Derek and Emily,

  Excellent work on your final project on Christopher Clavius, S.J. the role 
  of mathematics in early Jesuit education, and the transmission of Euclid's 
  Elements to China through the missionary work of Matteo Ricci, S.J.
  This is extremely well-written and thorough.  The only thing I would have
  liked to see a bit more of was the actual mathematical content of some
  of Clavius's additions or revisions to the Elements, the contents of 
  his other textbooks, etc.  But that would also make the basis for a much
  larger project, I suspect.  


  Specific comments:

  Page 1: "The formation of a Jesuit curriculum therefore came at a time when the 
  cultural perception of mathematic and scientific pursuits ... "  Here, "mathematic" 
  looks odd to me; I think "mathematical" is much more common as the adjective form.

  Page 2:  "... following from the opinion of Plato."  It would be good to give a
  more detailed reference here.  These opinions about the place of mathematics
  in education are pretty clearly laid out in the Republic, 527.   A sample, in
  reference specifically to geometry: "Then, my good friend, it would tend to draw 
  the soul to truth, and would be productive of a philosophical attitude of mind, 
  directing upward the faculties that are now wrongly turned downward."

  Page 3:  "divulgation" is certainly correct here, but it's a rather unusual 
  word.  It smacks of the thesaurus and using it here makes you sound rather
  self-consciously learned.   "Publication" or "dissemination" would
  work just as well.

  Pages 3 - 4:  "Clavius scrutinized over Euclid’s fifth postulate about parallel 
  lines."  "Scrutinized over" sounds odd to me here -- how about "studied."

  Page 4: Your footnote 12: I think 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.  

  Page 7:  "This version of the Ratio was released at a crucial time in the history 
  of Jesuit educations ... "  Typo:  make that "Jesuit education ... ."

  Page 13: "For example, Fontana describes that one Chinese mathematician
  developed “a method of solving systems of equations ... that would have been 
  something new to Ricci."  I don't know if "developed" is quite the right 
  word here.  There was a tradition of techniques for solving systems of 
  linear equations in Chinese mathematics.  I suspect that is what Fontana
  is describing here.  Those techniques are extremely close to the 
  row operations on matrices that we teach in linear algebra now, but it
  would have been novel to a European mathematician at the time of Ricci. 

   
  Final Project: 

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

  Paper -- 50/55

  Total -- 95/100   (letter: A)