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 I seek historical references for the calculation/determination of the major and minor axes of an ellipse formed by:

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;

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!

earliestreference? $\endgroup$