[1] According to tradition there were four degrees of purity. 1. The ordinary purity required of every worshipper in the temple (‏טהרת חולין‎). 2. The higher degree of purity necessary for eating of the heave-offering (‏טהרת תרומה‎). 3. The still higher degree requisite for partaking of the sacrifices (‏טהרת הקודש‎). And 4. The degree of purity required of those who sprinkle the water absolving from sin (‏טהרת חטאת‎). Each degree of purity required a greater separation from the impurities described in Leviticus xi, 24–xv, 28. These impure subjects were termed the fathers of impurity; that which was touched by them was designated the first generation of impurity; what was touched by this again, was called the second generation of impurity; and so on. Now, heave-offerings—the second degree of holiness—became impure when touched by the third generation; the flesh of sacrifices—the third degree of holiness—when coming in contact with the fourth generation; and so on. These degrees of purity had even to be separated from each other; because the lower degree was, in respect to the higher one, regarded as impure, and any one who lived according to a higher degree of purity became impure by touching one who lived according to a lower degree, and could only regain his purity by lustrations (‏טבילה‎). The first degree was obligatory upon every one, the other grades were voluntary. Before partaking of the heave-offering, the washing of hands was required; and before eating of the flesh of sacrifices, immersion of the whole body was required—Comp. Babylonian Talmud, Tract Chagiga, 18 b. [2] Geschichte der Philosophie, vol. iii, part ii, p. 583 ff. [3] The figures before each point of comparison do not exit in the original German; I have inserted them in the translation in order to facilitate the references to these different points of comparison. [4] Comp. Diog. Laert. de Vitis Philosophorum, lib. viii. Vit. Pythagor. xii. It is true that Cicero represents Cotta as giving no credit to this story, because, as he apprehends, Pythagoras never offered animal sacrifices (De Natura Deorum, lib. iii. cap. xxxvi.), but it is also related by Athenaeus (Deipnosoph. lib. x.), Plutarch and others. [5] An excellent account of the Pythagorean system is given by Zeller, Geschichte der Philosophie. Erster Theil, Tübingen, 1856, pp. 206–365; Grote, History of Greece, vol. iv. London, 1857, pp. 527–553; and Mason, in Smith’s Dictionary of Greek and Roman Biography and Mythology, Article Pythagoras.