153 · At Athens they say that the sacred branch of the olive tree in one day buds and increases, but quickly shrinks together again.
154 · When the craters in Etna once burst forth, and the lava was carried hither and thither over the land like a torrent, the deity honoured the race of the [10] pious; for when they were hemmed in on all sides by the stream, because they were bearing their aged parents on their shoulders, and were trying to save them, the stream of fire, having come near to them, was cleft asunder, and turned aside one [15] part of the flame in this direction, another in that, and preserved the young men unharmed, along with their parents.
155 · It is said that the sculptor Phidias, while constructing the Athene in the Acropolis, carved his own face in the centre of her shield, and connected it by an [20] imperceptible artifice with the statue, so that, if any one wished to remove it, he must necessarily break up and destroy the whole statue.
156 · They say that the statue of Bitys in Argos killed the man who had caused the death of Bitys, by falling upon him while he was looking at it. It appears therefore that such events do not happen at random.
[25] 157 · Men say that dogs pursue wild beasts only to the summits of the so-called Black Mountains, but turn back when they have pursued them as far as these.
[30] 158 · In the river Phasis it is related that a rod called the ‘White-leaved’ grows, which jealous husbands pluck, and throw round the bridal-bed, and thus preserve their marriage from adultery.
159 · In the Tigris they say there is a stone found, called in the barbarian language Modon, with a very white colour, and that, if any one possesses this, he is not harmed by wild beasts.
160 · In the Scamander they say a plant grows, called the Rattle, resembling [35] a chick-pea, and that it has seeds that shake, from which fact it has obtained its name: those who possess it (so it is said) fear neither demon nor apparition of any kind.
161 · In Libya there is a vine, which some people call mad, that ripens some [846b1] of its fruit, others it has like unripe grapes, and others in blossom, and this during a short time.
162 · On Mount Sipylus they say there is a stone like a cylinder, which, when pious sons have found it, they place in the sacred precincts of the Mother of [5] the Gods, and never err through impiety, but are always affectionate to their parents.
163 · On Mount Taÿgetus (it is said) there is a plant called the love-plant, which women in the beginning of spring fasten round their necks, and are loved more passionately by their husbands.
[10] 164 · Othrys is a mountain of Thessaly, which produces serpents that are called Rotters, which have not a single colour, but always resemble the place in which they live. Some of them have a colour like that of land snails, while the scales of others are of a bright green; but all of them that dwell in the sands become like these in colour. When they bite they produce thirst. Now their bite is not rough and [15] fiery, but malicious.
165 · When the dark-coloured adder copulates with the female, the female during the copulation bites off the head of the male; therefore also her young ones, as though avenging their father’s death, burst through their mother’s belly. [20]
166 · In the river Nile they say that a stone like a bean is produced, and that, if dogs see it, they do not bark. It is beneficial also to those who are possessed by some demon; for, as soon as it is applied to the nostrils, the demon departs. [25]
167 · In the Maeander, a river of Asia, they say that a stone is found, called by contradiction ‘sound-minded’; for if one throws it into any one’s bosom he becomes mad, and kills some one of his relations.
168 · The rivers Rhine and Danube flow towards the north, one passing the Germans, the other the Paeonians. In the summer they have a navigable stream, but [30] in the winter they are congealed from the cold, and form a plain over which men ride.
169 · Near the city of Thurium they say there are two rivers, the Sybaris and the Crathis. Now the Sybaris causes those that drink of it to be timorous, while the Crathis makes men yellow-haired when they bathe in it. [35]
170 · In Euboea there are said to be two rivers; the sheep that drink from one of them become white—it is called Cerbes; the other is the Neleus, which makes them black.
171 · Near the river Lycormas it is said that a plant grows, which is like a [847a1] lance, and is most beneficial in the case of dim sight.
172 · They say that the fountain of Arethusa at Syracuse in Sicily is set in motion every five years.
173 · On Mount Berecynthius it is said that a stone is produced called ‘the [5] Sword’, and if any one finds it, while the mysteries of Hecate are being celebrated, he becomes mad, as Eudoxus affirms.
174 · On Mount Tmolus it is said that a stone is produced like pumice-stone, which changes its colour four times in the day; and that it is only seen by maidens who have not yet attained to years of discretion.
175 · On the altar of the Orthosian Artemis it is said that a golden bull [847b1] stands, which bellows when hunters enter the temple.
176 · Among the Aetolians it is said that moles see, but only dimly, and do not feed on the earth, but on locusts.
[5] 177 · They say that elephants are pregnant during the space of two years, while others say during eighteen months; and that in giving birth they suffer hard labour.
178 · They say that Demaratus, the pupil of the Locrian Timaeus, having fallen sick, was dumb for ten days; but on the eleventh, having slowly come to his senses after his delirium, he declared that during that time he had lived most [10] agreeably.
**TEXT: O. Apelt, Teubner, Leipzig, 1888
1Retaining ἐπ’ αὐτῶν.
2Reading τoὺς κόλπoυς.
3Reading μὴ εἶναι.
4Odyssey XII 67.
MECHANICS**
E. S. Forster
Our wonder is excited, firstly, by phenomena which occur in accordance with [847a10] nature but of which we do not know the cause, and secondly by those which are produced by art despite nature for the benefit of mankind. Nature often operates contrary to human interest; for she always follows the same course without [15] deviation, whereas human interest is always changing. When, therefore, we have to do something contrary to nature, the difficulty of it causes us perplexity and art has to be called to our aid. The kind of art which helps us in such perplexities we call Mechanical Skill. The words of the poet Antiphon are quite true: [20]
Mastered by Nature, we o’ercome by Art.
Instances of this are those cases in which the less prevails over the greater, and where forces of small motive power move great weights—in fact, practically all those problems which we call Mechanical Problems. They are not quite identical [25] nor yet entirely unconnected with Natural Problems. They have something in common both with Mathematical and with Natural Speculations; for while Mathematics demonstrates how phenomena come to pass, Natural Science demonstrates in what medium they occur.
Among questions of a mechanical kind are included those which are connected [847b10] with the lever. It seems strange that a great weight can be moved with but little force, and that when the addition of more weight is involved; for the very same weight, which one cannot move at all without a lever, one can move quite easily with it, in spite of the additional weight of the lever. [15]
The original cause of all such phenomena is the circle. It is quite natural that this should be so; for there is nothing strange in a lesser marvel being caused by a greater marvel, and it is a very great marvel that contraries should be present together, and the circle is made up of contraries. For to begin with, it is formed by [20] motion and rest, things which are by nature opposed to one another. Hence in examining the circle we need not be much astonished at the contradictions which occur in connexion with it. Firstly, in the line which encloses the circle, being without breadth, two contraries somehow appear, namely, the concave and the [25] convex. These are as much opposed to one another as the great is to the small; the mean being i
n the latter case the equal, in the former the straight. Therefore just as, if they are to change into one another, the greater and smaller must become equal [848a1] before they can pass into the other extreme; so a line must become straight in passing from convex into concave, or on the other hand from concave into convex and curved. This, then, is one peculiarity of the circle.
Another peculiarity of the circle is that it moves in two contrary directions at [5] the same time; for it moves simultaneously to a forward and a backward position. Such, too, is the nature of the radius which describes a circle. For its extremity comes back again to the same position from which it starts; for, when it moves continuously, its last position is a return to its original position, in such a way that it [10] has clearly undergone a change from that position.
Therefore, as has already been remarked, there is nothing strange in the circle being the origin of any and every marvel. The phenomena observed in the balance can be referred to the circle, and those observed in the lever to the balance; while [15] practically all the other phenomena of mechanical motion are connected with the lever. Furthermore, since no two points on one and the same radius travel with the same rapidity, but of two points that which is further from the fixed centre travels more quickly, many marvellous phenomena occur in the motions of circles, which will be demonstrated in the following problems.
[20] Because a circle moves in two contrary forms of motion at the same time, and because one extremity of the diameter, A, moves forwards and the other, B, moves backwards, some people contrive so that as the result of a single movement a number of circles move simultaneously in contrary directions, like the wheels of [25] brass and iron which they make and dedicate in the temples. Let AB be a circle and CD another circle in contact with it; then if the diameter of the circle AB moves forward, the diameter CD will move in a backward direction as compared with the circle AB, as long as the diameter moves round the same point. The circle CD [30] therefore will move in the opposite direction to the circle AB. Again, the circle CD will itself make the adjoining circle EF move in an opposite direction to itself for the same reason. The same thing will happen in the case of a larger number of circles, [35] only one of them being set in motion. Mechanicians seizing on this inherent peculiarity of the circle, and hiding the principle, construct an instrument so as to exhibit the marvellous character of the device, while they obscure the cause of it.
[848b1]1 · First then, a question arises as to what takes place in the case of the balance. Why are larger balances more accurate than smaller? And the fundamental principle of this is, why is it that the radius which extends further from the centre is displaced quicker than the smaller radius, when the near radius is moved [5] by the same force? Now we use the word ‘quicker’ in two senses; if an object traverses an equal distance in less time, we call it quicker, and also if it traverses a greater distance in equal time. Now the greater radius describes a greater circle in equal time; for the outer circumference is greater than the inner.
[10] The reason of this is that the radius undergoes two displacements. Now if the two displacements of a body are in any fixed proportion, the resulting displacement must necessarily be a straight line, and this line is the diagonal of the figure, made by the lines drawn in this proportion.
Let the proportion of the two displacements be as AB to AC, and let A1 be brought to B, and the line AB brought down to GC. Again, let A be brought to D [15] and the line AB to E; then if the proportion of the two displacements be maintained, AD must necessarily have the same proportion to AE as AB to AC. Therefore the small parallelogram is similar to the greater, and their diagonal is the same, so that [20] A will be at F. In the same way it can be shown, at whatever points the displacement be arrested, that the point A will in all cases be on the diagonal.
Thus it is plain that, if a point be moved along the diagonal by two displacements, it is necessarily moved according to the proportion of the sides of the parallelogram; for otherwise it will not be moved along the diagonal. If it be moved [25] in two displacements in no fixed ratio for any time, its displacement cannot be in a straight line. For let it be a straight line. This then being drawn as a diagonal, and the sides of the parallelogram filled in, the point must necessarily be moved according to the proportion of the sides; for this has already been proved. Therefore, [30] if the same proportion be not maintained during any interval of time, the point will not describe a straight line; for, if the proportion were maintained during any interval, the point must necessarily describe a straight line, by the reasoning above. So that, if the two displacements do not maintain any proportion during any interval, a curve is produced.
Now that the radius of a circle has two simultaneous displacements is plain from these considerations, and because the point from being vertically above the [849]a1 centre comes back to the perpendicular,2 so as to be again perpendicularly above the centre.
Let ABC be a circle, and let the point B at the summit be displaced to D, and come eventually to C. If then it were moved in the proportion of BD to DC, it would [5] move along the diagonal BC. But in the present case, as it is moved in no such proportion, it moves along the curve BEC. And, if one of two displacements caused by the same forces is more interfered with and the other less, it is reasonable to suppose that the motion more interfered with will be slower than the motion less interfered with; which seems to happen in the case of the greater and less of the radii [10] of circles. For on account of the extremity of the lesser radius being nearer the stationary centre than that of the greater, being as it were pulled in a contrary direction, towards the middle,3 the extremity of the lesser moves more slowly. This is the case with every radius, and it moves in a curve, naturally along the tangent, [15] and unnaturally towards the centre. And the lesser radius is always moved more in respect of its unnatural motion; for being nearer to the retarding centre it is more constrained. And that the less of two radii having the same centre is moved more [20] than the greater in respect of the unnatural motion is plain from what follows.
Let BCED be a circle, and XNMO another smaller circle within it, both having the same centre A, and let the diameters be drawn, CD and BE in the large [25] circle, and MX and NO in the small; and let the rectangle DYRC be completed. If the radius AB comes back to the same position from which it started, i.e. to AB, it is plain that it moved towards itself; and likewise AX will come to AX. But AX moves [30] more slowly than AB, as has been stated, because the interference is greater and AX is more retarded.
Now let AHG be drawn, and from H a perpendicular upon AB within the circle, HF; and, further, from H let HZ be drawn parallel to AB, and ZU and GK [35] perpendiculars on AB; then ZU and HF are equal. Therefore BU is less than XF; for in unequal circles equal straight lines drawn perpendicular to the diameter cut off smaller portions of the diameter in the greater circles; ZU and HF being equal.
[849b1] Now the radius AH describes the arc XH in the same time as the extremity of the radius BA has described an arc greater than BZ in the greater circle; for the natural displacement is equal and the unnatural less, BU being less than XF [5] Whereas they ought to be in proportion, the two natural motions in the same ratio to each other as the two unnatural motions.
Now the radius AB has described an arc GB greater than ZB. It must necessarily have described GB in this time; for that will be its position when in the two circles the proportion between the unnatural and natural movements holds [10] good. If, then, the natural movement is greater in the greater circle, the unnatural movement, too, would agree in being proportionally greater in that case only, where B is moved along GB while X is moved along XH. For in that case the point B comes by its natural movement to G, and by its unnatural movement to K, GK being [15] perpendicular from G. And as GK to BK, so is HF to XF. Which will be plain, if B and X be joined to G and H. But, if the arc described by B be less or greater than GB, the result will not be the same, nor will the natural movement be proportional to the unnatural in the two circles.
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[20] So that the reason why the point further from the centre is moved quicker by the same force, and the greater radius describes the greater circle, is plain from what has been said; and hence the reason is also clear why larger balances are more accurate than smaller. For the cord by which a balance is suspended acts as the centre, for it is at rest, and the parts of the balance on either side form the radii. [25] Therefore by the same weight the end of the balance must necessarily be moved quicker in proportion as it is more distant from the cord, and some weight must be imperceptible to the senses in small balances, but perceptible in large balances; for there is nothing to prevent the movement being so small as to be invisible to the eye. [30] Whereas in the large balance the same load makes the movement visible. In some cases the effect is clearly seen in both balances, but much more in the larger on account of the amplitude of the displacement caused by the same load being much greater in the larger balance. And thus dealers in purple, in weighing it, use [35] contrivances with intent to deceive, putting the cord out of centre and pouring lead into one arm of the balance, or using the wood towards the root of a tree for the end [850a1] towards which they want it to incline, or a knot, if there be one in the wood; for the part of the wood where the root is is heavier, and a knot is a kind of root.
2 · How is it that if the cord is attached to the upper surface of the beam of a balance, if one takes away the weight when the balance is depressed on one side, the beam rises again; whereas, if the cord is attached to the lower surface of the beam, it does not rise but remains in the same position? Is it because, when the cord is [5] attached above, there is more of the beam on one side of the perpendicular than on the other, the cord being the perpendicular? In that case the side on which the greater part of the beam is must necessarily sink until the line which divides the beam into two equal parts reaches the actual perpendicular, since the weight now [10] presses on the side of the beam which is elevated.
The Complete Works of Aristotle Page 226
