As I mentioned in my last post, I've been reading through Arithmetic Made familiar and easy to Young Gentlemen and Ladies. In general it covers basic math using the same rules that I was taught as a child. A few things stand out as being different from what I learned, however.
First, the word "cypher" is used instead of "zero". This is easy enough to get used to, and, to my ears at least, sounds quaint and colonial. The author also uses "units" instead of "ones" to describe the right-most digit in a number.
Next, when teaching addition, the author describes arranging numbers in the same way that I was taught, but the numbers are added from the bottom to the top instead of from top to bottom. After reading this, the phrase "add up the numbers" does make more sense now.
Subtraction was described just as I had learned it. Multiplication was slightly different. Where I was taught to draw a zero when moving to the next line of a multiplication, the author leaves a blank space, only drawing a cypher if the multiplicand contains one. One thing that hasn't changed is the recommendation to memorize a multiplication table.
Division is the rule that looks the most different to my modern eye. The process of dividing a number is the same, but the layout of the numbers is different. The author uses parentheses to separate the divisor, dividend, and quotient.
For example, 612 divided by 3 would look like this: 3 ) 612 ( 204
As someone who might portray a colonial shopkeeper, these slight differences in format are interesting, as they could add detail to a character as they keep their books, or teach others the basics of mathematics.
In addition to teaching basic arithmetic, Arithmetic Made familiar and easy contains a wealth of other period information. The author uses examples of money, weights, measures, and time to illustrate the concepts that he is teaching. In some cases, he has provided conversion tables, so that the student can see, for example, that 16 drams is equal to 1 ounce.
As I read through the text, I started making notes of all the measures that were mentioned. I think I'm going to put together a page of conversion charts that I can keep handy, and possibly build a small application that will convert items for me. I think this will be useful as I read other period sources, at least until I become familiar enough with the various terms to not need the cheat-sheet.
My favorite example problem so far:
"A Man overtaking a Maid, who was driving a Flock of Geese, said to her, Goodmorrow, Sweetheart, whither are you going with your 99 Geese? Sir, said she, you mistake the Number; for if I had as many more, and half as many more, and one fourth part as many, then I should have but 99. The Question is, how many Geese she had?"
 Arithmetic Made familiar and easy to Young Gentlemen and Ladies, Being the Second Volume of the Circle of the Sciences, &c., (London: John Newbery, 1748) http://books.google.com/ (accessed May 25, 2012), 3.
 Ibid. 11.
 Ibid. 56.
 Ibid. 52.
 Ibid. 73.
 Ibid. 21.
 Ibid. 183.