Square

The square is an aspect of ninety degrees, formed when two planets stand a quarter of the circle apart. It is one of the five major, or Ptolemaic, aspects, and the foremost of the hard or challenging aspects. Ninety degrees links signs of the same mode but incompatible element, fire with water or air with earth, so the planets involved work at cross purposes, and the tradition reads the square as friction, obstacle, and the pressure that forces action. Yet it is not read as purely negative: the tension of a square is held to be the spur to effort and achievement, the resistance against which strength is built. It is given one of the wider orbs among the aspects. These are the interpretive conventions of the astrological tradition for this angular relation, in which the square supplies the dynamic challenge that the harmonious aspects lack.

Ptolemy's Tetrabiblos, compiled in Alexandria in the second century CE, calls the square a quartile, the figure of signs three apart, and ranks it with the opposition among the two hard aspects of the four he names in Book I.13, alongside the trine and sextile; the conjunction he treats separately as no aspect at all. Hellenistic practitioners such as Vettius Valens, writing his Anthology around 175 CE, worked the square by whole sign and read the relation as directional: of two planets so placed, the one standing in the tenth sign counted from the other was held to overcome it, an asymmetry that degree-based orb systems, which treat the square as a single mutual figure, generally no longer preserve. The wider orb usually granted the square reflects how forcefully the tradition has always rated this contact.

Ninety degrees is a quarter of the circle, which is why the square belongs to the fourth harmonic and shares its family with the semi-square and the sesqui-quadrate. Where it differs from its relatives is in status: the square has been a major aspect in every system that has used aspects at all, while the eighth-harmonic angles were latecomers and remain optional.

The older way of finding a square is by sign. Signs of the same modality, cardinal with cardinal, fixed with fixed, mutable with mutable, stand three signs apart and are therefore in square to one another as whole signs, regardless of the exact degrees involved. This is why the modalities and the squares are the same fact stated twice. Degree-based practice narrows this: a square exists when the angular distance falls within an allowed orb of ninety degrees, and a planet at the beginning of a cardinal sign has no degree square to a planet at the end of the next cardinal sign, though both sit in squared signs. Charts read the two ways diverge most sharply here, because the square is the aspect people act on.

The rank of the square has also moved. Traditional sources treat it as straightforwardly harmful, one of the two aspects of enmity alongside the opposition, and pair it with the malefic planets. Twentieth century practice recast it as productive difficulty, the friction that makes a chart do something rather than merely be something. The angle did not change; the reading of what difficulty is for did. Both positions are still held, and a reader who does not say which one they are working from is reporting a conclusion without its premise.

The square is part of the Hellenistic aspect doctrine codified by Ptolemy, its geometry that of the fourfold division of the circle, and its glyph is simply a plain open square, the regular quadrilateral that a ninety-degree division inscribes. Like the trine, the square's sign was not given a dedicated codepoint of its own when aspect symbols were added to the Unicode Standard; it is written instead with the general geometric character WHITE SQUARE at U+25A1, a mark used across mathematics and typography for the same shape, so the aspect glyph and the ordinary drawn square are, in digital text, one and the same character rather than two related but distinct signs, as the conjunction and opposition are.

The mark itself is old and stable: square aspect signs are attested with the rest of the aspect set in the medieval Byzantine codices copying Hellenistic Greek horoscopes, and the glyph needed almost no adjustment when astronomical and astrological tables began to be set in type during the Renaissance, since a square drawn with a straightedge and one set in a printer's font are naturally close to identical. That continuity is part of why the square, alongside the trine, never needed a purpose-built astrological codepoint when the Unicode Standard incorporated aspect symbols: the ordinary geometric shape already did the job a specialised mark serves for the conjunction, opposition, sextile and several of the minor aspects.