Marginal Math

This semester I've been teaching a large Shakespeare lecture course in one of the precious few auditorium classrooms on campus. The class that meets immediately before ours couldn't be more different: an Engineering course called "Dynamics" which is described with phrases I haven't thought about in years (vector calculus? multiparticle systems?)  The instructor of that course always leaves cryptic formulas on the chalkboard, which, of course, we often promptly transform into a symbolic trajectory of the play we happen to be reading (we can plot Hamlet's trajectory on this axis; Ophelia, unfortunately, remains static...). More to my immediate purpose, though, it's reminded me of the intersection of early modern reading practices and math problems -- or, to put it more prosaically, the penchant of readers to scribble math problems in the  margins of their books, utilizing the valuable real estate of the page as a piece of proverbial scrap paper. Here are three examples I've come across in our Special Collections library.

The first can be found on the well-worn title-page of A Christian Dictionary (InfoHawk record here) which also features a number of practice flourishes. It appears to be a simple matter of addition--perhaps the record of a transaction of some sort?

The next example, on the title-page of Christs Combate and Conquest (InfoHawk record here) is more involved. As you can see, there are several problems here, which the owner has carefully placed around the rules in the top and outer margins, so as to preserve, for the most part, the printed space of the title-page:

Our trusty and careful mathematician -- one "W. Hickman" -- seems to have identified himself on another page:

The final example is the most interesting, by far, and is found in John White's The Way to the True Church:

This volume is still in its original binding, and you can just make out the title written on the spine:

This book only houses the math problems, though, since they are found in a loose sheet stuck in the middle:

Here's a closeup of the side of the loose sheet containing the math problems -- if memory serves correct, this is a version of the lattice method -- and you can also see at the edges that this is only part of the sheet, which has been torn away from a larger sheet at some point.

All three of these books happen to be religious in nature -- and this loose sheet is no different, since it includes transcribed biblical verses and notes on the other side:

It's a bit difficult to make out, but I've made a preliminary transcription of these notes:

Micha 7:9:

Potentates may forfeit their thrownes by their
impieties none enabled to take the forfeiture
but god Saul forfeited by his sacrilegious
intrusion into the office & function of the
Priesthood  1 Sam: 13:8  & [Governing ?] A
Agag & the spoile  1 Sam:  15:9  [david?]
Durst not lifte his hand against Saul   1 Sam
24 & 26:  Si [salis?] accusasse quis tandem innocens

The notes do not have any discernible connection to the page opening in which the loose sheet was found. So, in a way, both the biblical notes and the math problems are at yet another remove from the content of the book -- the book has simply served as a container, housing and protecting an unattached sheet with which it holds an almost purely material connection.