Part Four, Chapter 3: The Fourth Book — On the Earth and Its Waters

Introduction

Chapter 1. The eye as Source of Astronomical Illusions

Chapter 2. Atmospheric Refraction Through Different Mediums

Chapter 3. Mirrors

Chapter 4. Reflection in Dense and Transparent Bodies

Chapter 5. Visual Pyramids

Chapter 6. Nature of the Elements

Chapter 7. Centres of the Elements and the World

Chapter 8. Light and Shade

Chapter 9. The Sun as Only Light Source

Chapter 10. Diminution of Earth's Light

Chapter 11. The Moon's Waters

Chapter 12. The Moon's Elements

Chapter 13. Earth and Moon

Chapter 14. The Earth as a Star

Conclusion

1. Introduction

In the period 1505-1508 Leonardo begins to plan a treatise on the moon. On CA74va, for instance, he jots down two chapter headings:

On the water that is in the moon.

In 1508, on BM94r, an outline follows:

On the moon.

In modern terms this outline could read as chapter headings one to five in Chart 30. Other notes in Manuscript F help provide outline sketches of later chapters. A note on F41v, for instance, indicates that he plans to write a chapter on the earth's position at the centre of its elements (see chapter seven in Chart 30):

A discussion of the balance of the elements assumes a knowledge of their nature and weight and hence it is likely that he planned a chapter on this (see chapter six in Chart 30). On F77v (1508) he draws the sun's rays reflected from the wavy surface of the moon (89) with a one line caption: "this will be preceded by the treatise on shadow and light," which must also have constituted a chapter in his book on astronomy (see chapter eight in Chart 30). Leonardo's theory is that the earth reflects the sun's light as do the moon and the stars. This requires that he must eliminate a contending theory that the moon has light of its own and establish that the sun is the sole source of light. He alludes to this on F4v while praising the sun: “All souls descend from it because the heat that lives in these animals comes from such souls and there is no other heat nor light in the universe as we shall show in the fourth book.” If the reflection of sunlight depends on water, then the earth which was covered with water at the time of the Flood must have lost a considerable amount of its former light. This too is to be included in the treatise on astronomy (chapter ten in Chart 30) as is confirmed by a note on F69v (1508):

Having discussed how the earth's waters reflect light he intends to explain how the moon's waters also reflect light (chapter eleven in Chart 30). There is a contemporary theory which contends this, claiming that water being heavier than air would fall back onto the earth. To refute this Leonardo needs to show that the moon has its own elements which remain in equilibrium (see chapter twelve in Chart 30). If the nature of the moon is essentially the same as the earth's, it follows that the moon also has its days, months and seasons as does the earth or as he puts it on F63r (see chapter thirteen in Chart 30): “Define the earth with its long and its short days in the North and in the South and do the same for the moon and determine them accurately.” Having established that the nature and function of the earth and moon are fully equivalent, he wishes to push the comparison further and argue that the earth from a great distance is like a star (chapter fourteen in Chart 30) or as he puts it on F56r:

Taken as a whole the above notes provide important clues concerning the structure of Leonardo's proposed treatise on astronomy. To gain some impression of the contents of the treatise, we need to consider what material exists for each of the hypothetical chapters listed in Chart 30.

Chapter 1: The Eye as Source of Astronomical Illusions

In the outline on BM94r Leonardo states that his book is to open with "the nature of the luminous ray." A passage on F25v clarifies what he means by this:

Order to prove that the earth is a star

And how the rays of the stars arise in the eye.

In other words he considers the nature of the "luminous ray" (which is his term for the light that causes twinkling of stars) to be an optical illusion. Another optical illusion in astronomy interests him also as becomes clear from F5r/4v where he discusses why Epicurus and others maintain that the sun is only as large as it appears:

These illusions interest him so much that he decides to make it the opening theme of his fourth book as he epxlains on F94v:

From our earlier analysis (see above pp. ) we know that this passage marks the beginning of a treatise which continues on F95r, skips to F40r and then proceeds in revcerse until F28v. The chief themes of this treatise are (1) why lights further in the distance do not appear smaller and (2) the role fo the eye, and the pupil in particular, in producing these illusions, i.e., precisely the themes with which he proposes to open his book on astronomy. But this treatise within Manuscript F is, in turn a development of Manuscript D. Hence Leonardo's two principal works on optics are intended to serve as an introduction to his projected astronomical treatise.

Chapter 2: Atmospheric Refraction Through Different Mediums

The outline on BM94r also alludes to illusions from atmospheric refraction. A note on F25v clarifies what this chapter was to entail:

This problem, why planets appear larger at the horizon than overhead, had been mentioned by Ptolemy, Alhzen, Witelo and Pecham, Leonardo's interest in it can be traced back to A64v (1492) in a passage headed:

Proof of the growth of the sun in the west

On A64r he gives a succint explanation (fig. 1594)

Why the sun appears larger at the horizon than at midday which is closer.

Every body which is seen by a curved medium appears of a larger size than it is.

He returns to this problem on Mad II 5v (fig. 1595):

On F25r he draws two further diagrams (figs. 1598-1599) and adds a caption for the first of these:

In 1492 he had rejected thickness of the air as a factor. Here on F25r he explicitly accepts it. On F60r (00) he pursues the theme of atmospheric refraction:

The proof to which he alludes my well have been an experimental demonstration using a model (see Appendix ).

Chapter 3: Mirrors

In his outline on BM 94r he mentions a further chapter on "mirrors plane, convex and concave and the conditions producing the most powerful reflection." There is a particular incentive for this interest: a contemporary theory claims that the moon is a /convex/ mirror. Leonardo therefore studies the properties of convex mirrors. On CA353rb (74) for instance, he asks:

On CA251ra he again broaches the question of reflection from convex surfaces under the heading "of the mirror between the centric line /of sight/ and the pyramid," this time with three diagrams (figs. 1601-1604) to which he alludes as proofs in the caption that follows:

This "proof" is based purely on geometry and not on observation. Soon afterwards, however, observation brings him to a different conclusion. On CA125vb (c. 1492), for instance, he studies reflection in and from transparent glass spheres and discovers that an image is reflected in but a tiny part of its surface, hence (04 cf. figs. 1605-1613): "In n, ab will appear...the size of rt."

Over a decade later he alludes to the problem again in three diagrams on BM107r (figs. 1611-1613, 1506-1508). On CA131vb (figs. c. 1508) in a text cited elsewhere (see below p. ) he suggests that from a sufficient distance the reflection would appear larger than the surface of the object reflecting it. Further studies lead him to abandon this possibility. On F76r (1508), for instance, he simply claims: “The image of the sun in a convex mirror increases in going further from this mirror and the solar body would disappear in going /still/ further.” On CA28ra (1505-1508), he makes a careful drawing (14):

To find here the position and size of the image of the sun.

He uses effectively the same diagram on BM28r (15, c. 1508) where he applies these mirror studies to speculations on the nature of the moon:

He restates this idea that the moon cannot be a spherical mirror on F93r (1508) in a passage headed:

Of the moon and if it is polished and spherical.

Hence his study of mirrors leads him to refute the possibility that the moon is a mirror. In the meantime his fascination with mirrors has become a study in itself, the details of which will be discussed elsewhere (see Appendix , pp. ).

Chapter 4. Reflection in Dense and Transparent Bodies

The outline on BM94r (c. 1508) suggests that a next chapter would consider whether reflection is greater in dense or transparent bodies. Although we know that he studied reflection in transparent spheres, spheres of polished gold and various mirrors, there is no record of his studying reflection in objects of different densities in a systematic fashion. Even so the reason for his interest in this problem can be reconstructed. There is a theory among his contemporaries that the spots on the moon are due to different degrees of density in the surface: as he notes on F85r (1508):

Of the spots of the moon

On F84v, opposite he pursues this problem:

Concerning the spots of the moon.

Having dismissed existing theories concerning spots on the moon, he is challenged to propose his own explanation. On Leic 5r he mentions "how the spots of the moon are different from that which they once were as a result of the course of their waters." This idea he develops on CA112va: “If you look at an island surrounded by waves filled with images of the sun it appears to you as if you see one of the spots of the moon surrounded by its brightness.” As early as 1490 he had considered another explanation concerning the haloes of the moon on CA349vc:

On the circles of the moon.

On F84r (1508) he mentions the possibility that these vapours or clouds could also account for spots on the moon, but rejects the idea:

Spots of the moon

Nonetheless, he is prompted to make extended observations of the moon and record the results (figs. 1668-1673). Thereby he discovers that the spots of the moon do indeed vary considerably. Hence on BM19r (c. 1508) he adopts the theory which he had previously rejected:

Chapter 5: Visual Pyramids

The outline on BM94r refers to a further chapter:

Interest in the nature of visual pyramids was part of his Euclidean heritage (see above pp. ). But that which Euclid had studied purely geometrically in two planes Leonardo explores in terms of three-dimensional situations complete with interposed planes (figs. (1191-1193).

This leads to systematic diagrams, first rough as on BM62v (figs. 1618-1621), then more polished as on BM94r (figs. 1616-1617, 1622). On CA112ra, va he relates this three-dimensional pyramid to the sun's image in water (figs. 1547-1557). Frontal views of the same situation on F63r (figs. 1559-1560) CA237ra (fig. 1558), and CA243rb, vb (figs. 1537, 1700) go hand in hand with these. And as is clear from the passage on G20r (fig. 1524, see above p. ) he intended to analyse this pyramid quantitatively. Whether he intended to include the Euclidean comments concerning pyramids in this short chapter is not certain.

Chapter 6: The Nature of the Elements

Leonardo wished to establish that the earth is at the centre of its elements (see chapter seven in Chart 30). A preliminary discussion of the nature and weight of these elements was therefore fitting (chapter six in Chart 30). His interest in the elements earth, air, fire and water can be traced back to CA284va (c. 1497) where he mentions: "I believe that the air will have that proportion in resistance with fire that air will have with water," and discusses the balancing of weights of water and air. On CA180ra (c. 1505) he refers to the weights of elements in each other, a theme which he puruses on CA79va (1505-1508) where he makes a list of combinations: fire, earth > in water and in air; water, fire > in air and earth, air> in water. On CA79rb he makes mention of a fifth element, discusses the transformation of elements and conjectures concerning their relative weights: “one measure of fire weights 2 weights, and one measure of air weighs 4, one of water, 8, one of earth 16, and one of gold 32.” On CA72va (1508-1510) this conjectural discussion of weights is pursued: “Let us posit that air has 4 of lightness being under water and 8 if it is under simple earth. Hence water has 4 of gravity between air and earth has 8.” This leads, on CA72va and ra, to discussion of how elements interpenetrate one another posed in the form of problems such as:

I have air that weighs two and water 4 and earth 8.

A complex explanation describes what must be done to make this combination possible. On CA244va (1508) there is further discussion of fire in air, water in air, and air under water (cf. CA131rb and CA190rb, c. 1508) this time in connection with weights being attracted to the centre of the world. On F62v (1508) he draws a cubic piece of lead inside a spherical dew drop (23) and explains that this is intended to simulate the relation of earth ot water:

The convertibility of elements into another interests him increasingly. On CA172vc (1508), for instance, he claims:

The elements are equal if they are made with equal subtlety.

This tenfold ratio of the elements is mentioned again on Leic. 35v (1506-1509). As might be expected Manuscript F, which contains numerous astronimical notes, develops this theme of the elements at some length. On F69v, for instance, there is a general discussion concerning their weight:

Earth is heavy in its sphere but the more so to the extent that it is in a lighter element.

Fire is light in its sphere and the more so to the extent that it is in a heavier element.

A specific discussion of the shape of the elements follows on F27v:

On the 5 regular solids.

This passage is of great importance because it helps explain why Leonardo devotes so much attention to the centre of gravity of pyramids (see figs. 1625-1651 and below p. ). On F27r, he considers relative weights of the elements and their motion:

He next discusses the:

Shape of the Elements.

In 1515 he returns to the theme of elements. On CA200ra, for instance, he points out:

This idea of changing gravity and levity he pursues on CA219ra (1515):

Chapter 7: Centres of the Elements and the World

If the earth's stability depends on its being in the centre of the world, then the moon's stability must depend on something else. If he can show, however, that the earth's stability arises through its being at the centre of its elements, he is then free to argue that the moon's stability also arises through its being at the centre of its elements. This would help support his further aim of showing that the earth and moon are equivalent to one another. His interest in these problems can be traced back to 1492. On A20v, for instance, he describes a method of measuring the distance from the surface of the earth to its centre. On A58v he ponders

On the centre of the ocean.

He develops these ideas in a series of drafts on CA153va (1495-1496) beginning with a general claim:

A long discussion of common centres and centres of true gravity follows which leads to the claim:

He next demonstrates how a weight b will descend to a common centre a, and not rise up to the centre of the earth. This leads to a further distinction between different kinds of centres:

He broaches the question of the earth's centre in passing on CA284v (1499) and CA120=rd (1504-1507). How to find these various centres becomes a practical question in the Codex Arundel. On BM111v (c. 1505), for instance, he notes:

Beneath this he draws a geometrical diagram with a pyramid (corresponding to the element earth) which he lables (45):

c is the centre of natural gravity of the cone: acrm

b is the centre of natural gravity of the bisected cone anec

d is the centre of natural gravity of the pyramid cnr.

This diagram he develops on BM108r (46, c. 1505) with a more developed caption:

abc is a conical body

zt is the centre of its size

op is the centre of its accidental gravity

de is the centre of its natural gravity

kh is the centre of natural gravity of the greater pyramid which

the cone has

gi is the accidental centre of the pyramid.

He also drafts another method for finding various centres. On BM124r (c. 1505) this diagram is further developed (47) and explained:

Of the cone abc the centre of its magnitude is the line de.

The centre of accidental gravity of this pyramid is in the line rt.

The centre of gravity of such a pyramid is in the line hi.

He then outlines another practical problem:

This time he provides a solution as well (44 cf. figs. 1640-1643):

On BM72v (1505-1508) he pursues this theme, now providing a succinct description of the different centres:

In every heavy body there are found to be 3 centres of which one

is the centre of natural gravity, the 2nd accidental gravity, 3rd of

the size of the body.

He goes on to relate these to the question of the earth's centre:

On F27r (1508) Leonardo disagrees with Plato and argues that the shape of the earth must be pyramidal (see above p. ). Out of context this appears to be merely a philosophical quibble. This series of folios in the Codex Arundel reveal that he had studies the gravitational properties of his earth-pyramid very carefully and had related it to his general studies of different centres of weight. In the Codex Leicester he pursues the question of the earth's centre and the centre of the world. Following a preliminary passage on Leic. 36r (figs. 1653, 1657), he distinguishes, on Leic. 34v (figs. 1658-1659 cf. 51), between a universal and a particular centre of sphericity of water. This leads to a long discussion on Leic. 35v (figs. 1624-1626, 1660-1664) of the relation of this sphere of water to the centre of gravity of the earth and centre of the world, the conclusion of which is that there are only:

2 ways /that/ the gravity of the earth is concentric with the centre of the world.

In other words the gravity of the earth could only be concentric with the centre of the world in hypothetical situations. In practice they are separate (51). Conscious that this is a dramatic claim he adds: “It is in the power of the orders of Nature to make it that the earth stands by itself through its shape, outside the whole sphere of the water.” He pursues these problems in a series of passages on F22v, 27r, 69r, 70r, and 83v which, as he explains on F41v, all have the purpose of showing:

Chapter 8: Light and Shade

On F77v (1508) he draws a viewer looking at a wave filled moon reflecting sunlight (89). Above this he writes: "This will have in front of it the treatise on light and shade." What this treatise entailed is not indicated, but almost certainly it would have included basic definitions and his distinction between explanding, contracting and parallel shade. It is likely that it would have included most of his first two books on light and shade (see above pp. ). Given the specialized problems of the later books it is improbable that he intended to include all of his work on light and shade as an intermediary chapter in his treatise on the earth and its waters.

Chapter 9: The Sun as Only Light Source

In a eulogy of the sun on F4v (1508) he mentions that: "there is no other heat nor light than it in the universe as I shall show in the fourth book." On a number of occasions, A64r, BM28r, 104r and 94v, Leic 30r he merely states that the moon has no light of its own without further explanation. However, in the Codex Leicester, he examines the problem in greater detail, beginning with a draft passage on Leic 36v (1506-1509):

At this point the text breaks off but he takes up the problem afresh on Leic 2r:

He adds two further explanations:

He now reformulates the whole problem of the moon's light:

Here the text breaks off once more but the thrust of the argument is clear. Leonardo claims that apparent differences in light intensity on the moon are due to contrast effects of light and dark backgrounds (see above pp. ). He concludes his discussion on Leic 2r with an outline of an experiment:

Accompanying these passages are diagrams (figs. 1750-1752, 1754-1755) which demonstrate the same point visually. The largest of these (fig. 1752) serves, in turn, as the starting point for a more elaborate diagram on Leic 7r (fig. 1753), to which he adds the caption: “ Here it is proved that in any part of the sky the umbrous part of the moon has some luminosity and that in no part of the heavens is it deprived of this light.” In short, by visualising the various relationships between the sun, earth and moon, he can demonstrate how sunlight reflected from the earth accounts fully for all light on the moon (see below pp. ). That which applies to the moon applies equally to the stars, as he mentions in passing on D6r (1508):

On F57r (1508) he pursues this problem:

Whether the stars have light from the sun or from themselves.

Another objection is now raised:

This objection he again counters (fig. 1727):

His passing comment on CA300rb (1508-1510) "The sun never sees shadow" (cf. W12700v) is probably intended as a further demonstration that the sun is the only light source in the universe.

Chapter 10: Diminution of the Earth’s Light

On F 69v (1508) he mentions a further problem to be dealt with in his treatise:

This may account for a series of passages on Leic 3r, 8v, 9v, 10v and 20r (1506-1509) as well as those on CA155rb and 92vc (c. 1515) in which he considers the evidence of different layers of shells in the mountains which suggest that the seas reached this height more than once. During the deluge he estimates that the water reached a point seven cubits (Leic 8v, 1506-1509) or ten cubits (CA155rb, c. 1515) above the highest mountains. This chapter on the earth's waters might also have included passages such as those on CA112ra 915050-1508) where he considers the refelctive properties of waves:

It is possible that this chapter would have included his various demonstrations to show that waves of water function as cylindrical mirrors (see above pp. and figs. 1565-1573).

Chapter 11: The Moon’s Waters

Consideration of how the earth's waters reflect the sun's light leads to a discussion how the moon's waters do the same. That the moon has oceans he appears to assume from the outset of his writings. On CA80rb (c. 1490-1492), for instance, he mentions that "the moon cannot move the seas as it can move the lakes," without further explanation. On A64r (1492) he refers to the moon's ocean:

When he broaches this theme anew on Mad II 62v (c. 1503-1505) he draws (99) the sun reflecting from a wave ruffled body which as the caption explains shows the "moon or if you wish the earth, that is, waves of water." Thus far he has discussed the oceans of the moon as if no one doubted their existence. On CA112va (c. 1505-1508), however, he reports a conflicting opinion:

A heading on CA74va (1506-1508) indicates that he plans to write a chapter on these problems:

A series of passages in the Codex Leicester very probably constitute advanced drafts of this intended chapter. By of introduction he reminds himself on Leic 36v to list "all the contradictions of the adversary to say that in the moon there is no water." Chief among them is the notion that if the moon had water it would spill off and fall to the earth (see below p. ). On Leic 1r he begins with the idea that the moon is a mirror, rejects it and argues that it must have water with waves (fig. 1722):

Here the text is interrupted. Directly following is a further passage (fig. 1701):

In the accompanying diagram is a further caption: "the part of the sun that regards the earth and the waves of the ocean and the other waters." On Leic 5r he pursues these problems more systematically beginning with a demonstration why the moon must have waves:

On the moon.

He interjects, in draft form, what would happen if the moon's waters had no waves:

Immediately following he returns to the idea that water with waves produces darker reflections and explains why:

An exception to this rule follows:

]Figs. 1682-1686: Reflection from the moon's oceans. Figs. 1682-1684, Leic. 7v; figs. 1685-1686, Leic. 30r.

Which leads him to return to the question of the moon having light of its own (see above p. ):

These passages on Leic 5r serve, in turn, as a draft for a still more comprehensive discussion on Leic 30r where he begins by eliminating the mirror hypothesis:

This leads him to claim that the moon must have water with waves:

He proceeds to explain why the light reflected by such waves is much dimmer than sunlight reflected in calm water:

As on 5r, exceptions to this rule again follows:

When he returns to this problem on Leic 2r he merely refers to

Even so he is not yet satisfied. On BM104r (c. 1508) he again mentions why sunlight reflected from water with waves is less intense than sunlight seen directly:

On BM94v he devotes another folio to the problem of the moon's waves. As in the Codex Leicester (now Hammer) he begins with a claim that the moon has no light:

On the moon

This leads to discussion of the moon's waves:

What would happen if the moon had no waves is now mentioned:

The effects of water with waves are again contrasted with this:

The remainder of the passage is devoted to a comparison of light from the new moon and full moon:

A marginal note summarizes this discussion:

On F77v (1508) he draws another diagram (fig. 1689) of the eye looking at sunlight reflected in the full moon, this time adding only a brief caption: “The extremities of the moon will be that much more illuminated and will show themselves that much more luminous because in these there only appear the summits of the waves of its waters.” He refers to the moon's waters once more on CA155rc (1516-1517, see above p. ) and on CA174vb (1516-1517) again discusses reflection from terse globulent surfaces:

When the moon is nearer the sun it has a lesser quantity of light from it and conversely.

The uniform sphericity of the terse body renders a single image to the single eye that sees it.

As a result of these discussions he has convinced himself that the moon has oceans like those of the earth and that their function in reflecting light is identical. This is a first step in his aim to show that earth and moon are interchangeable in their functions as planets.

Chapter 12: The Moon’s Elements

The claim that the moon had water contradicted the contemporary theory of cosmology which held that the earth is the centre of the universe. According to this theory, if there were water on the moon, it would fall back to earth, because the heavens were strictly the domain of air, fire and the empyrean. Leonardo does not broach this problem until K1r (1503-1505) where he asks: "The moon /is/...dense and heavy. How does the moon stay /up?/." In the next years he arrives at an ingenious answer. If the moon has water, it must also have elements and will therefore have its own centre of gravity around which it turns, or as he puts it on CA112va (1505-1508):

By 1508 the problem is playing on his mind. On BM94r, for instance, he jots down a series of prelininary thoughts:

No very light object is opaque.

No lighter object remains below a less light /object/.

If the moon has a site in the middle of its elements or not?

And if the moon is lighter than another element, why is it solid and not transparent?

On BM94v (fig. 1703, 1508) he describes an unexpected analogy to this phenomenon of the moon not falling from its position:

On the same folio he decides that

In the Codex Leicester (1506-1509) the problem of the moon's elements is discussed in mored etail. On Leic 1r, for instance, he begins by describing a paradox of optics (fig. 1722):

This passage prompts an adversary to challenge his theory concerning the moon's waters;

The adversary opposes

The adversary's own solution to the problem is duly recorded:

Which solution, in turn, is dismissed:

On Leic 2v, Leonardo answers the problem with an appeal to common sense and experience:

On Leic 2r under the heading "On the moon" he opens with the claim: "No solid is lighter than the air." He refers to how he has shown that the moon has waves (see above p. ) and then returns to the question of the moon's weight:

In short the moon, like the earth, has its own elements and centre of gravity, and as such is not in danger of falling to the centre of the universe. On Leic 36v he reformulates these ideas beginning with the adversary's objections:

Leonardo then gives his defence:

When he returns to this theme on cA243va (c. 1515) he simply repeats his conclusion without further ado:

Chapter 13: Earth and Moon

As early as 1492 Leonardo had begun playing with the idea that the earth and moon have identical functions as planets. On A86v (BN 2038 16v), for instance, he mentions that: “it might be proved that the moon is another world identical to ours and that the part of it which shines is a sea which reflects the sun and the part which does not shine is earth.” On A64r (1492) he takes this comparison further:

To prove that the earth and moon are fully equivalent, he needs to show that the moon has its cycle of days, months and seasons as does the earth. This requires a systematic study of positions of the moon relative to the sun and earth. This leads him to study the phases of the moon with elementary sketches such as those on CA300rb (figs. 1704-1706, 1508-1510). On BM212r (1500-1505) he sketches eight phases of the moon (fig. 1712, cf. figs. 1710-1711). Further drafts follow on W12326v (1506-1508). Here he keeps constant the moon and systematically alters the position of the sun (fig. 1708) adding a caption which has been interrupted: "the moon in the east which from the...." In a further diagram (fig. 1707) he keeps the sun constant while systematically changing the position of the moon. This approach he develops on CA208ra (c. 1513) where he points out (fig. 1713):

Beneath this he draws (fig. 1714) twenty phases of the moon, adding a caption which refers to more phases:

He draws the chief phases of the moon again on CA243vb (c. 1513) for which he drafts an explanation, which has been rendered almost incoherent through a mutilated left-hand corner of the folio:

Here is shown...in 15 days being consumed in night in...

In spite of mutilation, the basic sense is clear: he is outlining the chief phases of the moon's thirty day cycle. In the moon's monthly cycle he sees an equivalent to the earth's yearly cycle, as he points out on CA303vb (1505-1508):

The moon has a summer and a winter every month.

And it has greater cold and greater heat and its equinoxes are colder than ours.

Or, as he puts it on CA208vb (c. 1513): "The moon has a year of 12 days and 12 nights."

A preliminary diagram on CA303vb (fig. 1720) helps us understand his reasoning: each month the moon's orbit around the earth brings it closer to the sun than the earth, and these monthly summers can therefore be hotter than those of the earth. At the other extreme of its orbit, the moon is much further from the sun than the earth. These monthly winters can also be colder than those of the earth. The rough diagram on CA303vb (c. 1508 /-1510/) serves as a starting point for a series of sketches on BM104r (figs. 1716-1719) above which he writes:

In one series he draws the sun in the north with the moon and earth beneath (figs. 1716-1718), which configuration he draws in more elaborate form on Leic 7v (fig. 1721) and Leic 1r (fig. 1722) and again in slight diagrams on BM100r, CA28raand F57r (figs. 1723-1725). Complementary to these he draws two other diagrams on BM104r (figs. 1726-1727) in which the sun is in the south and the moon and earth are above. Such diagrams may have been a starting point for his plan on F63 (1508) to

Just as he studies the sun in the north and south, so too does he study it in the east and west. On CA300rb (1508 /-1510/), for instance, he shows (fig. 1728) the sun in the east and the moon in the west, with the caption: “If the moon is mirror of our earth, if it is in the fifteenth /day/, the earth will be ahlf dark and half illumined or perhaps more than half dark.” Corresponding to this he draws a further sketch (fig. 1731) with the sun in the west* and the moon in the east.

* Leonardo who writes in mirror script also reverses west and east such that west is on the right and east on the left.

A more complex version (fig. 1732) follows on BM104r (c. 1508) where he adds a caption both above: "the earth between the moon on its 15th /day/ and the sun" and to the side: "Here the sun is in the west and the moon in the east on its fifteenth /day." Beneath this he draws a reciprocal situation (fig. 1729) and again adds captions both overhead "moon between the earth on /its/ fifteenth /day/ and the sun" and to the side: "Moon between the earth on the fifteenth /day/ and the sun." This leads in turn to a systematic study of days and nights on the earth and moon. On F64v (1508), for example, he writes the heading:

Obscuration of the sun, moon and earth

Beneath this he draws (fig. 1733) a situation where the sun is again in the west and the moon in the east, with the caption:

He redraws this diagram (fig. 1734) on CA208rb (1513) with the caption: “Here the night of the moon sees eclipsed the ocean of the earth (and the earth sees ecli) and the day of the earth sees the sun eclipsed.” On CA208va (c. 1513) he draws the diagram a third time (fig. 1735), now adding a more elaborate introduction and caption:

This is proved.

On F64v (1508) he also draws a complementary diagram (fig. 1737) showing the sun in the west and the moon in the east, with the caption:

This diagram he redraws (fig. 1738) on CA208rb (c. 1513) with the comment: "Here the day of the moon sees eclipsed...the sun, and the night of the earth sees the moon eclipsed." On CA208va (c. 1513) he draws this a third time (fig. 1739), with almost the same caption: "Here the day of the moon sees the sun obscured and the night of the earth sees obscured the light, day of the moon." In addition to these situations he draws a case where the moon stands at right angles to the earth and sun, first on A64r (fig. 1740, 1492), again on CA208rb (fig. 1741, c. 1513) and a third time on CA208va (fig. 1742, c. 1513) to which he adds the caption:

On CA208rb (c. 1513) he also draws a composite diagram (fig. 1744) showing the moon in four different positions relative to the earth and sun, explaining:

As an afterthought he interjects the question: "What difference does it make to the light of the moon /reflected/ from the ocean whether it is in storm or in fair weather?" Another composite diagram (fig. 1745) follows on CA208va (c. 1513) this time showing the sun in two different places, which leads him to conclude: “In approximately 30 days every part of the moon /has/ had sun and its night antipodal to the full moon requires 15 days in order to see the sun.” His next step is to integrate drawings such as those on F64v, CA208rb and CA208va into synthetic diagrams such as those on CA208ra (figs. 1713-1714) to which he adds both general comments (see above p. ) and particular ones:

Such systematic studies convince himt hat the earth and moon are fully equivalent in their functions and hence he claims, on F94v (1508), for instance: "Our sea has the same influence on the moon as the moon has on us." Even so, he decides to study more carefully situations in which the moon is between the earth and the sun. On F64r (1508), for example, he draws the situation twice (figs. 1746-1747), and adds an unfinished caption:

This leads to a further sketch on F84r (fig. 1749, 1508) which he then develops dramatically on Leic 2r (figs. 1750-1751) and Leic 7r (fig. 1478) where he asdds a long explanation:

On the water of the moon.

He goes on to mention another situation:

He ends with a consideration when moonlight is brightest:

In the late period he returns to this question of where moonlight is brightest on CA243va (c. 1513):

Which leads him to ask:

This he demonstrates (fig. 1677):

Chapter 14: The Earth as a Star

Leonardo shown that at a certain distance the earth functions as a planet equivalent to the moon. But the ultimate aim of his treatise of astronomy is to show that at a great distance the earth functions as a star. This aim emerges gradually. On F5r (1508) where he describes looking at stars through a small aperture (see above p. ) and begins thinking about his future treatise, this aim is still implicit:

By F25r (1508) his aim is clear and hence his outline has the heading: "Order to prove that the earth is a star." This aim he restates on F93r:

On F94v, he puts it even more clearly:

A slightly more detailed statement of purpose follows on F56r

And likewise you will make a discourse on the size of many stars, according to the authors.

Although no lists of the sizes of stars have come down to us, a few scattered notes give us hints concerning this intended final chapter of the treatise on astronomy. On CA112va (c. 1505-1508), for instance, he describes:

How the earth is a star.

He develops this idea on D6r:

Which leads him to raise a related question:

How distance makes stars many times larger than the earth appear minimal.

In the late period he returns to this phenomenon once more on CA208vb (fig. , c. 1513).

Leonardo's quest to establish that the earth is a star may, in turn, have prompted his interest in overies. He drafts such an instrument on B21v (fig. 1756, 1490-1491) with the caption: "Instrument of the spheres." This he develops on B13r (fig. 1757, 1490). It is likely that his diagrams on CA8va (figs. 1758-1759, 1493-1495) also relate to an overy. Hence, just as he had built models in order to understand the human body (microcosm, see vol. one, part II.3), he also builds models to understand the planetary system (macrocosm).