Primary Directions: Placidus vs Regiomontanus

Primary directions are one of the oldest and most venerated predictive techniques in astrology. Their origin dates back to Hellenistic times during which direction of the natal Ascendant through the terms (bounds) of the signs utilizing the ascensional times of the signs was a basic technique. Ptolemy described a method of primary directing in the Tetrabiblos III.10 in his explanation of how to estimate the length of life. According to Ptolemy, there were three possible scenarios, each of which utilized a distinct timing technique:

1) if the Asc (on the eastern horizon) signified the life of the native and a killing planet or its aspect were rising toward the Asc, the arc on the Equator measured in oblique ascension would indicate the length of life, with one equatorial degree being equivalent to one year of life.

2) if the MC (on the meridian axis) signified the life of the native and a killing planet or its aspect were rising toward the Asc, the arc on the Equator measured in right ascension would indicate the length of life, with one equatorial degree being equivalent to one year of life.

3) if a point or planet intermediate between the horizon or meridian signifies the life of the native (for example, the Sun, Moon or Part of Fortune which were possible “hylegs”), then the arc on the Equator between the hyleg and the killing planet would need to be measure by the method of proportional semi-arcs, utilizing temporal hours. Here is what Ptolemy wrote about this third scenario (from Robbins translation, text capitalized and italicized by me for emphasis):

“For a place is similar and the same if it has the same position in the same direction with reference both to the horizon and to the meridian.
This is MOST NEARLY TRUE of those which lie upon one of those semicircles which are described through the sections of the meridian and the horizon, each of which at the same position makes NEARLY the same temporal hour.”

Ptolemy apparently realized that the mathematic procedure for calculating directions via proportional semi-arcs was quite complex, so he offered an alternative using “semicircles described through the sections of the meridian and horizon, which mark nearly the same temporal hour.” Regiomontanus in the 15th century developed a mathematical technique grounded in spherical trigonometry, which he learned from a  twelfth-century text by the Andalusian scholar Jabir ibn Aflah and to which he contributed further advancements. A translation of Regiomontanus’ book on triangles is available in English.

Regiomontanus apparently was unable to operationalize in a mathematical procedure Ptolemy’s method of proportional semi-arcs, so he opted instead for Ptolemy’s suggested close approximation to the method, utilizing “circles of position” (the second sentence in the quote from Ptolemy above). These circles of position were great circles, whose center was the center of the Earth, and which passed through the body of a planet creating a kind of artificial horizon circle (or plane in 3-dimensional space) which every point or planet of a birth chart would have to intersect at some moment during the 24-hour rotation of the Earth after the moment of birth. Using spherical geometry Regiomontanus was able to calculate and closely approximate the timings of the perfection of primary directions to intermediate points in the horoscope.

William Lilly understood that the Regiomontanus “circle of position” method was a close approximation to the method originally proposed by Ptolemy in the 2nd century, but he also realized that there was no method available to calculate proportional semi-arc directions accurately, so at the time the Regiomontanus method (and the Tables he published) was the best option available. Lilly wrote in Book 3 of Christian Astrology (bold mine):

“…before Regiomontanus did frame Tables, Antiquity was much perplexed in directing a Significator which was not upon the cusps of the House by reason they had no exact method for finding out the true circle of position of any planet, when elongated from the cusps of a house; they did then direct either by Tables of Houses fitted for the latitude where the native was born, or by the Diurnal and Nocturnal Horary Times, a laborious, difficult and obscure way, yet the only method Ptolemy left…”

Lilly says here that the only method Ptolemy left was that of proportional semi-arc (using diurnal and nocturnal horary times, that is, planetary hours) but doing what Ptolemy did was too laborious, difficult and obscure mathematically, so the use of Regiomontanus method and Tables was the reasonable, though less accurate, alternative.

Lily also noted in Book Three that the primary directions calculated by the Regiomontanus circles of position for planets and points intermediate between the horizon and meridian could not be used reliably in chart rectification. Lilly states explicitly that only primary directions to the Angles are reliable when doing chart rectification. Directions to other hylegiacal points, such as the Sun, Moon or Part of Fortune, will not help you to rectify a chart (bold mine): “… verily a Nativity cannot well be rectified but by Accidents belonging to one or both those Angles [MC or Asc]. The Sun in every Nativity is a principal Significator, so is the Moon and the Part of Fortune, yet a significant rectification from these cannot be had.”

It should not be surprising that a method, like that of Regiomontanus, which is only an approximation to Ptolemy’s actual and recommended method of proportional semi-arc for intermediate points, is not reliable for rectifying a chart. Ptolemy also changed the prevailing definition of the Part of Fortune used by practicing astrologers of his epoch, so that directions to the Part of Fortune, as defined by Ptolemy, were really directions to the Part of Daimon in night charts, which would make the use of his version of the Part of Fortune inconsistent with the standard of astrological practice in Ptolemy’s time. Ptolemy was a natural scientist and not a practicing astrologer. Lilly followed Ptolemy is re-defining the Part of Fortune from the point of view of natural science and discarding the original definition in which its pairing with the Part of Daimon was symbolically and philosophically significant. Because Lilly was using Ptolemy’s altered definition of the Part of Fortune, it is not surprising that he found it unreliable for rectification.

Fortunately, Placidus in the mid-17th century found a way to mathematically operationalize Ptolemy’s original method of directing intermediate points between the Angles of a horoscope, utilizing “horary times.” Although Ptolemy did not specifically link his method of primary directing to the domification of a chart, later astrologers appear to have made this connection. Deb Houlding notes that the Placidus House system was described long before Placidus was born (italics mine): “The Placidus system is named after the Italian Benedictine monk, Placidus de Titis (1603-1668), who popularized its use during the 17th century. Again, it is accepted that Placidus did not invent the method; tables were already available for it in 1604, a year after Placidus’s birth, and it earlier appeared on an astrolabe in 1305. The 12th century Hebrew astrologer Abraham Ibn Ezra acknowledged it as the system employed by Ptolemy, and Placidus appears to support this view within his work where he respectfully notes ‘I desire no guides but Ptolemy and reason’.”

The work of Placidus was brilliant and inspired the British astrologers to cease using the method of Regiomontanus and instead adopt the method of Placidus, based on proportional semi-arc, as Ptolemy had originally proposed. To better understand the conceptual framework of Placidus, I recommend watching Luis Ribeiro’s Astrology Podcast #313 with Chris Brennan in which he reviews the mathematics of house division. Here is a quote from the translation of Placidus into English in which he states the the circle of position method is inconsistent with Ptolemy’s teachings:

It is important to realize that the method of primary directing is distinct from the method of house division, although, as Lilly pointed out, traditionally astrologers “did then direct either by Tables of Houses fitted for the latitude where the native was born.” The fact is that you can do Placidian or Regiomontanus directions with a chart using any house system.

From the 15th century, when Regiomontanus first published his method of circles of position and his Tables, until late in the 17th century when the work of Placidus became known, the main method of primary direction was that of Regiomontanus. It was used by renowned astrologers such as Lilly in England and by Morin de Villefrache in France. As mentioned, Lilly realized that the only method proposed by Ptolemy was that of proportional semi-arc for intermediate points in a chart, but he valued the ease and convenience of using the Regiomontanus Tables despite the decrease in the accuracy of the timing of events. He did notice, however, that he was unable to use Regiomontanus circles of position to reliably rectify a chart when directing to the Sun, Moon or Part of Fortune when they were not on an Angle or house cusp.

Often directions to intermediate points in either system (Placidus or Regiomontanus) are quite close, within a few months, but not uncommonly they can indicate timings years apart, which would explain the inadequacy of the Regiomontanus primary directions for intermediate points when used for chart rectification. Primary directions to the Angles are done the same way by both Placidus and Regiomontanus, following the method originally laid down by Ptolemy, so they are more reliable for rectification.

Some modern astrologers have promulgated the belief that primary directions are an extremely precise timing technique. Traditionally, primary directions grew out of a time-lord technique (directing the Asc through the bounds) and were used in a similar manner to identify years in which certain events might occur. Both Lilly and Morin allowed primary directions a period of influence of about 2 years or longer. Morin states that the false claim that primary directions provide precise timing of events was a common tactic used by critics to discredit astrology. He cites Sixtus ab Hemminga who claimed astrology is without validity because primary directions do not provide precise dates for the occurrence of the events which they signify. Morin makes a clear comparison of primary directions to time lords when he writes in Book 22, Chapter 6 (my translation and italics): “when the direction of a promissor to a significator becomes exact, its effect can be delayed by a year or two until a conformable [solar] revolution occurs; and even if the effect were to occur at the very moment of perfection, the force of the direction can remain in effect until a different promissor arrives at the significator [by primary motion].”