Conic Sections

Conic Sections

‘CONIC SECTIONS: If a Circle describ’d upon stiff Paper (or any other pliable Matter) of what Bigness you please, be cut into two, three, or more Sectors, either equal or unequal, and one of those Sectors be so roll’d up as that the Radius’s may exactly meet each other, it will form a Conical Superficies.’

John Ward, The Young Mathematician’s Guide, p. 356.

A conic section is any of three types of shape formed by slicing a cone with a flat plane. The three types of shape that occur are called an ellipse, a hyperbola and a parabola. Apollonius of Perga (c.262 BC-c.190 BC) was an astronomer and mathematician in ancient Greece. Although often overshadowed by the great inventor Archimedes who lived around the same time, Apollonius’ name became synonymous with the branch of geometry known as conic sections. He is most famous for his work Conics: a treatise of eight books of which seven have survived to the modern day. A 1566 edition, printed at Bologna, was collected by Worth and bound, in one volume, together with his 1558 Aldine Archimedes.

Apollonius of Perga, Conicorum libri quattuor vnà cum Pappi Alexandrini lemmatibus, et commentariis Eutocii Ascolonitae. Sereni Antinsensis philosophi libri duo nunc primum in lucem editi. Quæ omnia nuper Federicus Commandinus (Bologna, 1566), p. 5.

The figure above comes from Apollonius’ publication on conic sections which is the earliest text on the subject in Edward Worth’s collection. It features alongside other influential works such as L’Hopital’s Traité analytique des sections coniques (Paris 1707), and Van Ceulen‘s De circulo et adscriptis liber (Leiden 1619).

Also of great interest to Worth was another geometer named Robert Steell (d. 1726). His work A treatise of conic sections was published in Dublin in 1723, and in Steell’s own words demonstrates ‘the principal Properties of the Conic Sections, in a most easie manner’.

Robert Steell, A treatise of conic sections (Dublin, 1723), p. 60.

Like Apollonius, Steell made no apologies for printing theorems and proofs attributed to other mathematicians since these theorems formed the basis of much of his own original work which followed.

Robert Steell, A treatise of conic sections (Dublin, 1723), composite image.

Text: Fionnán Howard.