The Elements of Hydrostatics

equal to the rectangle contained under the highest part of its axis, and the rational line of the parabola.

A small floral ornament (fleuron) serves as a decorative paragraph marker.

If you desire the following 12th proposition of the first book described above, see how longer and darker material is turned into something short and clear.

If a cone is cut by a plane through the axis, and is also cut by another plane cutting the base of the cone along a straight line which is perpendicular to the base of the triangle through the axis, and the diameter of the section produced meets one side of the triangle through the axis outside the vertex of the cone, the straight line drawn from the section equidistant to the common section of the cutting plane and the base of the cone up to the diameter of the section will be capable of [forming] a space adjacent to the line, to which the line that is set in a straight direction with the diameter of the section is subtended by an angle outside the triangle, having the same proportion as the square of the line which is drawn equidistant to the diameter from the vertex of the section to the base of the triangle has to the rectangle contained by the parts of the base created by it, having as width the line which is cut off from the diameter, placed between itself and the vertex of the section, and exceeding by a figure similar and similarly placed to that which is contained by the line subtended by the angle outside the triangle and that along which those lines applied to the diameter are capable. Let such a section be called a hyperbola a conic section formed by a plane cutting both nappes of a cone.

The translation thereof is as follows.

The square of the ordinate a line segment perpendicular to the axis of a conic section of the hyperbola is equal to the rectangle contained under its axis