Wednesday, October 7, 2009
Wednesday Math, Vol. 91: Robinson's New Higher Arithmetic, part 1
Years ago, a friend bought a copy of a math textbook first published in the 19th Century at a yard sale and gave it to me. I never asked how much it cost, though given it was a yard sale I expect it was about a quarter or so. This is one of those examples of that quaint old phrase "It's the thought that counts."
Over the next few weeks, I'm going to use Wednesday Math to discuss Robinson's New Higher Arithmetic, a textbook used at high schools, academies and mercantile colleges one hundred years ago or more.
The book itself. The copyright is 1895. The only inscription is inside the front cover, the name "Henry Mountain" with no date given. There are no mentions of first printing, second printing, etc. It's possible that the copy I have actually left the book binders in the 19th Century, but the text was in print for a long time. I assume the ink was dry on my copy well before the start of World War I.
The cover is dirty and the pages are yellow, but for a book ninety years old or more, it's in remarkable shape. I treat it gently, no leafing through it as high speeds to find a particular passage, but it the binding is still strong and no pages are at risk of falling out.
Any of us would be glad to show so little wear and tear when we are past ninety.
As you can see from my hand on the cover, it's a handbook. While it's over 500 pages long, it's very light and compact, something I wish was true about textbooks today. The "new" part of Robinson's New Higher Arithmetic is the fact it is a second edition. In the preface, mention is made that the first version of the book had been available for some thirty five years.
Textbooks were handbooks and there could be thirty five years between changes of editions. The textbook industry back in the day is nothing like the rapacious beast it has now become.
Saved for posterity: If I should lose my copy, there is no worry that all of Robinson's knowledge will fade from the scene forever. Some company still has reprints of the 1895 book available in paperback. It can't be used as a text today, so I'm not sure who pays the big bucks to buy it. More practically, Google has a version of the book online saved as a .pdf file.
This is a wacky series of tubes, I tell ya.
Arithmetic, not algebra: This is a book about addition, subtraction, multiplication and division. It also uses exponents and roots. In the 19th Century, using exponents was called involution and using roots was evolution.
The most surprising topic in the book to me is the inclusion of different base systems, like binary or ternary, which back then were called scales of notation. Understanding base 2 or base 8 or base 16 has a practical value now for people who use computers. Tom Lehrer made fun of it making a comeback into the curriculum in the 1960's in his song New Math. I'm not sure how these would have been practical back in Robinson's day, and the people who wrote this thing are all about practicality.
There is no assumption on Robinson's part that his readers need to learn the mathematical methods that lead to the study of calculus. Abbreviations and symbols in formulas are not used. For example, the area of a triangle is not given as A = bh/2, or even Area = base x height x 1/2, but instead by this sentence.
RULE. - Divide the product of the base and altitude by 2. Or, Multiply the base by one half the altitude.
Robinson banished the symbol π from his book. If a calculation needs it, the approximation 3.1416 is used. If the formula calls for π/4, the decimal .7854 will do.
I'm having a lot of fun going through the book. The next few Wednesdays will be devoted to some of the interesting things I've found in Robinson's, most of them amusingly quaint but some that still have practical purposes today.
Ooh, I'm serializing an account! I think I might get the hang of this 19th Century style of writing!