kind is called a visible vespertine location in the mid-heaven; when the star is found there immediately after sunset: another is the precise vespertine location in the mid-heaven; when the star is found there at the moment of sunset; another is the vespertine precedent location in the mid-heaven, invisible; when the star arrives there immediately before sunset. 9. The ninth aspect is called vespertine setting; when the star, together with the Sun, is on the occidental horizon. One form of this aspect is the vespertine, succedent and visible setting; when the star, at the commencement of its occultation, sets immediately after the Sun: another is the precise vespertine setting; when the star sets at the same moment with the Sun: another is the precedent, invisible setting; when the star, before it emerges from its occultation, sets before the Sun.