To these should be added his version from the Arabic (which language he acquired for the purpose) of the treatise of Apollonius De sectione rationis, with a restoration of his two lost books De sectione spatii, both published at Oxford in 1706; also his fine edition of the Conics of Apollonius, with the treatise by Serenus De sectione cylindri et coni (Oxford, 1710, folio).
The generality of treatment is indeed remarkable; he gives as the fundamental property of all the conics the equivalent of the Cartesian equation referred to oblique axes (consisting of a diameter and the tangent at its extremity) obtained by cutting an oblique circular cone in any manner, and the axes appear only as a particular case after he has shown that the property of the conic can be expressed in the same form with reference to any new diameter and the tangent at its extremity.
In 1522 there was published an original work on conics by Johann Werner of Nuremburg.
Conjointly with Giovanni Borelli he wrote a Latin translation of the 5th, 6th and 7th books of the Conics of Apollonius of Perga (1661).
His treatise on Conics gained him the title of The Great Geometer, and is that by which his fame has been transmitted to modern times.
The Conics of Apollonius was translated into Arabic by Tobit ben Korra in the 9th century, and this edition was followed by Halley in 1710.
A method of generating conics essentially the same as our modern method of homographic pencils was discussed by Jan de Witt in his Elementa linearum curvarum (1650); but he treated the curves by the Cartesian method, and not synthetically.
If one of the foci be at infinity, the conics are confocal parabolas, which may also be regarded as parabolas having a common focus and axis.
In it Maclaurin developed several theorems due to Newton, and introduced the method of generating conics which bears his name, and showed that many curves of the third and fourth degrees can be described by the intersection of two movable angles.
From this conception all the properties of conics can be deduced.