Arithmetics

More than just mathematics or simply workbooks with rote questions, early arithmetics emphasize useful tools for post-school life such as compounding interest, foreign exchange, and weights and measures. While they include topics such as addition, subtraction, and fractions, they, according to Nietz, expect much of the basic math to be done mentally, and a great deal of the topics in arithmetics were arranged "like a catechism, by means of questions and prepared answers to be committed to memory." Additionally, unlike many other types of old textbooks, a portion of the text was addressed directly to the teacher in order to describe the most effective ways to use the books.

Physiologies

Unlike the other kinds of old textbooks, most physiologies were not mere reprints of English texts. In fact, the study of physiology and the human body mainly began due to the willingness of the authors of the books to educate their fellow citizens about physiology and the importance of health and wellness. Other aims of the physiology textbooks were to promote the study of higher-level natural sciences in general, to promote student project mainly in the form of laboratory work, and to dispel major prejudices that existed concerning health at the time. Finally, toward the latter half of the 1800s, many state legislatures began to pass laws requiring students be taught about the dangers of alcohol abuse, and many authors of physiology textbooks followed suit by providing this information to be used by schools. 

Sciences

While not mentioned in his book Old Textbooks, Nietz does mention sciences outside of physiology in his later work on the collection, The Evolution of the American Textbook. Compared to the other subjects, science came late to American schools. Prior to 1900, the main sciences taught in American schools were chemistry, physics (then called natural philosophy), zoology (or natural history), and botany. Ultimately, after 1900, zoology, botany, and physiology were combined in American high schools and the three main sciences of biology, chemistry, and physics were established.