Section 3

Element means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable.

(b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean.

(c) The term is applied with a very similar meaning to the elements of geometrical figures, and generally to the elements of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations are called elements of demonstrations. 1 Such are the primary syllogisms consisting of three terms and with one middle term.

(d) The term element is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an element.

(e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles.

(f) Therefore since what are called genera 2 are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing.