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 class should or should not precede the Natural Philosophy class. It was with the study of mathematics that the ancients commenced the investigation of nature, for which reason they gave them the name of “The Sciences”; while Plato forbade those who were ignorant of geometry to enter his Academy. Their reasons for holding this view are easy to understand, since the sciences that deal with number and quantity make a special appeal to the senses, and are therefore easy to grasp; besides, they make a powerful impression on the imagination, and thus prepare the mind for studies of a more abstract nature.

8. All this is very true, but we have some other considerations to take into account: (1) In the Vernacular-School we advised the education of the senses, and the development of the mind through their means, and as our pupils have by this time been through a course of arithmetic they can scarcely be considered quite ignorant of mathematics. (2) Our method advances step by step. Before proceeding to complex problems of magnitude, we should deal with bodies in the concrete, and thus prepare our minds to grasp more abstract notions. (3) The curriculum of the Mathematical class, as drawn up by us, embodies most of the arts, and these cannot be thoroughly mastered without some knowledge of natural philosophy. But indeed, if others suggest a different order, and justify their preference by theoretical or practical reasons, I have no wish to gainsay them. My own view is opposed to theirs, and I have given my reasons for it.

9. As soon as a fair knowledge of Latin has been acquired (by the aid of the Vestibulum and the Janua, which are to be used in the first class), the pupils should be instructed in the science of first principles, commonly called metaphysics (though in my opinion it should be called prophysics or hypophysics, that is to say, ante-natural or sub-natural). For this science embraces the primary and the most important principles of existence, dealing with the essential hypotheses on which all things depend, their attributes, and their logical differences; and