The circle, semicircle, segments, and kinds of triangle
Definitions of the circle and its parts, and the three natures of triangle
Folio 140r defines the circle as a plane figure bounded by one line, the circumference, with a center from which all radii are equal, and the diameter as the line through the center that halves it. It goes on to the semicircle, to the greater and lesser segments of a circle, and to the classification of rectilinear figures as triangular, quadrilateral, or multilateral. The page ends by dividing triangles into equilateral, isosceles, and scalene, matched to the acute-angled (oxygon), right-angled (orthogon), and obtuse-angled (amblygon) kinds, each with a marginal figure.
On this page
The circle and its diameter
The circle is a plane figure contained by a single line, the circumference, with a middle point (the center) from which all straight lines drawn to the circumference are equal. The diameter is a straight line that, passing through the center to its ends on the circumference, divides the circle into two equal parts.
Semicircle and circular segments
The semicircle is bounded by the diameter and half the circumference. A segment (portion) of the circle is bounded by a straight line and part of the circumference, and may be greater or lesser than the half-circle. Rectilinear figures are then divided into triangular, quadrilateral, and multilateral.
The three kinds of triangle
Triangles are of three natures: three equal sides, two equal sides, or three unequal sides. These are named oxygonia, orthogonia, and amblygonia; the oxygonia has all three angles acute, the orthogonia one right and two acute, the amblygonia one obtuse and two acute.