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‘The possibility of the beginning of anything implies also that of the end: for nothing impossible comes into being or begins to do so, as for example the commensurability of the diameter (with the side of the square) never either begins to, nor actually does, come into being. To begin implies to end, says Tennyson, Two Voices [line 339]. In interpreting a rhetorical topic which is to guide men's practice, it is plain that we must keep clear of metaphysics. The beginning and end here have nothing to do with the finite and infinite. Nor is it meant that things that can be begun necessarily admit of being finished: the Tower of Babel, as well as other recorded instances of opera interrupta, shew that this is not true. And though it may be true of the design or intention, of any attempt, that it always looks forward to an end, immediate or remote, still to the public speaker it is facility and expediency, rather than the mere possibility, of the measure he is recommending, that is likely to be of service in carrying his point. All that is really meant is, that if you want to know whether the end of any course of action, plan, scheme, or indeed of anything—is possible, you must look to the begining: beginning implies end: if it can be begun, it can also be brought to an end: nothing that is known to be impossible, like squaring the circle, can ever have a beginning, or be brought into being. Schrader exemplifies it by, Mithridates coepit vinci, ergo et debellari poterit. Proverbs and passages on the importance of ἀρχή are cited in the note on I 7. 11.

The incommensurability of the diameter with the side of the square, or, which is the same thing, the impossibility of squaring the circle, is Aristotle's stock illustration of the impossible: see examples in Bonitz ad Metaph. A 2, 983 a 16. Euclid, Bk. X. Probl. ult. Trendelenburg, on de Anima III 6. 1, p. 500, explains this: the diameter of a square is represented by the root of 2, which is irrational, and therefore incommensurable with the side. He also observes that Aristotle cannot refer to the squaring of the circle; a question which was still in doubt in the time of Archimedes could not be assumed by Aristotle as an example of impossibility. The illustration, which passed into a proverb, ἐκ διαμέτρου ἀντικεῖσθαι, is confined to the side and diameter of the parallelogram. See also Waitz on Anal. Pr. 41 a 26.

‘And when the end is possible, so also is the beginning, because everything takes its origin, is generated, from a beginning’. The end implies the beginning: everything that comes into being or is produced —everything therefore with which the orator has to deal in his sphere of practical life—has a beginning. Since the beginning is implied in the end, it is clear that if the end be attainable or possible, so likewise must the beginning be.

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