Where the matter that we study is the entire genus, we must begin by distributing it into its lowest species; _e.g._ number into dyad, triad, &c.; in like manner, taking straight line, circle, right angle, &c.[38] We must first search out the definitions of each of these lowest species; and these having been ascertained, we must next look above the genus, to the Category in which it is itself comprised, whether _Quantum_, _Quale_, &c. Having done thus much we must study the derivative attributes or propria of the lowest species through the common generalities true respecting the larger. We must recollect that these derivative attributes are derived from the essence and definition of the lowest species, the complex flowing from the simple as its _principium_: they belong _per se_ only to the lowest species thus defined; they belong to the higher genera only through those species.[39] It is in this way, and not in any other, that the logical Division of genera, according to specific differences, can be made serviceable for investigation of essential attributes; that is, it can only be made to demonstrate what is derivative from the essence. We have shown already that it cannot help in demonstrating essence or Definition itself. We learn to marshal in proper order the two constituent elements of our definition, and to attach each specific difference to the genus to which it properly belongs. Thus we must not attempt to distribute the genus animal according to the difference of having the wing divided or undivided: many animals will fall under neither of the two heads; the difference in question belongs to the lower genus winged animal, and distributes the same into two species. The characteristic or specific difference must be enunciated and postulated by itself, and must be attached to its appropriate genus in order to form the definition. It is only by careful attention to the steps of legitimate logical Division that we can make sure of including all the particulars and leaving out none.[40] [Footnote 38: Ibid. b. 18. The straight line is the first or lowest of all lines: no other line can be understood, unless we first understand what is meant by a straight line. In like manner the right angle is the first of all angles, the circle the first of all curvilinear figures (Julius Pacius, ad loc. p. 504).] [Footnote 39: Analyt. Post. II. xiii. p. 96, b. 19-25: [Greek: meta\ de\ tou=to, la/bo/nta ti/ to\ ge/nos, oi(=on po/teron tô=n posô=n ê)\ tô=n poiô=n, ta\ i)/dia pa/thê theôrei=n dia\ tô=n koinô=n prô/tôn. toi=s ga\r suntitheme/nois e)k tô=n a)to/môn] (speciebus infimis) [Greek: ta\ sumbai/nonta e)k tô=n o(rismô=n e)/stai dê=la, dia\ to\ a)rchê\n ei)=nai pa/ntôn to\n o(rismo/n kai\ to\ a(plou=n, kai\ toi=s a(ploi=s kath' au(ta\ u(pa/rchein ta\ sumbai/nonta mo/nois, toi=s d' a)/llois kat' e)kei=na.]