Umberto and Kelly, 

  Your paper on Christopher Clavius is a very good (and well-written) historical survey 
  of what we know about his life, as well as his mathematical and educational contributions.  
  You have identified an interesting and varied collection of sources and you have absorbed
  the information they present very well.  

  The only critical comment I have is that I think it would have been good to go into more 
  detail about the attempted proof of the parallel postulate in the paper (more like what 
  you did in the presentation).  However, the presentation was also a little rushed so that 
  might have been improved a bit too.  About one of the points, for instance, Theorem 3.4 
  in McCleary's book clearly explains why assuming that the equidistant curve to a line 
  is also a line is equivalent to Postulate V, so it would have been good to discuss that 
  point in more detail.  

  Specific comments:

  Page 3:   The issue with the Julian calendar (one leap year every four years) was that 
  it was set up to work perfectly if the year was 365.25 days long on average. But the actual 
  length of the year is slightly shorter (more like 365.2425 days).  So over a period of 15 
  or 16 centuries the discrepancy built up to the point that the seasons were out of whack 
  with the calendar by about 10 or 11 days).  The Gregorian calendar is set up so that years 
  divisible by 100 but not by 400 are not leap years.  The Gregorian system would be perfect
  if the year was exactly 365.2425 days long.  But of course, that's not quite true either, 
  and the rotation of the earth is slowing down slightly, too.  So there will need to be 
  additional adjustments from time to time.  The Gregorian calendar was originally adopted
  only in Catholic countries.  In the British empire, including the colonies that later
  became the US, it was not adopted until 1752, by which time the Julian calendar was 
  almost two weeks out of whack with the seasons.  There were quite significant protests
  about it at that time for the reason you mention -- working people thought they were being 
  cheated of pay for the days they were "missing."

  Page 4: "His proofs include a proof of proportionality, but the ones that
  had the greatest impact on Geometry are his attempted proofs of Euclid’s flawed parallel 
  postulate."  I agree that there was a school of thought (as seen in works of Proclus, 
  later Islamic mathematicians, etc.) that the 5th postulate represented a sort of *flaw*
  in Euclid's geometry.  However, from our current understanding of geometry, it's clear
  that that postulate is *necessary* (along with the others) to describe the geometry of
  the Euclidean plane.  In that sense, it doesn't represent a "flaw" at all; in fact Euclid
  showed remarkable understanding by including it as one of his postulates(!)

  Page 5: About the quotation from Palmieri's article:  Since you are giving this a fairly
  prominent place, it might have been good to say some more about this point and how it
  connects to other things.  The "equimultiples" here refer back to Definition 5 in Book 
  V of the Elements, which is Euclid's statement of the definition of proportions going 
  back to Eudoxus.  (This was one of the topics Brady Parsons was explaining in his presentation.)  
  The issue was:  how do you define a ratio of magnitudes x:y when they are not commensurable 
  (i.e. when no integer multiple of x equals any integer multiple of y)?  The Greeks had shown 
  that some magnitudes (like the square root of 2) are irrational (= not commensurable with
  a unit length) and understanding this was a major theoretical advance. Going forward to 
  the 19th century, these ideas were still developing and the ultimate outcome was the theory 
  of the real number system and its properties -- things like the Completeness Axiom we studied 
  in Principles of Analysis.

  Page 12:  Your consultation of the HC, BC, and Fairfield U web pages regarding the role
  of mathematics today is a nice touch.  However, I think that you would probably find 
  very similar statements on the web pages of virtually all liberal arts college mathematics
  departments.  Of course, that might also be evidence that the way Clavius championed
  the teaching of mathematics in the Jesuit schools eventually had wider influences too.

  Final Project: 

  Annotated Bibliography -- 10/10
   
  Presentation -- 32/35  

  Paper -- 50/55

  Total -- 92/100   (letter: A-)