Definitions of the circle and quadrature of curved surfaces
Numbered propositions defining the circle, its center and circumference, and the ratio of circles as squares of their diameters
The leaf sets out geometrical definitions under the heading 'Quadratures of infinite variety of curvilinear surfaces.' Two parallel statements observe that the compass-opening that describes a circle enters twice into the diameter and six times into the circumference. Numbered propositions then define the circle as a plane surface bounded by one curved line called the circumference, with a central point (the center) from which all straight lines drawn are equal, and conclude that circles are equal when their circumferences pass through each other's centers, the proportion of circle to circle being as square to square formed by multiplying the diameters into themselves.
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Definition of the circle, its circumference and center
The circle is defined as a plane surface surrounded by a single curved line called the circumference, in the middle of which is a point called the center of the circle, from which all straight lines drawn are equal among themselves. This 'First' proposition establishes the terms for the constructions that follow.
The compass-opening in diameter and circumference
The length of the space between the points of the compass that describes the circle enters twice into the diameter of that circle and six times into its circumference. A second, parallel statement repeats the observation for the straight line spanning the compass points.
Circles are in the ratio of the squares of their diameters
Circles are equal among themselves when, at their intersections, their circumferences pass over their centers. The proportion from circle to circle is as that from square to square, formed by the multiplication of the diameters of those circles into themselves.