by Aristotle
7 · Why is it that the mouths of those who have eaten nothing, but are fasting, have a stronger odour, ‘the smell of fasting’, as it is called, but when they eat the odour ceases, when one would expect it to increase? Is it because, as the stomach becomes empty, the air becomes hotter from the absence of motion and causes the breath and the excretions of phlegm to putrefy? That the air becomes hotter is [15] proved by the fact that fasting also induces an increase of thirst. When food is taken, the odour ceases because it is less than that of the food; for the heat in the food overcomes the internal heat, so that it cannot undergo any process of change.
[20] 8 · Why has the armpit a more unpleasant odour than any other part of the body? Is it because it is least exposed to the air? Such parts have a particularly unpleasant odour because putrefaction takes place in them owing to the stagnation of fat. Or is it because the armpit is not moved and exercised?
9 · Why is it that those who have a goaty odour are still more unpleasant [25] when they anoint themselves with unguents? Is it because this kind of thing happens in many instances; for example, if something acid and something sweet are mixed, the resulting whole is sweeter? Now any one who perspires has an unpleasant odour, and unguents are productive of heat and therefore induce perspiration.
10 · Why is it that the odour of the breath of those who are bent and [30] deformed is more unpleasant and oppressive? Is it because the region round the lungs is contracted and bent out of an upright position, so that it does not give a free passage to the air, but the moisture and the breath, which tends to be enclosed within, putrefies?
11 · Why is it that most unguents are unpleasant when they mingle with [35] perspiration, but others have a sweeter or at any rate not a more unpleasant odour? Do those which change as a result of movement or friction deteriorate in odour, whereas those which do not are improved? There are some such perfumes, just as [909a1] there are some flowers from which scents are made, which deteriorate when rubbed or heated or dried, white violets, for example; but others remain the same, for instance roses. The unguents too made from flowers of the former class change, while those made from the latter do not; and so rose-perfume is least liable to [5] change. Also unguents have a more unpleasant odour on those whose perspiration is malodorous, through mingling with their opposite, just as honey when mixed with salt becomes not sweeter but less sweet.
12 · Why do objects always produce a stronger odour when they are in motion? Is it because they fill up the air? The result is that the odour is thus [10] transmitted more quickly to our perception.
BOOK XIV
PROBLEMS CONNECTED WITH THE EFFECT OF LOCALITY ON TEMPERAMENT
1 · Why are those who live under conditions of excessive cold or heat brutish in character and aspect? Is the cause the same in both cases? For the best mixture [15] of conditions benefits the mind as well as the body, but excesses of all kinds cause disturbance, and, as they distort the body, so do they pervert the mental temperament.
2 · Why is it that in Pontus corn, if exposed to the cold, keeps intact for many years? Is it because the extraneous moisture is evaporated together with the heat, as happens in grapes? For some things are evaporated by the cold and others with the [20] heat.
3 · Why do burning fevers occur more frequently in the coldest season? Is it because the cold imprisons the heat within? In the summer the contrary occurs, the interior of the body being cooler than the exterior. Burning fever is the inflammation in which,1 the exterior of the body being cold, the interior is in a condition of [25] excessive heat.
4 · Why are the Ethiopians and the Egyptians bandy-legged? Is it because the bodies of living creatures become distorted by heat, like logs of wood when they become dry? The condition of their hair too supports this theory; for it is curlier than that of other nations, and curliness is as it were crookedness of the hair. [30]
5 · Why is it that in damp regions copulation is more likely to lead to the birth of female offspring? Is it because a large amount of moisture thickens more slowly, and in damp regions the semen is moister owing to the presence of more moisture in the temperament?
6 · Why is it that in marshy districts sores on the head are quickly cured, but [35] those on the legs only with difficulty? Is it because the moisture, since it contains an earthy element, is heavy, and heavy things are carried downwards? Thus the upper parts of the body are easily concocted, because the impurities are carried downwards; but the lower parts become full of abundant excretion which easily putrefies.
7 · Why is it that those who live in airy regions grow old slowly, but those [909b1] who inhabit hollow and marshy districts age quickly? Is it because old age is a process of putrefaction, and that which is at rest putrefies, but that which is in motion is either quite free from, or at any rate less liable to, putrefaction, as we see in water? In lofty regions, therefore, owing to the free access of the breezes, the air [5] is in motion, but in hollow districts it stagnates. Furthermore, in the former, owing to its movement, the air is always pure and constantly renewed, but in marshy districts it is stagnant.
8 · Why are the inhabitants of warm regions cowardly, and those who dwell in cold districts courageous? Is it because there is a natural tendency which [10] counteracts the effects of locality and season, since if both had the same effect mankind would inevitably be soon destroyed by heat or cold? Now those who are hot by nature are courageous, and those who are cold are cowardly. But the effect of hot regions upon those who dwell in them is that they are cooled, while cold regions [15] engender a natural state of heat in their inhabitants. Both races are large of stature—those who live in cold regions because of the innate heat in them, and those who inhabit hot districts owing to the heat in which they live; for increase of stature occurs both in those who are hot and as a result of heat, whereas cold has a contracting effect. Since then those who live in cold districts have a powerful [20] principle of growth in themselves, and those who live in hot regions encounter no external cold which prevents their growth, both naturally admit of considerable increase in stature. But this is less true of those who live in our latitudes, because the principle of growth in them is less strong, and those who live in cold regions feel the contracting effect of cold.
[25] 9 · Why are those who live in hot regions longer-lived? Is it because their natural condition is drier, and that which is drier is less liable to putrefaction and more lasting, and death is as it were a kind of putrefaction? Or is it because death is due to the chilling of the interior heat, and everything is chilled by a surrounding [30] medium which is colder than itself? Now in warm regions the surrounding air is hot, but in cold regions it is cold and so more quickly and effectively destroys the interior heat of the body.
10 · Why are those who live in hot regions longer-lived? Is it because they [35] preserve their heat and moisture better? For death is the corruption of these.
11 · Why is it that we become drowsier in marshy districts? Is it because there we are more cooled, and cooling, being a kind of rest, induces sleep, and sleep occurs during rest?
[910a1] 12 · Why is it that those who live on board ship, though they spend their time on the water, have a healthier colour than those who live in marshes? Is the weather and the free access of the breezes the cause? Now water makes men pale when it putrefies, a process which is due to the absence of movement; that is why those who live in marshy regions are rather pale.
[5] 13 · Why is suffocating heat very frequently experienced in wintry regions, much more so than in warm districts? Is it because of the moisture in the air? For as a result of the same heat applied to it water becomes hotter than air, and therefore damper air2 becomes hotter than dry air.3 Or perhaps the air is not really hotter4 in these regions, but only seems so by contrast with the general coolness, as the sun [10] emerging from a cloud seems hotter in contrast with its effect when it is behind a cloud.
14 · Why do those who live in southerly climes tend to have black eyes? Is blueness of the eyes due
to excess of internal heat, whereas blackness is due to its absence, as Empedocles affirms? Just, therefore, as those who dwell in the north [15] have blue eyes, because the internal heat is prevented from escaping owing to the external cold; so in those who dwell in southerly climes the moisture cannot escape owing to the surrounding heat, but the heat escapes because there is nothing to bar its exit, and the moisture left behind causes blackness; for when light departs that [20] which is left behind is dark. Or does the pigmentation of the eye assimilate itself to the colour of the rest of the body? If so, the eyes of those who live towards the north are blue, because they are themselves white (for blue is akin to white); and those who dwell in the south being black, their eyes also are black. [25]
15 · Why are those who live in warm regions wiser than those who dwell in cold districts? Is it for the same reason as that for which the old are wiser than the young? For those who live in cold regions are much hotter, because their nature recoils owing to the coldness of the region in which they live, so that they are very like the drunken and are not of an inquisitive turn of mind, but are courageous and [30] sanguine; but those who live in hot regions are sober because they are cool. Now everywhere those who feel fear make more attempt to inquire into things than do the self-confident, and therefore they discover more. Or is it because the race of those who live in warm regions is more ancient, the inhabitants of the cold regions having perished in the Flood, so that the latter stand in the same relation to the [35] former as do the young to the old?
16 · Why are the inhabitants of warm regions cowardly, and those who dwell in cold regions courageous? Is it because human beings have a natural tendency which counteracts the effect of locality and season (for, if both had the [910b1] same tendency, they would soon be destroyed)? Now those who are hot by nature are courageous and those who are cold are cowardly. The effect of hot regions upon their inhabitants is to cool them (for, their bodies having rarities, the heat escapes out of them), but those who live in a cold climate become heated in their nature, [5] because their flesh is condensed by the external cold, and when it is in this condition the heat collects internally.
BOOK XV
PROBLEMS CONNECTED WITH MATHEMATICAL THEORY
1 · Why is it that of all the lines which divide a rectilinear figure into two [10] parts that drawn from angle to angle alone bears the name of diameter? Is it because the diameter, as its name implies, divides the figure of which it is the diameter into two parts without destroying it? The line therefore which divides it at [15] its joints (by which I mean the angles) will be the diameter; for it does not destroy the figure but divides it, like those who divide up implements of war for distribution. But a division which cuts through a composite figure in the lines which form it destroys the figure; for a rectilinear figure is constructed on angles.
2 · Why is the diameter so called? Is it because it is the only line which divides a rectilinear figure into two parts, as though one should call it the [20] ‘dichameter’?1 And why2 is it the only one that bears this name of all the lines which divide a rectilinear figure into two parts? Is it because it is the only line which divides the figure at the points where its limbs bend, whereas all other lines divide it in its sides?
3 · Why do all men, barbarians and Greeks alike, count up to 10 and not up to any other number, saying for example, 2, 3, 4, 5 and then repeating them, [25] one-five, two-five, just as they say eleven, twelve?3 Or why do they not stop at some point beyond ten and repeat from there? For every number is made up of one, two, &c, combined with a preceding number, and thus a different number is formed; but the counting always proceeds in fixed sets of ten. For it is clearly not the result [30] of chance that all men invariably count in tens; and that which is invariable and universal is not the result of chance, but is in the nature of things. Is it because ten is a perfect number? For it combines every kind of number, odd and even, square and cube, length and surface, prime and composite. Or is it because ten is the original [35] number, since one, two, three, and four together make ten? Or is it because the bodies which move in the heavens are nine in number? Or is it because in ten proportions four cubic numbers result, from which numbers the Pythagoreans declare that the whole universe is constituted? Or is it because all men have ten fingers and so, as though possessing counters that indicate the numbers proper to [911a1] man, they count all other things by this quantity? One race among the Thracians alone of all men count in fours, because their memory, like that of children, cannot extend farther and they do not use a large number of anything.
[5] 4 · … because the earth is a centre? For the shapes which appear to us are always similar. This does not seem4 to be so unless one views them from the centre, but they would sometimes appear triangular, sometimes irregular foursided figures, and sometimes take other forms. Now the earth would appear to us to be the centre of the universe, if we could view it from the heavenly bodies.5 For the earth being spherical, the centre of the universe and of the earth will be the same. But we dwell [10] on the surface of the earth, so that it is not from the centre but at the distance of half the diameter that the heavenly bodies appear to have the shapes that they do appear to have. What reason then is there why the appearance of their shapes should not remain the same when the distance is increased?
5 · Why is it that, although the sun moves with uniform motion, yet the increase and decrease of the shadows is not the same in any equal period of time? Is [15] it because the angles to the objects seen, that is the angles made by the rays of the sun and subtending equal arcs, are equal? Now if these are equal, so also are the angles which the rays when produced6 make in the triangle formed by the first ray and the object seen and the shadow. If the angles are equal, the line which is farther from the object seen must be greater than that which is less far; for we know that [20] this is so. Let the circumference, therefore, be divided into any number of equal parts, and let the object seen be H. When therefore the sun at A falling on H makes the shadow HL7 the ray must fall on L. But when the sun comes to B, the ray from B will fall within HL, and similarly again when the sun comes to C; otherwise one [25] straight line will touch another straight line at two points. Since therefore AB is equal to BC, the angles which subtend them at D will also be equal, for they are situated about the centre. But if the angles on this side of D are equal, so also are the corresponding angles in the triangle; for they are at the apexes of the first pair of angles. So while the angle is divided into two equal parts, the line LE will be greater [30] than the line EF within LH.8 So too with the other angles formed by the rays from the circumference. At the same time it is clear that the shadow must be shortest at midday and that then its increases are least. For the sun is most over our head at midday, and stifling heat occurs both for the reason just mentioned and because [35] there is no wind; for wind is caused when the sun dissipates the air near the earth. If therefore it does so simultaneously in both hemispheres, midnight and midday [911b1] would naturally be windless.
6 · Why does the sun penetrating through quadrilaterals form not rectilinear shapes but circles, as for instance when it passes through wicker-work? Is it because the projection of the vision is in the form of a cone, and the base of a cone is a circle, [5] so that the rays of the sun always appear circular on whatever object they fall? For the figure also formed by the sun must be contained by straight lines, if the rays are straight; for when they fall in a straight line on to a straight line, they form a figure contained by straight lines. And this is what happens with the rays; for they fall on [10] the straight line of the wicker-work, at the point where they shine through, and are themselves straight, so that their projection is a straight line. But because the parts of the vision which are cut off towards the extremities of the straight lines are weak, the parts of the figure about the angles are not seen; but what there is of straight line [15] in the cone describes a straight line, while the rest does not, but the sight falls on part of the figure without perceiving it. For there are many th
ings to which the sight penetrates without our seeing them, objects, for instance, which are in darkness. A similar phenomenon is the fact that a quadrilateral figure appears polygonal, and at a greater distance circular. Now since the projection of sight is in the form of a cone, [20] when the figure is removed to a distance the parts of the vision which are cut off towards the angles, because they are weak and few, do not see anything when the distance is increased; but the parts of the vision which fall upon the centre of the [25] figure, being numerous and strong, are more persistent. When, therefore, the figure is near at hand, they can9 see the parts in the angles; but, when the distance is greater,10 they cannot do so. For this reason too a curved line removed to a distance appears straight, and the moon on the eighth day seems to be contained by straight [30] lines, if the vision falls upon the line which encloses it and not on its breadth. For when the circumference is near, the sight can discern how much nearer one part of the circumference is than another; but when it is distant, the sight does not perceive it clearly, and it seems to be equally distant; and so it appears to be straight.