In many of my preceding Examinations I have already explained what should be understood by this celebrated Tetrad, and here would perhaps be the time to reveal its constitutive principles; but this revelation would lead me too far. It would be necessary in order to do this, to enter into details of the arithmological doctrine of Pythagoras which, lacking preliminary data, would become fatiguing and unintelligible. The language of Numbers of which this philosopher made use, following the example of the ancient sages, seems today entirely lost. The fragments which have come down to us serve rather to prove its existence than to give any light upon its elements; for those who have composed these fragments wrote in a language that they supposed understood, in the same manner as our modern writers when they employ algebraic terms. It would be ridiculous if one wished before having acquired any notion concerning the value and use of the algebraic signs, to explain a problem contained in these signs. This is, however, what has often been done relative to the language of Numbers. One has pretended, not only to explain it before having learned it, but even to write of it, and has by so doing rendered it the most lamentable thing in the world. The savants seeing it thus travestied have justly scorned it; as their contempt was not unreasonable they have made it reflect, by the same language upon the ancients who have employed it. They have acted in this as in many other things; they themselves creating the stupidity of ancient sciences and saying afterwards: antiquity was stupid. One day I shall try, if I find the time and the necessary facilities, to give the true elements of the arithmological science of Pythagoras and I will show that this science was for intelligible things what algebra has become among us for physical things; but I shall only do so after having revealed what the true principles of music are; for otherwise I should run the risk of not being understood.