Ptolemy's Tetrabiblos

by Ptolemy

[41] “Of the fixed stars in general,” Whalley says, “Those of the greatest magnitude are the most efficacious; and those in, or near, the ecliptic, more powerful than those more remote from it. Those with north latitude and declination affect us most. Those in the zenith, influence more than others, more remote. Likewise such as are in partial conjunction with, or in the antiscions of any planets, or which rise and set, or culminate with any planet, or are beheld by any planet, have an increase of power: but of themselves the fixed stars emit no rays.”

[42] This sentence shows the futility of the objection raised against astrology (and mentioned in the Preface to this translation) that the signs have changed and are changing places. It is clear from this sentence that Ptolemy ascribes to the 30 degrees after the vernal equinox, that influence which he has herein mentioned to belong to Aries; to the next 30 degrees, the influence herein said to belong to Taurus; and so of the rest of the zodiac. We should rather say that the stars have changed places, than that the parts of heaven, in which they were once situated, have done so. Ptolemy himself seems to have foreseen this groundless objection of the moderns, and has written, in the 25th chapter of this book, what ought completely to have prevented it. It has certainly been one of the misfortunes of astrology to be attacked by people entirely ignorant of its principles.

[43] In other words, the Sun then begins to diminish his declination, which, at the first points of the said signs, is at its greatest amount.

[44] Whalley, in his note upon this chapter, seems to have been surprised that no mention is made here by Ptolemy of the conjunction; but he overlooked the fact that the chapter treats only of parts of the zodiac configurated with each other; and that it was not possible for Ptolemy to conceive how any part could be configurated with itself. It is, therefore, by no means wonderful that the conjunction is not inserted here along with the rest of the aspects; although it is frequently adverted to in subsequent chapters, and its efficacy particularly described.

[45] From the tenor of this chapter it was formerly doubted whether the author intended to admit in his theory only zodiacal aspects, and to reject those which are called mundane; but Placidus has referred to the 4th Chapter of the 8th Book of the Almagest (which will be found in the Appendix to this translation) to prove that Ptolemy distinctly taught two kinds of aspect; one in the zodiac and one in the world. Whalley quotes the opinion of Placidus, which he says is farther confirmed by the 12th Chapter of the 3rd Book of this very treatise, where it is stated that the ascendant and the eleventh house are in sextile to each other; the ascendant and the mid-heaven in quartile; the ascendant and the ninth house in trine; and the ascendant and the occidental angle in opposition; all which certainly seems to be applicable to mundane aspects in particular.

[46] Whalley has a very lengthy note upon this and the preceding chapter, to show that Ptolemy here speaks of zodiacal parallels, or parallels of declination, and to point out the necessity of observing a planet’s latitude, in order to ascertain its true parallels. It is, however, to be recollected, that the parallels now alluded to are distinct from the mundane parallels, which are equal distances from the horizon or meridian, and are considered by Ptolemy in the 14th and 15th Chapters of the 3rd Book of this work; although not under the express name of mundane parallels.

[47] It has never been very clearly shown how the followers of Ptolemy have reconciled the new aspects (called the semiquadrate, quintile, sesquiquadrate, biquintile, &c.) with the veto pronounced in this chapter. Kepler is said to have invented them, and they have been universally adopted; even Placidus, who has applied Ptolemy’s doctrine to practice better than any other writer, has availed himself of them,† and, if the nativities published by him are to be credited, he has fully established their importance.

Salmon, in his “Horæ Mathematicæ,” before-mentioned, gives a long dissertation (from p. 403 to p. 414) on the old Ptolemaic aspects, illustrative of their foundation in nature and in mathematics; and, although his conclusions are not quite satisfactorily drawn, some of his arguments would seem appropriate, if he had but handled them more fully and expertly; particularly where he says that the aspects are derived “from the aliquot parts of a circle, wherein observe that, although the zodiac may have many more aliquot parts than these four (the sextile, quartile, trine, and opposition), yet those other aliquot parts of the circle, or 360 degrees, will not make an aliquot division of the signs also, which in this design was sought to answer, as well in the number 12, as in the number 360.” The passage in which he endeavours to show that they are authorized by their projection, also deserves attention.

All Salmon’s arguments, however, in support of the old Ptolemaic aspects, militate against the new Keplerian ones; and so does the following extract from the “Astrological Discourse” of Sir Christopher Heydon: “For thus, amongst all ordinate planes that may be inscribed, there are two whose sides, joined together, have pre-eminence to take up a semicircle, but only the hexagon, quadrate, and equilateral triangle, answering to the sextile, quartile, and trine irradiated. The subtense, therefore, of a sextile aspect consisteth of two signs, which, joined to the subtense of a trine, composed of four, being regular and equilateral, take up six signs, which is a complete semicircle. In like manner, the sides of a quadrate inscribed, subtending three signs, twice reckoned, do occupy likewise the mediety of a circle. And what those figures are before said to perform” (that is, to take up a semicircle) “either doubled or joined together, may also be truly ascribed unto the opposite aspect by itself; for that the diametral line, which passeth from the place of conjunction to the opposite point, divideth a circle into two equal parts: the like whereof cannot be found in any other inscripts; for example, the side of a regular pentagon” (the quintile) “subtendeth 72 degrees, of an octagon” (the semiquadrate) “but 45; the remainders of which arcs, viz. 108 and 135 degrees, are not subtended by the sides of any ordinate figure.”

† Except the semiquadrate, which he has not at all noticed.