Arcane Drawing Inspiration

The usage of arcane glyphs and diagrams to power a wide variety of occult rituals.
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nobody
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Arcane Drawing Inspiration

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Suppose a circle such that a straight line segment which touches the circle twice and passes through it's center always has length 2, or in other words, a circle with diameter 2. Division into even thirds may be done in a variety of ways, the most direct of which is done with three line segments originating at the center and moving outward such that the circumference and the area are evenly divided into thirds. The technique for this is simple and detailed in most basic texts on drawing geometric figures. For reference, see figure 1.
circle2-1.png
Figure1-A circle divided into thirds by central lines
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(a circle divided into three regions as cut like a pie)

Another method is to create a lesser central circle with an area one third of that of the greater circle, centered on the center of the greater circle. Then, draw a line segment from one edge of the greater circle, through the center, and across to the opposite edge, and subsequently erasing the portion of the line segment within the lesser circle. The diameter of the lesser circle should be a number that when multiplied by itself, is a third of diameter of the greater circle multiplied by itself. Using the reference circle with diameter 2, the lesser circle's diameter may be approximated as eight sevenths. Scale this appropriately to circles you draw.
circle2-2.png
Figure2-A circle divided into thirds by a central circle
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(a circle divided into three regions, a central circle, and then an exterior ring divided into halves)

The last method is to divide the circle's area with two lines, either with a common vertex, or as parallel lines. This technique is the least intuitive to the beginning geometrician to get correct, in part because it must be learned by long experience and practice as the solution is not easily calculated and looks deceptively uneven. However, it may be approximated by dividing the circumference of the circle into twelfths and marking first the central vertex, then placing marks five twelfths of the circumference out on either side, and connecting the second and third marks to the first; this is the common vertex approximation. For the parallel lines approximation, again divide the circumference of the circle into twelfths and place an initial mark, a second mark after five twelfths, a third mark after an additional twelfth, and the last mark after another five twelfths. The fourth mark and the first mark should be a twelfth apart.
circle2-3.png
Figure3-A circle divided into thirds by lines from a common vertex
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(a circle divided into three regions, a semi-circle on either side of a triangular wedge)

Submitted to the Library of Qamar, Natural Philosophy stacks for publication by Tii.
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