ON APOLLONIUS, FROM PAPPUS.

An ornamental woodcut initial "E" features a seated figure and architectural elements.When Apollonius had completed the four books of Conics by Euclid and added four others, he produced eight books of conics. However, Aristaeus, who writes on the things that have been handed down to this time, called the five books of solid loci that cohere with the conics original: "solidorum locorum libros quinque conicis cohærentes". And those who were before Apollonius called the three conic lines the section of an acute-angled cone, the section of a right-angled cone, and the section of an obtuse-angled cone, respectively. Since three lines are produced in each of these three differently cut cones, Apollonius, being in doubt, as it appears, as to why those who had finished this treatment before him called one the section of an acute-angled cone, which can also be the section of a right-angled and obtuse-angled cone; another the section of a right-angled cone, which can also be found in an acute-angled and obtuse-angled cone; and the third the section of an obtuse-angled cone, which can also exist in an acute-angled and right-angled cone; he changed the names. That which is named the section of an acute-angled cone, he calls an ellipse a deficiency; that of the right-angled, a parabola a placement side by side; and that of the obtuse-angled, a hyperbola an excess, imposing a name on each from some property of its own. For a certain space compared to a certain line is deficient by a square in the section of an acute-angled cone; in the section of an obtuse-angled cone, it exceeds by a square; and in the section of a right-angled cone, it neither lacks nor exceeds. This happened to them because they did not consider that, according to only one case of the plane cutting the cone and producing the three lines, a different line is made in each of the cones, which they named from the property of the cone. For if the cutting plane is drawn equidistant to one side of the cone, only one of the three lines is always produced, which Aristaeus called the section of that cone.

FROM EUTOCIUS AND GEMINUS.

Apollonius the geometer was born in Perga, which is a city of Pamphylia, in the time of Ptolemy Euergetes, as Heraclius records in the life of Archimedes. He also writes that Archimedes was indeed the first to have approached the conic theorems, but that Apollonius, when he had discovered them, published them as his own, though they had not yet been published by Archimedes. I do not believe this to be true, for Archimedes seems to make mention of an older foundation of conics in many places.