Pythagoras the Samian, the son of Mnesarchus, from another origin deduces the principles of all things; it was he who first gave philosophy its name. He assigns the first principles to be numbers, and those symmetries resulting from them which he styles harmonies; and the result of both combined he terms elements, called geometrical. Again, he enumerates unity and the indefinite binary number amongst the principles. One of these principles tends to an efficient and forming cause, which is Mind, and that is God; the other to the passive and material part, and that is the visible world. Moreover the nature of number (he saith) consists in the ten; for all people, whether Grecians or barbarians, reckon from one to ten, and thence return to one again. Farther he avers the virtue of ten consists in the quaternion; the reason whereof is this,—if any person reckon from one, and by addition place his numbers so as to take in the quaternary, he shall complete the number ten; if he exceed the four, he shall go beyond the ten; for one, two, three, and four being cast up together make up ten. The nature of numbers, therefore, if we regard the units, resteth in the ten; but if we regard its power, in the four. Therefore the Pythagoreans say that their most sacred oath is by that God who delivered to them the quaternary. By th’ founder of the sacred number four, Eternal Nature’s font and root, they swore. Of this number the soul of man is composed; for mind, knowledge, opinion, and sense are the four that complete the soul, from which all sciences, all arts, all rational faculties derive themselves. For what our mind perceives, it perceives after the manner of a thing that is one, the soul itself being a unity; as for instance, a multitude of persons are not the object of our sense nor are comprehended by us, for they are infinite; our understanding gives the general notion of _a man_, in which all individuals agree. The number of individuals is infinite; the generic or specific nature of all being is a unit, or to be apprehended as one only thing; from this one conception we give the genuine measures of all existence, and therefore we affirm that a certain class of beings are rational and discoursive beings. But when we come to give the nature of a horse, it is that animal which neighs; and this being common to all horses, it is manifest that the understanding, which hath such like conceptions, is in its nature unity. The number which is called the infinite binary must needs be science; in every demonstration or belief belonging to science, and in every syllogism, we draw that conclusion which is the question doubted of, from those propositions which are by all granted, by which means another proposition is demonstrated. The comprehension of these we call knowledge; for which reason science is the binary number. But opinion is the ternary; for that rationally follows from comprehension. The