What textbooks were used to teach Neo-Latin in primary, secondary, and higher education schools during the 19th century?
The late 19th century primarily used grammar books for teaching Latin.
Latin was used for all subjects (including recess time!) as late as the end of the 18th century in France. Physics was first taught in French in 1783; cf. Lucien Gagne, C.Ss.R.'s preface to Victor Coulombe's transl. of Fr. William Most's Latin by the Natural Method.
In the 13th-16th centuries, all oral lectures and textbooks for all subjects for children 6-14 were entirely in Latin, despite it not having been a vernacular for almost a millennium.
Ganss, George E., S.J., "Appendix 1: A Sketch of the History of Latin Teaching." In Saint Ignatius' Idea of a Jesuit University a Study in the History of Catholic Education, Including Part Four of the Constitutions of the Society of Jesus, 218-58. Milwaukee: Marquette University Press, 1954.
- cf. the foreword of Latin by the Natural Method (vol. 1) for a summary.