His schoolbooks all originated in the necessities of his own work as a teacher. The first thus to force itself upon his attention was an arithmetic. He was already at work on it in 1868, and it went to press while his brother John was superintending the plant at Shanghai. The preparation of such a book, to one unacquainted with the conditions under which this one was made, may seem to have been a rather easy undertaking, and to have required little more than a sufficient mastery of the Chinese language and of English; yet there were some perplexing questions that arose in connection with it. For instance, the method of writing numbers horizontally was wholly unknown to the Chinese. Should the new arithmetic use the western, or should it retain the Chinese method? To retain the Chinese would be to train the pupils in a usage that would be confusing in subsequent reading of western mathematics; to abandon it would be equally confusing in printing the text of the book, which, according to Chinese usage, must be arranged perpendicularly. The difficulty was gotten over by duplicating each pattern example, giving it once horizontally and once perpendicularly. Pupils using the book were permitted to take their choice in performing their work, but in the text proper all numbers appeared vertically. Such lines as those dividing the numerator and denominator of a fraction stood perpendicularly, with the figures to the right and the left. Until he published his arithmetic, the Chinese numerals had been employed; he introduced the Arabic. At the dawn of the new era subsequent to the Boxer outbreak, almost the first book in demand by Chinese teachers and pupils outside the mission schools was a western arithmetic; and among others put upon the market were many “pirated” editions of Mateer’s book, printed on cheap paper and with wooden blocks. The publishers had not yet learned the significance of “copyright.” The circulation of the book, however brought about, had at least the effect of immediately increasing the reputation of its author among the scholarly classes outside the church. Of the editions issued by the press at Shanghai tens of thousands of copies have been sold. Dr. Fitch writes that “it is impossible to state the total number,” and that “the book has gone into all parts of the empire.” In October, 1884, he submitted to the schoolbook committee of the Educational Association the manuscript of his geometry, and in doing so he said of it: