Historical View of the Conic Sections

In this hypertext, we consider the conic sections, which have been studied for over 2000 years. Many people have contributed to this study, and many historical references and texts exist to document this study.

Apollonius of Perga, one of the greatest Greek mathematicians of the time (circa 200 B.C.), appears to have been the first to have rigorously studied the conic sections. He applied his work to his study of planetary motion and used this to aid in the development of Greek astronomy.

(Recall that Perga was one of the cities visited by the apostle Paul during his first missionary journey as recorded in Acts 13:13. Paul would have been in Perga less than 300 years after Apollonius' development of the topic of conic sections.)

More information on Apollonius, as well as many other mathematicians, is held at the MacTutor History of Mathematics Archive at the University of St. Andrews. You may view pages dealing with Apollonius, Hypatia, Euclid and many other people who played important roles in the development of conics.

There are even Biblical references to such geometric objects. I Kings 7:23 discusses Solomon's "sea", which was to be a circular basin used for ceremonial cleansing. The verse reads as follows:

Now he made the sea of cast metal ten cubits from brim to brim, circular in form, and its height was five cubits, and thirty cubits in circumference.

New American Standard Bible

As a sidenote, observe that the value of is being estimated here, in some sense, by the integer 3. That is to say,

or

where C is the circumference and d is the diameter of a circle.

To close this section, I have included three images below which are reproductions of works held in the Vatican Exhibit Main Hall. This site contains many old manuscripts of writings in the areas of mathematics and astronomy, as well as concise background material to shed light on the historical significance of the documents.

Fuller descriptions of the three images below can be obtained at the Vatican Exhibit site. Moreover, the images below are black and white versions of the color originals held in the museum. If you click on the titles of the texts from which these images are taken, you can see the color originals as held in the collection. Note that these require quite a bit of time to download, so do this only when convenient for you. I strongly encourage you to view these at some point, as the beauty of these documents can only be appreciated fully after one sees the color images.

The first of the images is a page from a Latin translation of Euclid's Optics written in 1458.

Secondly, here is a page from a Greek version (circa 1536) of Apollonius' Conics.

Finally, an elaborately developed page from a Latin translation of Ptolemy's Almagest.