What was advertised in a colonial American newspapers 250 years ago today?
“Various Branches of the Mathematicks taught by WILLIAM CORLETT.”
In the summer of 1767 William Corlett placed an advertisement in the Boston Post-Boy to announce that he had commenced teaching “ARITHMETICK, And various Branches of the Mathematicks.” He indicated that his pupils could learn “the first five Rules of Arithmatick,” navigation, surveying, and bookkeeping “after the Italian Method.” This curriculum suggests that Corlett worked as a tutor for youths and adult learners rather than as a schoolmaster for children. He taught specialized skills of particular value to those who pursued (or wished to pursue) occupations that depended on numeracy. Unlike schoolmasters who advertised their lessons, he also indicated specific outcomes so potential students could anticipate the time and total fees they could expect to invest. They learned the basics, “the first five Rules,” in forty hours. They became competent in navigation and surveying in forty-eight hours, each. Double-entry bookkeeping, “the Italian Method,” required additional study; Corlett’s students devoted an entire month to learning this skill.
What were the first five rules of arithmetic? Addition, subtraction, multiplication, and division accounted for four of them, but the final rule creates some confusion among historians of mathematics education. It may have been basic numeration, simple counting and the ability to identify and express numbers set down in numerals. Given the rest of his curriculum, however, Corlett may have included the Rule of Three (also known as the Golden Rule) in his introductory course of study. In “Numeracy in Early Modern England,” Keith Harris describes the Rule of Three as “a rule of proportion whose aim was to find a fourth number when three were known.” He offers this example: “if the wages of three carpenters are 24d, what would the wages of seven carpenters be?” Solving this problem requires multiplication and division; students needed to master those skills before attempting proportions.
Some prospective students likely found the “various Branches of Mathematicks” intimidating, but Corlett assured them that “any one of a moderate Capacity” could fairly quickly learn the skills he taught. By specifying how many hours of instruction were necessary to attain each skill, he signaled that he would not prolong the process or attempt to wring as much tuition as possible out of his pupils.
 Keith Thomas, “Numeracy in Early Modern England: The Prothero Lecture,” Transactions of the Royal Historical Society 37 (1987): 114-115.