Plane geometry is woefully lacking in education nowadays. The situation is so sad that some of these questions are very similar to the geometry questions in the USAMO/IMO

Plane geometry was, at the time, perhaps the premier formal system to be studied as such; now, we get the same concepts across using calculus (which doesn't seem to be mentioned on the exam) and set theory (which would only really take shape in the 1870s).

(The history of mathematics doesn't get so much as a mention, either, but I don't expect it to.)

This is an interesting "book" that reduces geometry to automated symbol pushing.

http://www.math.rutgers.edu/~zeilberg/GT.html

Actually from a cursory look at the Latin part, it seemed that all of the sentences and things they chose for you to translate were very specific cases of applying rules.

Maybe a bit harder than some of the other stuff, but still regurgitation.

look at the bigger picture: there is a lot to be said about mastering a classical language to such a degree that you can translate these sentences back. Sure, on the surface it looks simplistic, but students with such a command of Latin would equally possess a rich knowledge in Roman and European history and culture through the process of acquiring classical Latin. Someone mentioned "modern history" missing...well, maybe because they still thought highly of the renaissance value of "ad fontes"?

> Someone mentioned "modern history" missing.

That would be me. 1869 might be a bit early for Civil War history to show up, but nothing on the War of 1812 or even the Revolution? Nothing on the history of Westward Expansion?

I understand going back to the sources ("ad fontes") and education for its own sake, but I've never seen something that implies an education that is so divorced from anything of the time the people receiving it are living in.