Book 13
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at least they generate the derivatives, e.g. the void, proportion, the odd, etc., from within the decad. Some, such as motion, rest, good and evil, they assign to the first principles; the rest to numbers.From the Dyad were derived void (Theophrastus, Met. 312.18-313.3) and motion (cf. Aristot. Met. 1.9.29, Aristot. Met. 11.9.8). Rest would naturally be derived from unity. For good and evil see Aristot. Met. 1.6.10. Proportion alone of the derivatives here mentioned appears to be derived from number. As Syrianus says, the three types of proportion can be illustrated by numbers from within the decad—arithmetical 1. 2. 3, geometrical 1. 2. 4, harmonic 2. 3. 6.
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Hence they identify the odd with Unity; because if oddness depended on 3, how could 5 be odd?sc. because (on their theory) 3 is not contained in 5. Thus oddness had to be referred to not a number but a principle—unity.
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Again, they hold that spatial magnitudes and the like have a certain limit; e.g. the first or indivisible line, then the 2, and so on; these too extending up to 10.The indivisible line or point was connected with 1, the line with 2, the plane with 3 and the solid with 4 (Aristot. Met. 14.3.9); and 1+2+3+4=10.
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Again, if number is separable, the question might be raised whether Unity is prior, or 3 or 2.
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Now if we regard number as composite, Unity is prior; but if we regard the universal or form as prior, number is prior, because each unit is a material part of number, while number is the form of the units. And there is a sense in which the right angle is prior to the acute angle—since it is definite and is involved in the definition of the acute angle—and another sense in which the acute angle is prior, because it is a part of the other, i.e., the right angle is divided into acute angles.
