By Dorian Grimault, astrologer · Published · updated
The sesquiquadrate aspect links two bodies 135° apart, a square and a half. Ptolemy did not know it: it is one of the aspects Johannes Kepler proposed in the 17th century. Discreet, it is hard to spot by eye on a wheel, and it is the aspect grid that brings it to light. Here is its origin, its tolerance, its place in your birth chart report, and the two sesquiquadrates of Camille Morel, AstralPro's sample chart (fictional data).
The Latin prefix sesqui means “one and a half”: 135° is 90° plus 45°, or three eighths of the circle. The sesquiquadrate belongs to the same family as the square (90°) and the semi-square (45°), that of the divisions of the circle by eight. It is also found under the names sesquisquare or trioctile.
Unlike Ptolemy's aspects, it is not counted in whole signs: 135° is four and a half signs. Two bodies in sesquiquadrate can therefore fall in very different signs depending on their degrees, and only calculating the gap brings it to light.
Johannes Kepler (1571-1630), an astronomer who practiced astrology as imperial mathematician, wanted to ground astrology in geometry and musical harmony rather than in the signs. According to David Plant's study of him on Skyscript, he added three new aspects to Ptolemy's: the quintile (72°), the biquintile (144°) and the sesquiquadrate (135°), which he likened to the minor sixth, in the ratio 5 to 8. He rejected other divisions, such as the one by seven, because the corresponding figures cannot be constructed with ruler and compass.
William Lilly took up the aspect a few years later. In Christian Astrology (1647, book III), he gives the table of “new aspects” with their symbols, including the sesquiquadrate of 135°, and notes at the end of the work that the semi-square and the sesquiquadrate “participate of the nature of the square.”
Lilly does not stop at defining it: he uses it in the directions of an English merchant's nativity, which fills the end of his book III. When the Midheaven reaches the sesquiquadrate of Mars, he warns that the native's reputation could suffer, “in some small measure,” from false aspersions. The tone is telling: a sesquiquadrate signals a real but limited trouble, a second-order tension.
That is still how it is read. The legend of the aspect table in your report groups the semi-square and the sesquiquadrate together: minor frictions, background tension. The two functions linked do not agree spontaneously; they spur each other on through a kind of discomfort, which pushes toward adjustment rather than rupture.
In your birth chart, the orb of the sesquiquadrate is 3°: two bodies 132° to 138° apart are in sesquiquadrate. That is the same tolerance as the semi-square, narrower than the quincunx's (5°), and the same for all bodies. The report spells it Sesquiquadrate, as a single word, and its name appears in the orange of the squares.
Like any minor aspect, it appears in the complete natal grid, but neither on the wheel nor in the Book's table, which is reserved for major aspects. It rarely makes it into the aspects the chapters discuss, where the majors come first. Its line is not silent for all that: a sesquiquadrate under 3° is among the lines the Reading column comments on. In Camille's grid, the Lilith-Midheaven sesquiquadrate, on line 9, even comes ahead of every square in her chart.
Camille Morel, AstralPro's sample chart (fictional data), has two sesquiquadrates, both to Lilith, at 14°01' Aries:
Both lines have their reading, since the column here covers the first twenty lines of the grid. Neither is drawn on the wheel, and neither is among the twenty aspects discussed in chapter I, all of them majors in this chart.
The sesquiquadrate and the semi-square are complementary: 135° and 45° add up to 180°. A body in sesquiquadrate to a point is therefore always in semi-square to the opposite point. This helps to understand what the grid does not write twice.
In Camille's chart, Lilith at 14°01' Aries is sesquiquadrate the Midheaven, at 0°15' Virgo. At the same time she is 43°46' from the Imum Coeli, at 0°15' Pisces, a semi-square with a 1°14' orb. The grid connects only the Ascendant and the Midheaven: this contact appears there only once, as the sesquiquadrate. Both readings describe the same tension on the axis of public life and home. It is not a missing aspect: it is the same contact, seen from the other end of the axis.
Lilly, who introduces them together, also treats them as a family: in his directions, the Ascendant reaching the sesquiquadrate of Mercury means the native “is still questioned for accounts,” while the Part of Fortune at the semi-square of the Moon raises the fear that former associates will come to trouble him again.
On a wheel, a sesquiquadrate does not jump out: it corresponds to no simple distance between signs. To estimate it, add four and a half signs to a body's position. From Lilith at 14°01' Aries, four signs take you to 14°01' Leo, and half a sign more to 29°01' Leo: Camille's Midheaven, at 0°15' Virgo, is 1°14' from that point.
The simplest way is still to read the Orb column of your grid: the aspects are ranked there from tightest to widest, majors and minors together. A sesquiquadrate can slip in very high, ahead of wider squares or trines, and that is a sign it deserves a closer look.
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