selfAdjoint

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## Main Question or Discussion Point

I am researching the history of the focus-directrix property of the conic sections. Here is what I've found so far.

Aristaeus (fl.c. 300 bce - contemporary of Euclid) was

The great Greek geometers of the Hellenistic era did not discuss f-d.

Pappus (c. 300 CE) gave the focus-directrix property of the parabola (only?) He discussed Aristaeus, apparently had the latter's now lost book before him, and maybe got the property from that.

Kepler (fl c. 1620 CE) gave the names focus and directrix.

There's an awful lot of missing geometry between Pappus and Kepler. Who first defined the f-d properties of ellipses and hyperbolas? Was the writer in the Greek, Arabic, or Latin tradition? At what point did the geometric facts Newton used and attributed to "old geometers" appear?

Can anyone help me fill in the blanks?

Aristaeus (fl.c. 300 bce - contemporary of Euclid) was

*conjectured*to have discussed the f-d properties in his lost "Five Books on Solid Loci".The great Greek geometers of the Hellenistic era did not discuss f-d.

Pappus (c. 300 CE) gave the focus-directrix property of the parabola (only?) He discussed Aristaeus, apparently had the latter's now lost book before him, and maybe got the property from that.

Kepler (fl c. 1620 CE) gave the names focus and directrix.

There's an awful lot of missing geometry between Pappus and Kepler. Who first defined the f-d properties of ellipses and hyperbolas? Was the writer in the Greek, Arabic, or Latin tradition? At what point did the geometric facts Newton used and attributed to "old geometers" appear?

Can anyone help me fill in the blanks?