Do what thou wilt shall be the whole of the Law.
"In the sphere I am everywhere the centre, as she, the circumference, is nowhere found." AL II.3
In the sphere, every point on the surface is equidistant from the center, giving us a sublime expression of truth and integrity in a harmonized unity of perfected form. It is the three-dimensional version of the circle, which itself gives us a transcendental number called Pi and contains a radius that emanates from a central point.
"This book shall be translated into all tongues: but always with the original in the writing of the Beast; for in the chance shape of the letters and their position to one another: in these are mysteries that no Beast shall divine. Let him not seek to try: but one cometh after him, whence I say not, who shall discover the Key of it all. Then this line drawn is a key: then this circle squared in its failure is a key also. And Abrahadabra. It shall be his child & that strangely. Let him not seek after this; for thereby alone can he fall from it." AL III.47
The sphere and the circle are respectively, of the same nature as the planet we live on the solar system that our planet moves in. And yet we perceive the vertical and the horizontal as energy, described in the symbol of the cross of light. Further, the planets describe vertically aligned planes of being as we seem to move horizontally on the face of the Earth. Yet this is a transcendental reality described in Rosicrucian literature, defying even modern science, still.
"Also reason is a lie; for there is a factor infinite & unknown; & all their words are skew-wise." AL II.32
Crowley writes in his Minerval initiation for his version of the numerous O.T.O. bodies: “crosses and circles are therefore the true sign of Our Order.” Hadit as the manifestation of singularity, a ‘Logos’ provides differentiation in a field of unity, described by the circle. As such, in his message, he makes distinctions amongst us; kings and slaves, gods and dogs, et al. This is the circle divided and delineated by the cross within the circle, a failed square as noted in AL III.47. And as these four radii move from the center to the outer points we can project an infinite number of radii in the circle and in the sphere, though we normally divide the circle by 360 degrees or the 12 digits of the Zodiac in a three-fold count.
"I am the Magician and the Exorcist. I am the axle of the wheel, and the cube in the circle. "Come unto me" is a foolish word: for it is I that go." AL II.7
The circle squared is also a transcendental concept that belongs to Rosicrucian science. With the square itself, we are presented with a mathematical conundrum as the square root of two (1.414213562…), when multiplied by itself, does not return us to two. The number, when added to itself even brings us close to Pi (3.1416…). And of course, when this number expressed out into infinity is divided by itself, it returns us to Unity.
"Divide, add, multiply, and understand." AL I.25
"For I am divided for love's sake, for the chance of union." AL I.29
The unity may also be shown as Hadit moves to the perimeter to touch another’s center, giving us the Vesica Piscis. This shape also suggests the vagina, symbolized as the gate of Initiation. The Rosicrucians gave us this, covertly suggested by Isis leading Christian Rosencreutz to the 'Chemical Wedding'. Isis of course, is for us, Nuit in her highest expression and Babalon when considering that sphere called the Earth. And Hadit seems to move between these two, creating that line segment called the radius; that infinite Logos expressed in finite form.
"I am the secret Serpent coiled about to spring: in my coiling there is joy. If I lift up my head, I and my Nuit are one. If I droop down mine head, and shoot forth venom, then is rapture of the earth, and I and the earth are one." AL I.26
Perdurabo as the name to be worshipped even figures in well here (Cf. my article: The Fire Opal and the work of Runar): In Hebrew Qabalah (the Jews have the half, so it is only natural that any analysis of AL be based on the Hebrew), P is 80, the lower line of a rectangular box box that can be traced into the Tree-of-Life. the R's are Resh; the Sun in the center of this box as if the Circle is Squared, which is a key also, according to Liber AL. The Daleth is the top line of the rectangle that can be traced onto the Tree. And that is followed by AB the force of attraction; the father…and O; Ayin, the Devil and the path that leads to Tiphareth; the Son as much as the Sun, but also by the shape of this letter in English suggests the vagina of the daughter. And in our English Qabalah, Perdurabo equals 640, which readily reduces to 10, the number of the Tree-of-Life.
"Lift up thyself! for there is none like unto thee among men or among Gods! Lift up thyself, o my prophet, thy stature shall surpass the stars. They shall worship thy name, foursquare, mystic, wonderful, the number of the man; and the name of thy house 418." AL II.78
The Phi Ratio may also be inferred from the "circle squared." This ratio, calculated by the ancient Greeks, shows two line segments, with the relationship of one to the other being equal to the relationship of that other to the two segments, connected together. This creates an aesthetic effect when these two lengths are employed in a rectangle (of which a square is but a specific form). The ancient Greeks built their Parthenon to this specification with a calculated ration of 1:161803398. Proportions in nature and of the human body also relate to this ratio, as well as the Vesica Piscis, which to the ancients represented the union of Heaven and Earth. The Phi ratio may also be applied to the Pentagram, the star of humanity.
Love is the law, love under will.