Quadrilaterals, parallel lines, and the five postulates
Euclid's naming of four-sided figures and his five geometric postulates
Folio 139v names and defines the four-sided figures: the square, the oblong rectangle, the rhombus (elmuayn), the rhomboid, and all other quadrilaterals lumped together as "elmuariffe" or irregular. It then defines equidistant (parallel) lines as those that, produced both ways in the same plane, never meet however far extended. The lower half lists Euclid's five postulates, each with a small figure, running from drawing a straight line between any two points to two straight lines enclosing no surface.
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The named quadrilaterals
Among four-sided figures one is the square; another the oblong (long tetragon), right-angled but not equilateral; another the rhombus (elmuayn), equilateral but not right-angled; and another resembling it whose opposite sides and angles are equal yet is neither equilateral nor right-angled. All the rest are called elmuariffe, that is, irregular.
Definition of parallel lines
Equidistant lines are those which, set in the same surface and produced on both the one side and the other, do not meet even if extended to infinity. A pair of parallel strokes labelled "paralelle" illustrates the definition.
Euclid's five postulates
A straight line may be drawn from any point to any other and extended as far as one pleases; a circle may be described on any center with any radius; all right angles are equal; if a line crossing two lines makes the interior angles on one side less than two right angles, those lines meet on that side; and two straight lines enclose no surface.
