Prologue I.

the principles to them, and the many knowledges exist around it and are referred back to it. For let the geometer say that when four magnitudes are proportional, the alternating ratio will also be proportional, and let him demonstrate it according to his own principles, 5 which the arithmetician would never use. And again, let the arithmetician say that when four numbers are proportional, the alternating ratio will also hold, and demonstrate this from the principles of his own science. Who, then, is the one who knows "the alternating" in itself, whether in magnitudes or in numbers, and the division of composed magnitudes or numbers, and likewise the synthesis of divided ones? For it is not the case that there are sciences and knowledges of the divisible things, but that we have no science of those things that are immaterial and placed closer to intellectual contemplation. Rather, the knowledge of the latter is science to a much greater degree, and from it the many receive their common logoi rational principles. Thus, there is an ascent of knowledge from the more particular to the more holistic, until we climb back to the very science of Being, insofar as it is Being. 19 For this science does not deign to look only at what belongs to numbers in themselves, nor what is common to all quantities, but contemplates the one and only substance and existence of all beings. For this reason, it is the most comprehensive of all sciences, and all others receive their principles from it. For those that are higher always provide the first hypotheses of proofs to those beneath them, while the most perfect of the sciences provides from itself to all others.