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A USEFUL

PREFACE

TO THE MATHEMATICAL

SYNOPSIS.

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BEFORE reading the following treatises, it should first be noted that it is worthwhile for anyone who wishes to usefully carry these treatises with them into the countryside to refresh their memory of all parts of mathematics, and to cite and find the propositions of the ancients and moderns, to add diagrams to the margin or to sheets of paper inserted between the printed leaves—whatever they judge necessary for understanding the propositions. This could not be done with printed type except at great expense. It will be sufficient, however, to add those figures to the propositions which you cannot understand without a drawing.

Second, the crosses applied to certain propositions of Euclid, Archimedes, Theodosius, and the Spherics original: "Sphæricorum." This refers to works on the geometry of the sphere, likely those by Menelaus or Theodosius of Bithynia. indicate that these are the most important and are to be learned most thoroughly. But since the more fruitful propositions of the other treatises should also have been distinguished with crosses, the printers omitted them. Anyone may transfer these from my own manuscript into their own copy.

III. Those who seriously embrace the study of geometry must begin with the elements of Euclid, which are called the royal road. These alone are sufficient for easily grasping the mathematical matters that Plato, Aristotle, and other philosophers published to date have interspersed in their writings; indeed, they also suffice for understanding the other geometers who follow. Moreover, it is evident from all arts and sciences how great, useful, and excellent their application is. On this subject, Blancanus, Bettinus, Proclus, and others may be consulted, if what we have said in our commentary on Genesis and on Harmonics is not enough. Mersenne refers to his own massive works, "Quaestiones Celeberrimae in Genesim" (1623) and "Harmonie Universelle" (1636). Giuseppe Biancani (Blancanus) and Mario Bettini (Bettinus) were influential Jesuit mathematicians and astronomers of the era.

IV. We have placed the Geometry of Ramus Petrus Ramus, or Pierre de la Ramée, was a 16th century philosopher known for his concise and often controversial restructuring of academic subjects. after that of Euclid on account of its extreme brevity, and because the terms and the order which he uses sometimes