Mathematical copy book, comprising 177 pages, indexed at the rear. Neatly written with numerous decorative calligraphic flourishes to the page headings. 32x20 cm (12½x8"), original blue paper wrappers.
Michael H. Trone's manuscript copy book covering numerous mathematical subjects including the Single Rule of Three, an ancient mechanical method for solving proportions. In the history of transmission of mathematical ideas, the Rule of Three forms an interesting case. It was known in China as early as the first century AD. Indian texts dwell on it from the fifth century onward. It was introduced into the Islamic world in the 8th century with renaissance Europe hailing it as the Golden Rule. The importance of the rule lies not so much in the subtlety of its theory as in the simple process of solving problems. This process consists of writing down the three given terms in a linear sequence (A->B->C) and then, proceeding in the reverse direction, multiplying the last term with the middle form and dividing their product by the first term (CxB:A). With this rule one can easily solve several types of problems even without a knowledge of the general theory of proportion. The manuscript shows numerous mathematical examples of using the Single Rule of Three. It further offers examples of a variety of other mathematical subjects including multiplication, division, compound interest, the Millers Rule, interest, discount, equation, barter, loss and gain, relationship of vulgar, reduction of vulgar, addition of fractions, multiplication of fractions, division of fractions, the rule of three in addition decimals, decimal fractions, subtraction of decimals, multiplication of decimals, division of decimals, reduction of decimals, square root, multiplication of the square roots of heights, ellipsis of regular polygons, spheres, carpenters and joiners, masons and brick layers work, proportion between similar surface and solids, motion, hydrostatics and gravity. On page 171 is written "Michael H. Trone - March 1858. I have finished." The calligraphy is bold and interesting with a number of fancy flourishes throughout.