# Historical question re: ellipses obtained by certain geometrical constructions

I am a faculty member in the Forensic Science Program at PennState (UP). I am trying to obtain information of a historical nature concerning two closely related topics. I seek historical references for the calculation/determination of the major and minor axes of an ellipse formed by:

1. the orthogonal projection of a circle onto a plane, where the axes of the resulting ellipse are expressed in terms of the inclination angle of the plane;

2. the intersection of a plane with a right cylinder (obliquely), where the axes of the ellipse are related to the inclination of the plane relative to the axis of the cylinder.

Hopefully, my descriptions are clear. I believe that Serenus may have described the latter scenario. However, I have been unable to confirm this hunch. This historical research is being done for a project that utilizes these calculations in a forensic science context. Any assistance or guidance you could provide would be greatly appreciated. Thank you!

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While I'm not going to close your question, I just thought I would let you know that this website probably isn't the best place to look for information like this. I suppose you never know who's lurking around, but as you can see, it's of quite a different nature from the other questions on the site. We're mathematicians here, not historians of math. Also, your question is a little unclear: are you looking for the earliest reference? – Ben Webster Nov 2 '09 at 0:18
Yes, the earliest reference(s). Any suggestions on where I could obtain this information? Thanks! – Ralph Ristenbatt Nov 2 '09 at 0:28
This is a little outside the usual range of questions here, but we're not going to close it (barring further discussion on meta!). This sort of question feels like asking a physicist for the first reference to a description of a lever! :-) – Scott Morrison Nov 2 '09 at 2:02
Just to be absolutely clear, you need a reference along the lines of "r radius of base circle, a is angle, axes are r/cos(a) and r?" – Jason Dyer Nov 2 '09 at 2:25
Correct, Mr. Dyer! The earliest reference possible...I realize that this is a daunting task...I wasn't sure where else to turn as this site was recommended by a PennState mathematician. Thanks again! – Ralph Ristenbatt Nov 2 '09 at 14:26

I have found the following avaialable on the web

http://www.archive.org/details/ahistorygreekma00heatgoog

It is the A History of Greek Mathematics (1921)

by Thomas Little Heath

it has a section discussing the two known works of Serenus "On the Section of a Cylinder" and "On the Section of a Cone" see pages 519 to 526.

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Thank you! I've got this reference but it doesn't seem to give me what I am looking for with this search. Maybe Serenus laid the foundation but didn't elucidate the relationship between the angle and the ellipse dimensions...Hmmmmmmmm.... – Ralph Ristenbatt Nov 2 '09 at 0:48

The earliest reference I have so far to #1 is The Mathematical Miscellany from 1836.