[Footnote 55: Ibid. a. 20-23: [Greek: e)/ti d' a)/llos tro/pos e)sti\ _kata\ to\ a)na/logon_ e)kle/gein]. He gives as examples, [Greek: sê/pion, a)/kantha, o)stou=n].] Problems must be considered to be the same, when the middle term of the demonstration is the same for each, or when the middle term in the one is a subordinate or corollary to that in the other. Thus, the cause of echo, the cause of images in a mirror, the cause of the rainbow, all come under the same general head or middle term (refraction), though with a specific difference in each case. Again, when we investigate the problem, Why does the Nile flow with a more powerful current in the last half of the (lunar) month? the reason is that the month is then more wintry. But why _is_ the month then more wintry? Because the light of the moon is then diminishing. Here are two middle terms, the one of which depends upon the other. The problem for investigation is therefore the same in both.[56] [Footnote 56: Analyt. Post. II. xv. p. 98, a. 24-34. Theophrastus is said to have made collections of "_like problems_," problems of which the solution depended upon the same middle term (Schol. p. 249, a. 11**, Brand.).] Respecting _Causa_ and _Causatum_ question may be made whether it is necessary that when the _causatum_ exists, the _causa_ must exist also? The answer must be in the affirmative, if you include the cause in the definition of _causatum_. Thus, if you include in the definition of a lunar eclipse, the cause thereof, viz., intervention of the earth between moon and sun--then, whenever an eclipse occurs, such intervention must occur also. But it must not be supposed that there is here a perfect reciprocation, and that as the _causatum_ is in this case demonstrable from the cause, so there is the like demonstration of the cause from the _causatum_. Such a demonstration is never a demonstration of [Greek: dio/ti]; it is only a demonstration of [Greek: o(/ti]. The _causatum_ is not included in the definition of the cause; if you demonstrate that because the moon is eclipsed, therefore the earth is interposed between the moon and the sun, you prove the fact of the interposition, but you learn nothing about the cause thereof. Again, in a syllogism the middle term is the cause of the conclusion (_i.e._, it is the reason why the major term is predicated of the minor, which predication is the conclusion); and in this sense the cause and _causatum_ may sometimes reciprocate, so that either may be proved by means of the other. But the _causatum_ here reciprocates with the _causa_ only as premiss and conclusion (_i.e._, we may know either by means of the other), not as cause and effect; the _causatum_ is not cause of the _causa_ as a fact and reality, as the _causa_ is cause of the _causatum_.[57]