Physics

1.    Introduction

Physical theories underlie all other theories in Greek science, for physics concerned the nature of stuff. It offered answers to the question ‘what is it made of?’, where the ‘it’ could be anything and everything. Consequently, all other subjects looked to one or another theory in physics for understanding of the nature of the stuff of their study, be it heaven, earth, soul or whatever. Consider two examples.

1. The author of On Colours ([Aristotle]) tries to explain what is going on when a mineral’s streak colour¹ is different from the external colour of the stone or metal by reference to his theory of matter and the formation of minerals:

‘Some objects, when smoothed by rubbing or by other forces, exhibit varied and different colours, like silver when it is rubbed and gold, bronze and steel. Some kinds of stones show different colours, like ***,² for though black they draw white lines, because they are originally composed of small elements which are thick and black, and by the dyeing process which takes place when they are made, all the passages through which the dye passes are coloured, so that a different appearance is given to the [overall] colour… But in the process of rubbing each of them to a homogeneous and smooth surface, as in treating on a touchstone, they lose their blackness, and recover their colour, the dye showing through when there is contact and continuity’ (793a20-b3, Hett trans.).

Now a modern geology book will explain the concept of a streak colour, but will not normally explain why the streak colour may differ from the colour of the stone.³ [Aristotle] was trying to explain it, and explanation at this level in any field ultimately rested on the author’s beliefs about matter and change.

2. Philon’s explanation of why solid bronze plates can be springy enough to fire missiles includes the statements that, on the one hand, heating softens metal because the particles become less densely packed, while on the other tempering and hammering harden them. Of the latter he says ‘for both processes cause the particles to become tightly packed, because the minute pieces of matter run together and the interstices of void are removed’, and thus the bronze plates from which the springs are made have hard faces on a soft middle, producing resilience.⁴

In the modern world physics is a diverse subject covering all sorts of things, from theoretical particles with rum names (e.g. gluons which, as their name suggests, stick other particles together), through mechanics and optics, to forces of nature such as gravity and magnetism. I shall divide the discussion into two parts: matter, and forces acting on matter, though this leaves subjects like optics difficult to place.⁵

With regard to matter, the ancients’ non-recognition of a clear distinction between organic and inorganic matter, together with their habit of drawing analogies and examples from the animal, vegetable and mineral kingdoms, means that in ancient sources there is no obvious dividing line between what we would call physics and what we would call biology or chemistry.⁶ The history of chemistry as usually written seems to be almost unique in having no ancient component, as if it did not exist.⁷ This is perhaps because ancient ideas about the combination and separation of bits of matter were usually dealt with in treatises entitled Physics, or, in the case of the most important ancient treatise on this subject, in a work entitled Meteorology (Aristotle’s work of that name, book 4).⁸ However, C Anne Wilson argues convincingly that distilling of wine can be traced back to the fifth century BC.⁹

With regard to forces, some texts adopt a more mathematical bent, such as Archimedes’ On Floating Bodies, while others adopt a more practical bent (and go under the name Mechanics) such as Hero’s Artillery-construction. It is becoming increasingly clear that ancient technology could reach extraordinary degrees of sophistication, matching and sometimes surpassing the complexity found in treatises on mechanics. Various Archimedean, Ktesibian and Heronian machines which are described more or less fully in surviving texts¹⁰ were formerly considered by some scholars either to be purely theoretical constructions or as ‘gadgets’ or ‘toys’. But the Antikythera mechanism (de Solla Price 1974) and the south-pointing chariot (Lewis 1992) make it abundantly clear that ancient technology was not exclusively low-tech, and should not be treated in isolation from ancient ideas and practices in mathematics and physics, a good understanding of which must have been necessary to make these machines.¹¹ Nor were machines unusual in ancient society. They were to be found in every home, many public buildings and spaces, on and under the ground and sea, for work and for pleasure. From looms and olive presses, locks and keys, hoists and windlasses, to water-clocks and thunder-makers, machines were a familiar part of life for the ancient Greeks and Romans.

This inevitably leads some to question why there was no scientific revolution, and no industrial revolution, in antiquity. I believe that this is the wrong question,¹² but nevertheless offer an answer to it. In my view, one reason is this. These modern revolutions depended on continuity of effort: many people building on many predecessors’ work. Years, decades, even centuries of intellectual and financial investment in research and development – this is what was missing in Greece.¹³ Babbage conceived the analytical engine (the first mechanical general purpose computer) before 1834; a long and winding set of paths (some dead ends), travelled by a lot of people, spending a lot of money, separate Charles Babbage and Bill Gates. As for the related idea that there was technological ‘stagnation’ in antiquity, this rests on two oversights. First, it more or less completely ignores the development of a technology, and second, it maintains an unelucidated and apparently unbridgeable chasm between ‘innovation’ and ‘improvement’. It is tantamount to saying that the internal combustion engine to be found in, say, a transit van (never mind a Formula 1 racing car), is the same as that designed by Diesel in the 1890s, which was bolted to the floor and had a cylinder 10 feet long.¹⁴

2.    Theories of Matter

Ancient physical theories attempted to identify and explain the nature of body and soul, of space and time, of generation and destruction. The apparent constant flux in nature was explained either as an illusion (by e.g. Parmenides), or as real change (by e.g. Aristotle), in which case further hypotheses were needed and were developed to explain how stuff of type A, e.g. water, could turn into stuff of type B, e.g. ice. Physicists strove for a reduction in the number of types of stuff in the cosmos, from the apparent bewildering countless varieties to some small set of basic ingredients. Four-elements theorists reduced the number of types of stuff to four, which when mixed would account for all that variety. Atomists reduced the types of stuff to one, but allowed for numerous different shapes and sizes of indivisible bits (atoms) of that stuff, and made the mixture of shapes and sizes explain the variety. Both of these basic and competing views on the nature of matter were developed early, before Plato and Aristotle: four-elements by Empedokles, fl. 495-35, atomism by Leucippus (dates unknown) and Demokritos, fl. 460-360 (a contemporary of Sokrates).

Aristotle developed Empedokles’ four-elements theory to explain how the elements are built up to form all the things that we see, hear, smell, taste and touch. The four elements – elemental earth, air, fire and water¹⁵ – combine to form homoiomers. These are homogenous substances such as blood, bone, bark, sap, sand or gold. Homoiomers of different types are combined (in the sense of juxtaposition rather than chemical synthesis) to form parts, such as a hand, a leaf, or a piece of ore. Different parts are joined together to form wholes, such as a human body, a tree, or a rock.

For Aristotle, matter was continuous. Everything in the universe was connected in a plenum. There might be spaces between homoiomers, parts or wholes, forming passages or gaps, but those spaces were filled with air or other substances – recall e.g. the except from On Colours quoted in the introduction to this page. Through such passages one substance might interpenetrate another, as in the dyeing process in that example, but such a juxtaposed mixture of two or more substances was distinguished from a synthesis of two homoiomers to create another homoiomer. Aristotle abhorred the notion of void, and spent about half of his time in the Physics arguing against atomism, which presupposed void. Although four-elements theory remained the more popular physical theory in antiquity, atomism was never ousted. It was developed by Epikouros and taken to Rome by Lucretius. Some of Aristotle’s colleagues and students put both theories to the test, and seem to have blurred the distinctions between them as a result. For example, Theophrastos investigated the nature of fire, and raised some very serious objections to the idea that fire could be an element (see his On Fire); for example, he pointed out that fire requires fuel, and that man can make fire, neither of which facts sit happily with the idea that fire is a first principle and elemental substance. Similarly Strato did a lot of work on void, and showed in a number of simple but telling demonstrations that void does exist, or at least can be created artificially: for example, take a small mouthed small jar, put it to your lips, suck the air out, and it will stick to your lips, trying to draw them into itself to fill the vacuum.¹⁶

One of the most famous stories from antiquity is all about the discovery of a fundamental idea in physics: specific gravity (though this term itself it not used). We are fortunate in this case in having not just the popular version of the discovery, but also the full text of Archimedes’ own published results of the same discovery. And the contrast between them is interesting and significant. Let us first hear the story as Vitruvius tells it in On Architecture 9.Pref.9-12 (Thomas trans.):

There are several things to note here. First, Vitruvius’ book On Architecture contains much more than one might expect from the title. Indeed, apart from several scientific discoveries which he understands and discusses well (see e.g. 7.8.3 on the comparative specific gravities of mercury and gold), this book is a mine of information on all sorts of ancient ideas and practices, from the sphericity of the earth and how to make a sundial at any particular location, to the identification of good and bad water sources and many different ways to make the colour black. Second, Hiero, despite his tyrannical power, and apparently taking this as an insult to himself (rather than to the gods), does not jump to the conclusion that the rumour about the goldsmith is true, or have the man tortured or tried or any other standard method available to Greek states to try to establish the truth, but asks the resident genius to apply his mind to the problem. Third, Vitruvius gives us much incidental information on daily life in Archimedes’ Syrakuse, for example that the customer supplied the raw material and the craftsmen was paid for his labour upon it¹⁷ (also true for Roman times); that domestic houses lacked bathing facilities (also true for most houses in Roman times); and that Greek baths were tubs not pools (not true of most Roman baths). Fourth, what we have here is a story of discovery. It explains in ordinary language a simple experiment, and draws out the crucial distinction between the weight of a body and its density (here in the sense of ‘mass’, lump or size). What it does not do is offer any general statement of the principle at work, nor any proof of it.

If we turn now to Archimedes’ own words on the same subject, we find a very different sort of story. The relevant work is entitled On Floating Bodies which, despite the title, is as much about bodies which sink, like the crown, as those that float. It deals with both matter and forces acting upon it, but since it is most famous for the discovery concerning matter, I include it in this section. It begins with one postulate (Heath trans.):¹⁸

‘Postulate 1

Let us assume that a fluid has the property that, if its parts lie evenly and are continuous, the part which is less compressed is expelled by that which is more compressed; and each of its parts is compressed by the fluid above it perpendicularly, unless the fluid is shut up in something and compressed by something else.’

From this very modest beginning he moves on to the propositions, which are proved geometrically one by one.

‘Proposition 1

If a surface be cut by a plane always passing through a certain point, and if the section be always a circumference [of a circle] whose centre is the aforesaid point, the surface is that of a sphere.

…

Proposition 2

The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the earth.

…

Proposition 3

Of solids those which, size for size, are of equal weight with a fluid will, if let down into the fluid, be immersed so that they do not project above the surface but do not sink lower.

…

Proposition 4

A solid lighter than a fluid will, if immersed in it, not be completely submerged, but part of it will project above the surface.

…

Proposition 5

Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced.

…

Proposition 6

If a solid lighter than a fluid be forcibly immersed in it, the solid will be driven upwards by a force equal to the difference between its weight and the weight of the fluid displaced.

…

Proposition 7

A solid heavier than a fluid will, if placed in it, descend to the bottom of the fluid, and the solid will, when weighed in the fluid, be lighter than its true weight by the weight of the fluid displaced.’

The seventh proposition is Archimedes’ own version of the discovery. Instead of a tale about crowns and kings, about sploshing around in a tub and the excitement of discovery, about dropping things in pots of water and measuring the volume of water required to refill the pot after removing them again, we have a completely general assertion of a fact about the weight of a solid in air and in water, and a proof that it is true. Note that it does not go on to say that different materials have different ratios of weight in water to what Archimedes calls its ‘true’ weight, i.e. weight in air, yet it is only by that fact that the alloyed nature of the crown could be proved, since silver and gold have different ratios. But the specific gravity of anything is something which can only be found by empirical means, and I think that Archimedes could not have made any general statements about it which he could have proved, so he said nothing.

When we look at the crucial set of experiments, they work on volumes in Vitruvius’ version, but the principle is expressed in weights in Archimedes’. Translated into modern mathematical formulae¹⁹ both methods end up with equivalent results, but in terms of practice they involve significant differences. For the method described by Vitruvius requires a waterproof pot big enough to hold the crown, the acquisition of a lump of gold and a lump of silver each equal in weight-in-air to the crown, and a jug. It is much more simple than the method implied by Archimedes, which requires in addition a balance or set of scales, with (at least) a bowl-type pan for the scales for weighing the water displaced. Archimedes’ method, however, would be much more exact, since ancient scales could weigh very finely indeed, whereas fluid measurements were much more rough and ready. It is possible that Archimedes made the discovery by the volume method, but then developed the more accurate and more complete weight method.

The concept of specific gravity became so well and so widely understood by Nero’s time that Seneca, in his popularizing work on natural science, considered it obvious, and discussed it without reference to Archimedes, the bath, crown, or any other element in the tale (NQ 3.25.5-6, Corcoran trans.):

‘It is well known that there are certain lakes which support people who do not know how to swim. There used to be a pond in Sicily, and there still is one is Syria, where bricks float and no objects thrown in sink no matter how heavy they are. The reason for this is obvious. Weigh anything you like and compare it with water, provided the volume (modus, measure) of both is equal. If the water is heavier it will support the object which is lighter and lift it as high above the surface as it is lighter. Objects heavier than the water will sink. But if the weight of the water is equal to the weight of the object you measure it against, the object will neither go to the bottom nor stick up. It will be in balance with the water and in fact will float but almost submerged and without any part sticking up. This is why some logs are elevated almost entirely above water, others are half-way submerged, others go down to the point of equal balance in the water. For, when the weight of both is equal neither yields to the other, but objects heavier than the water sink, the lighter objects are supported. However, heavy or light derives not from our own estimate but from a comparison with the water in which the object is to be carried. So, when water is heavier than a man’s body or a stone it does not permit anything to sink which does not overcome the water’s own heaviness’.

It is worth noting, finally, that the fact of the displacement of water was known, long before Archimedes’ lived, to a slave called Aesop. His fables were widely known, and one in particular may have played some small and perhaps subconscious role in this discovery. It is as follows (Vernon-Jones trans.):

‘A thirsty crow found a pitcher with some water in it, but so little was there that, try as she might, she could not reach it with her beak, and it seemed as though she would die of thirst within sight of the remedy. At last she hit upon a clever plan. She began dropping pebbles into the pitcher, and with each pebble the water rose a little higher until at last it reached the brim, and the knowing bird was enabled to quench her thirst.’

The essential difference between this and Archimedes’ behaviour – between being a wise old bird and being a scientist – is that Archimedes measured the amount of water displaced (by weight, volume or both), dropped lumps of different materials of the same weight into the water, and compared the amount of water displaced in each case.

3.    Forces

The earliest theories on forces were propounded in the context of cosmologies, for example Anaximander’s notions of ‘Love’ and ‘Strife’ as the forces which bring the elements together and rent them apart respectively, or Anaxagoras’ ‘Mind’ which controls the world. In due course theories developed two separate strands, one for sub-lunar phenomena (terrestrial and atmospheric), and another for the celestial bodies, which were thought to be composed of something else and to behave in a different way, in keeping with their perfection (unlike the imperfection of the earthly world). Our interest here is in their ideas about sub-lunar phenomena.

For Aristotle, it is the primary qualities or properties of Hot and Cold which act on passive Moist and Dry matter to change it. Change was understood very broadly, to include e.g. change of place, change of colour, and change of food into blood and excreta. The principal motive forces were innate heat and natural motion. Innate heat ‘concocted’ or cooked matter to bring it to more or less perfect form.²⁰ Imperfections arose from a disproportion in the type and ratio of matter to heat. The heaviest things were in the centre of the universe, the lightest at the edges. Natural motion drove heavy things, e.g. earth, down, and drove light things, e.g. fire, up, until they reached their proper place, or were obstructed from reaching it by something else. Things could also change place by forced motion, being pushed or pulled by something outside the thing itself. And living beings could exert voluntary motion by moving themselves intentionally. On this basis Aristotle built an elaborate theory of dynamics, and his ideas were dominant for over 1,500 years, despite some acute and powerful criticisms advanced against them in antiquity. Philoponus, for example, to large degree anticipated Galileo by pointing out that:

‘if you take two weights differing from each other by a very wide measure, and drop them from the same height, you will see that the ratio of the times of their motion does not correspond with the ratio of their weights, but the difference between the times is much less. Thus if the weights did not differ by a wide measure, but if one were, say, double, and the other half, the times will not differ at all from each other, or, if they do, it will be by an imperceptible amount, although the weights did not have that kind of difference between them, but differed in the ratio of one to two’.²¹

Ancient ideas on forces operating on bodies at rest (statics) were a lot stronger than their ideas on forces operating on bodies in motion (dynamics). Archimedes’ law of the lever, for example, is just one of many outstanding contributions he made to statics. The forces operating on bodies at rest were amenable to then current mathematical analysis (as was the presumed perfect circular motion of the heavenly bodies), but those operating on moving objects, such as thrown stones, were not. Although ancient engineers made significant progress with torsion catapults and other ballistic machines (on which see Marsden 1971), they worked with empirical arithmetical ratios based (usually) on the weight of the missile to be thrown, and theoretical understanding of the forces involved was relatively poor.²² Mechanics had numerous practical applications, from lifting massive masonry blocks into place in temple pediments to regulating the flow of water through a pipe, and was often more amenable to experiment and demonstration than it was to mathematical analysis.

Ktesibios, who lived in Alexandria probably in the C3 BC, was the son of a barber who started making mechanical aides for his father’s shop and went on to develop all manner of machines powered by water or compressed air, from his famous water-clock and equally famous force pump to an air gun. He was followed by Philo and Hero, who improved on some of his designs and added some more – particularly war machines – and the three are known collectively as the great Hellenistic Mechanicians.²³ Some scholars have thought some of the machines described in their surviving texts to be fanciful – even ‘Heath-Robinson’ – designs. But these scholars ignore other ancient literature which takes for granted the existence of such machines as real, working, and familiar to their audience. For example, the author of Aetna mentions a water-powered Triton horn, a water-organ, and a force-pump as analogies to explain how the blast from a volcano can be sustained for as long as the author claims it sometimes is.²⁴

In [Aristotle] Mechanics one finds lots of mathematical proofs of mechanical principles, presented as answers to problems. For example, in §1 we are offered an explanation with geometric proof for why bigger balances are more accurate than smaller ones, with a summary in plain language, and ending with a warning about purple traders’ methods of deceiving customers by rigging the balance in their favour. In §21 the question ‘why do dentists find it easier to extract teeth by using forceps rather than the bare hand?’ is explained with reference to the lever, as is the shadoof (a very simple water-lifting device) in § 28. That theory is following practice and trying to explain why mechanical things are the way they are is sometimes very obvious, for example in §25 we find the question ‘why do they string beds the way they do?’ Abstract science and everyday life are inextricably mixed here.

Problems §32-34 ask questions which Newton answered more satisfactorily with his Laws of Motion, while the author recognizes explicitly that he’s groping here.²⁵

§32 Why is it that an object which is thrown eventually comes to a standstill? Does it stop when the force which started it fails, or because the object is drawn in a contrary direction, or is it due to its downward tendency, which is stronger than the force which threw it? Or is it absurd to discuss such questions, while the principle escapes us? (Forster trans).

Not surprisingly, physics remained a subject of lively debate. In Roman times the same sort of problems and the same sort of answers were offered, though generally with a more rhetorical and less mathematical edge to them. For example, Seneca said (NQ 2.9.2-3, Corcoran trans.):

‘How could water be in tension without air? Take the jet of water that grows from the bottom of the centre of the arena and goes all the way to the top of the amphitheatre–do you think this happens without air tension? Yet neither the hand nor any sort of mechanical device can emit or force water out the way air can. The water responds to the air. It is raised up by the air, which is inserted in the pipe and forces it up. Although water naturally flows down, it struggles mightily against its nature and rises. How about ships laden with cargo? Do they not show that it is resistance of air, not water, that keeps them from sinking? Water would give way and be unable to maintain the weight if it were not itself sustained by air. A discus hurled from a higher position into a pond does not sink but bounces back. How could it do this unless it were beaten back by air?’

Seneca is engaging with theory, and his argument is replete with examples from Roman daily life – the theatre, shipping, and the perennial simple entertainment of making stones skip across water. Producing a jet of water high into the air was far from simple however, and a similar project preoccupied the great physicist and mathematician Leibniz in later times (at Wolfenbuttel). As we move in to the late empire, a number of scholars, notably the Aristotelian Alexander of Aphrodisias (late C2-early C3 AD) and the Neoplatonists John Philoponus (a Christian) and Simplicius (a pagan; both first half of the C6 AD) engaged much more deeply with the theories of the ancient Aristotle,²⁶ but still the arguments about space and time, matter and void, static and dynamic forces were unresolved.

Notes

1. ‘The streak colour of a mineral is the colour of its powder obtained by scraping or rubbing the specimen on a streak plate made of unglazed china, or other material harder than the mineral to be tested. The streak of a mineral may be quite different from its colour’, Rosenfeld 1965 p. 38. This is a technical definition of something familiar: graphite is a soft mineral with a grey streak colour – so soft that it leaves a streak on paper. Hence graphite is used to make pencils.

2. There is a lacuna in the text, long enough for a word or about 6 or 7 letters, which was probably the name of the stone. There is insufficient detail here for a positive identification, but Augite would fit the description (a common pyroxene which is black to dull dark green and has a white to murky green streak colour).

3. See n.1. Rosenfeld’s general discussion of colour in rocks makes an interesting comparison to [Aristotle]’s quoted in text: ‘When the colour of a mineral depends on its chemical composition it is said to be inherent. Many minerals have no inherent colour in the pure state, they are colourless or white. Such minerals may be coloured by minute inclusions of an impurity in chemical combination, or disseminated as small particles in the mineral. This type of colouration is called exotic. The exotic colours of minerals vary quite widely according to the type and amount of colouring material. The opaque white colour of many colourless minerals such as quartz, gypsum, and talc is usually due to reflection of light from countless minute cracks or bubbles of fluid in the mineral, and rarely to the inclusion of white impurity, such as kaolin in some feldspars’ p. 37f.

4. Belopoiika 71. He closes the discussion shortly after this ‘in case we inadvertently digress too far and enter deeper into physical arguments’ §72.3-4.

5. For this subject and its interconnections with much else in ancient physical thinking, see Berryman 1998. Smith 1996 has recently translated and commented upon Ptolemy’s Optics.

6. Note the difference with modern Physics, which is defined in the OED as being ‘the science, or sciences, treating of the properties of matter and energy, or of the action of the different forms of energy and matter in general (excluding Chemistry and Biology)’.

7. Thorndike’s volumes stand as a massive and valuable exception: volume 1 of a History of Magic and Experimental Science 1923 starts with Pliny, and fills nearly 300 pages with the Roman period alone.

8. Düring tried to overcome this problem by entitling his commentary on Meteorology 4 as Aristotle’s Chemical Treatise 1944. But like the ancients, most moderns discussing this subject tackle it in works with Physics, rather than Chemistry, in the title. Ancient chemical ideas may also be discussed in works with alchemy in the title, e.g. Keyser 1990a. 

9. ‘Distilling, sublimation and the Four Elements: the aims and achievements of the earliest Greek chemists’ in Tuplin & Rihll, to appear.

10. Hero’s Automatopoietikes (Automaton-making) has recently been translated into English by Murphy 1995.

11. The role of applied geometry in such things is noted by Proclus Comm. on Euclid’s Elements Book 1, Prologue Part 2, 63-4. His late antique [C5 AD] view on pure geometry is well summarised in § 49-56.

12. For many reasons, the most important of which is the general methodological principle that it is revolution, not the absence of revolution, which needs explaining. For a discussion of related points see White 1993 and Greene 1994.

13. See Lennox’s remarks to the same effect with respect to Aristotle’s zoological works, 1994. Occasional and brief periods of financial support, such as in early Ptolemaic Alexandria, are the exceptions which prove the rule, and were appreciated as such at the time. See, for example, Philo’s comment upon the great leap forward in mechanical technology, in Belopoiika 50.24-6: ‘Alexandrian craftsmen achieved this first, being heavily subsidized because they had ambitious kings who fostered craftsmanship’, Marsden trans. p. 108-9.

14. On Diesel see Nitske and Wilson 1965. There is perhaps an analogous situation in the modern scholarly habit of tracking back a scientific idea to the earliest source one can find, crediting that person with the ‘discovery’ or ‘creation’ of the idea (however hazily it might then have been expressed), and playing down its development and transformation in later authors.

15. These are distinguished from terrestrial earth, air, fire and water in being utterly pure, whereas terrestrial earth, air, fire and water are always subject to mixture with other elements.

16. Reported in the preface to Hero’s Pneumatics. Gottschalk 1965 concludes that this preface is ‘a jumbled but otherwise faithful version of an extract from a book by Strato, almost certainly the peri tou kenou [On the void] included in Diogenes’ catalogue of his works (5.59).

17. Which was the general practice for all but the simplest and cheapest items, such as domestic pottery, or the most expensive imported regional specialities, such as cloth made of a particular fabric or colour.

18. The translation of the postulate is from his little book Archimedes 1920, which reads more easily than his translation of the same in The works of Archimedes 1912. The rest of the translation is from the latter work.

19. Such formulae are given whenever this subject is discussed, e.g. in Thomas GMW 2 pp. 38-9 and 250-1, Heath 1912 pp. 260-1

20. Lloyd has an extended discussion of Aristotle’s views on pepsis (concoction) with reference to the biological works in 1996a chapter 4.

21. Corollary on Void, 683.17-25, trans. Furley 1991. Galileo knew and cited Philoponus’ works and, like many of his contemporaries, was clearly influenced by him. See Wolff 1987.

22. See e.g. Philo Belopoiika §50.26-9 ‘The fact that everything cannot be accomplished by the theoretical methods of mechanics, but that much is to be found by experiment, is proved especially by what I am going to say’ Marsden trans..

23. Drachmann 1948 focuses on their work on pneumatics. Also useful is Drachmann 1963, which contains a translation from the Arabic of much of Hero’s Mechanics with relevant passages from other authors. On Archimedes’ machines see Sleeswyk 1990 and Simms 1995.

24. Aetna 294-299, and 328 respectively. In a completely different time and context the early Christian author Tertullian referred to God playing the water-organ, De baptismo 8

25. Even the real Aristotle occasionally ventured out of his depth, for example on astronomy. Lloyd takes him to task for this (1996a chapter 8), perhaps a little unjustly; Aristotle was no mathematician. See Heath 1949.

26. The 15,000 pages of Greek texts by the late (c. AD 200-600) commentators on Aristotle are the subject of a large programme of English translations (over 60 volumes planned) under the general editorship of R Sorabji, published by Duckworth.

References

To follow

Further Reading

G Freudenthal Aristotle’s theory of material substance (Oxford, 1995) and L Judson (ed) Aristotle’s physics (Oxford, 1991) offer good recent discussions of Aristotle’s ideas on matter. For the atomists see D Furley Two studies in the Greek atomists (Princeton, 1967) and The Greek cosmologists: the formation of the atomic theory and its earliest critics (Cambridge, 1987). For the debates in late Antiquity, see R Sorabji Time, creation and the continuum (London, 1983) and Matter, space and motion (London, 1988). Older works provide good overviews but are prone to implicit translation of technical, especially mathematical, ideas. Some of the best amongst them are F Solmsen Aristotle’s system of the physical world (Ithaca, 1960) and O Pedersen & M Pihl Early physics and astronomy (London, 1974). The latter contains more than one would expect from the title and has a very useful biographical appendix which includes Arabic and Mediaeval writers as well as Greeks and Romans (by ‘early’ they mean up to Copernicus). S Sambursky’s Physical world of the Greeks (London, 1956), Physics of the Stoics (London, 1959), and Physical world of Late Antiquity (London, 1962) are still worth reading. On forces a good overview is provided by J Lindsay Blast, power and ballistics: concepts of force and energy in the ancient world (London, 1974), which also contains a great deal more than one might expect from the title. A G Drachmann Mechanical Technology of Greek and Roman Antiquity (Copenhagen, 1963) and K D White Greek and Roman Technology (London, 1984) provide good overviews of mechanics and machines in antiquity.