Preface.

...is worthy, and therefore there should be no school in which at least the basic principles of geometry and mechanics are not taught, which could be done without any special expense, simply through a well-ordered institution. But one must, alas! observe that those who ought to promote such an institution are most opposed to it—so much so that in a certain city, where Mathesin: mathematics (from the Latin 'mathesis') would be more necessary than anything else, the Gentlemen Inspectores: school inspectors or supervisors very harshly rebuked a Præceptorem: a teacher or instructor who wished to lead the youth into mathematics privately. Yet there is no other cause for such thoughtlessness than that these dear gentlemen themselves know and understand nothing of it, and are thus incapable of judging the benefit or harm.

Because we have lacked such an institution (though it is almost indispensable) until now, anyone who has a desire for such sciences can meanwhile make use of this Theatri: 'Theater,' referring to Leupold's multi-volume work 'Theatrum Machinarum' (Theater of Machines) with profit. Even if one thing or another should occur that involves calculation or geometry of which he is ignorant, the majority of the work will still serve him by showing what is of primary importance.

Those, however, who have practiced senses and at least possess a grasp of arithmetic, and who wish to do something necessary in geometry on their own due to a lack of formal instruction, can make good use of Court Councilor original: "Hof-Rath Wolffens." Refers to Christian Wolff (1679–1754), a titan of the German Enlightenment whose textbooks standardized much of German scientific terminology. Wolff’s Compendium of the Principles of Mathematics, because everything therein is presented very clearly and easily.

For young boys, who for the most part have an inclination toward such moving things, this book can be used merely for Recreation: leisure-time learning or play. First, one can teach them the simplest ratios from the figures, and later, with other machines, leave them to use and practice their own Judicium: judgment or critical faculty. This serves not only to learn mechanics almost as if in play, but also to sharpen the Ingenium: natural talent, wit, or ingenuity. As a man highly experienced in mechanics writes in his treatise Thorough Guide to Useful Sciences, but especially to Mathematics and Physica: Physics:

“The Studium Mechanicum: mechanical study is one of the most distinguished by which the study of physics can be perfectly attained; and through the knowledge of this study, even if only common people come to it early in their youth, very capable people are formed who are able to perform original: "præstiren," from the Latin 'praestare,' meaning to achieve, provide, or perform extraordinary things; of which very many examples have become known to me among all kinds of nations.”