IN THE SYNOPSIS

...hyperbolas and circles; and the discovery of a straight line equal to a parabola will be added.

VI. Next follow the spherical works, which are discussed by Theodosius, Menelaus, and Maurolycus. However, we have placed Trigonometry before these, as it measures triangles that are rectilinear, spherical, and mixed-line. To these, you can now add the area of spherical triangles formed by three great circles The "great circles" of a sphere are circles that have the same circumference as the sphere itself, like the equator on a globe.. This area is proportional to the great circle of the sphere as the difference of its three angles is to two right angles. For example, if the difference is one right angle, the area of the triangle will be half that of the great circle, as our Geometer has demonstrated.

Following the spherical works of Maurolycus are Autolycus on the Moving Sphere, Theodosius on Habitations, the Phenomena of Euclid, and Astronomical Cosmography combined with a comparison of habitations, which completes the section on spherical geometry. To these, we can add the theory of the planets once the work of Aristarchus of Samos on the System of the World comes into our hands, so that nothing at all is missing from this portable volume.

VII. Next follows Apollonius. To his four books are added four others on the same subject of conic sections by the most distinguished man, Claude Mydorge, who advances the work of the Pergaean original: "Pergæanos." This refers to Apollonius of Perga, the ancient Greek mathematician known as the "Great Geometer" for his work on conics. further. Once he has published the four remaining books he has prepared, there will be no reason for you to seek the four lost books of Apollonius. Nor will you desire anything further for the perfection of Optics The study of sight and the behavior of light., Catoptrics The branch of optics dealing with reflection, such as mirrors., or Dioptrics The branch of optics dealing with the refraction of light, such as through lenses.. Indeed, there is hardly anything to be said regarding reflections, refractions, the proper use of dioptrae Instruments used for sighting or measuring angles in surveying and astronomy., and other matters pertaining to vision that you cannot expect from him. I previously mentioned this on page 193 of my Hydraulics.

VIII. You will later read the condensed Collection of Pappus. In his seventh book, he lists many treatises published by the ancients, some of which have perished over time, while others still exist or have recently been restored by very learned men. Among these are the Data of Euclid, which Alealmus Jacques Aleaume, a French mathematician and engineer who studied under François Viète. has reduced into a summary and a table for this purpose.