### Thursday, November 02, 2006

## Algebra Problems From 1822

In terms of no-nonsense brevity, my favorite is Percey Smith's "Elementary Calculus" from 1902; a complete 1 semester Calculus course, with many exercises, plus a nice treatment of partial derivatives, in 89 pages of a 5" x 7" book. Most current Calculus texts take over 100 jumbo-sized pages just to get through the "preliminaries" chapter.

My newest acquisition is a copy of John Bonnycastle's "An Introduction to Algebra;" the British Edition came out in 1815, mine is a New York edition from "the twenty-eighth day of December in the forty-sixth year of the Independence of the United States of America," which, by my count would be 1822.

From Bonnycastle, here are some of my favorite "Miscellaneous Questions producing Simple Equations:"

3. A shepherd being asked how many sheep he had in his flock, said, "If I had as many more, half as many more, and 7 sheep and a half, I should have just 500;" how many had he?

4. A post is one fourth of its length in the mud, one third in the water, and 10 feet above the water, what is its whole length?

14. A servant agreed to live with his master for 8 pounds a year, and a livery, but was turned away at the end of seven months and received only 2 pounds, 13 shillings and 4 pence and his livery; what was its value?

19. A person at a tavern borrowed as much money as he had about him, and out of the whole spent 1 shilling; he then went to a second tavern, where he also borrowed as much as he had now about him, and out of the whole spent 1 shilling; and going on, in this manner, to a third and a fourth tavern, he found, after spending his shilling at the latter, that he had nothing left; how much money had he at first?

27. A person has two horses, and a saddle, which itself is worth 50 pounds; now, if the saddle be put on the back of the first horse, it will make his value double that of the second, and if it be put on the back of the second, it will make his value triple that of the first; what is the value of each horse?

(My favorite) 34. A man and his wife usually drank out a cask of beer in 12 days, but when the man was from home it lasted the woman 30 days; how many days would the man alone be in drinking it?

and "Questions producing Quadratic Equations:"

13. A grazier bought as many sheep as cost him 60 pounds, and after reserving 15 out of their number, sold the remainder for 54 pounds, and gained 2 shillings a head by them; how many sheep did he buy?

16. A company at a tavern had 8 pounds, 15 shillings to pay for their reckoning; but before the bill was settled, two of them went away; in consequence of which those who remained had 10 shillings a piece more to pay than before; how many were there in the company?

21. Two detachments of foot being ordered to a station at the distance of 39 miles from their present quarters, begin their march at the same time; but one party arrive there an hour sooner; required their rates of marching?

And, from a nice section on "Indeterminate Analysis," involving Euclid's Algorithm, and "Tower of Hanoi" type problems (no, he doesn't use these terms!)

10. I owe my friend a shilling, and have nothing about me but guineas, and he has nothing but louis d'ors; how must I contrive to acquit myself of the debt? (Fortunately, he adds the note that the louis are valued at 17 shillings a piece, and the guineas at 21 shillings.)

Notropis