Whether or not you feel a touch of autumn in the air, here’s a back-to-the-books kind of a mystery from the manuscript collection. What do you make of this colorful image?

Submit your guesses and comments below. We’ll be back with an explanation next week!

It’s easy to calculate that these are fractions of 60.

Are they minutes, or seconds? and if so, of time or of geometric degrees?

But anyone competent to do calculations of degrees of arc doesn’t need a ready reckoner to tell them the fractions of sixty.

It was easy find this month’s crocodile via hamnet, asking for “manuscript + arithmetic” .

It comes from the Arithmetic Exercice Book of Sarah Cole, created 1686, Folger shakespeare library coll. source call number : V.b.292.

This table gives the solution of this exercice :”Divide 60 amonghst 5 men and tell me each man’s part thereofe giveing to A I/2 , B 1/4 …” &c.

The entire page, title : “the Golden Rule”, can be seen here :

http://luna.folger.edu/luna/servlet/detail/FOLGERCM1~6~6~33279~102286:Arithmetic-exercise-book?sort=call_number%2Cmpsortorder1%2Ccd_title%2Cimprint&qvq=q:call_number%3D%22V.b.292%22%2B;sort:call_number%2Cmpsortorder1%2Ccd_title%2Cimprint;lc:FOLGERCM1~6~6&mi=0&trs=4

Yes, it had to be something simpler than astronomical calculations …

… or mesopotamian sexagesimal arithmetic !

I was about to say ‘cyphering book”, but it seems you have beat me to it.., But *what* questions are being asked in the rest of the page is interesting.

Looking at the numbers, it seems the problems on the page had something to do with calculating weights. The answers are given in a form similar to how 17thc. arithmetic books give answers to problems involving money ( Pounds, shillings & pence), weight ( Pounds, ounces, pennyweight) or length .

Looking at the title of the page, I think the questions have something to do with proportion. The “golden rule” was the name given to the following identity:

If A/B = C/X

Then X= (BC)/A (It was so called because it has so many applications across math)

As the bottom-most box of the page contains yet another set of answers, “A must have XXX, B. must have YYY, (etc)”, I shall hazard a guess: The question that Sarah must have been tasked with involved splitting 60 pounds./yards/ells of goods amongst 5 men, and coming up with the resulting fractions in that byzantine system of units.

The workings seem to bear this out. They involve multiplication and division (using the “galley” method no less) which would be expected in such problems. of proportion

In any case, Ms. Coke would probably have had to– and perhaps be better at — resolve far more complex math problems that most of us would today. A most accomplished young lady!