The Notebooks of Leonardo da Vinci

verdict of other philosophers as to the teaching of the Chaldaeans but says nothing as to the antiquity and origin of astronomy. CICERO further notes De oratore I, 16 that Aratus was "ignarus astrologiae" but that is all. So far as I know the word occurs nowhere else in CICERO; and the word Astronomia he does not seem to have used at all. (H. MULLER-STRUBING.)] Of time and its divisions (916-918). 916. Although time is included in the class of Continuous Quantities, being indivisible and immaterial, it does not come entirely under the head of Geometry, which represents its divisions by means of figures and bodies of infinite variety, such as are seen to be continuous in their visible and material properties. But only with its first principles does it agree, that is with the Point and the Line; the point may be compared to an instant of time, and the line may be likened to the length of a certain quantity of time, and just as a line begins and terminates in a point, so such a space of time. begins and terminates in an instant. And whereas a line is infinitely divisible, the divisibility of a space of time is of the same nature; and as the divisions of the line may bear a certain proportion to each other, so may the divisions of time. [Footnote: This passage is repeated word for word on page 190b of the same manuscript and this is accounted for by the text in Vol. I, No. 4. Compare also No. 1216.] 917. Describe the nature of Time as distinguished from the Geometrical definitions. 918. Divide an hour into 3000 parts, and this you can do with a clock by making the pendulum lighter or heavier. _XVI. Physical Geography. Leonardo's researches as to the structure of the earth and sea were made at a time, when the extended voyages of the Spaniards and Portuguese had also excited a special interest in geographical questions in Italy, and particularly in Tuscany. Still, it need scarcely surprise us to find that in deeper questions, as to the structure of the globe, the primitive state of the earth's surface, and the like, he was far in advance of his time. The number of passages which treat of such matters is relatively considerable; like almost all Leonardo's scientific notes they deal partly with theoretical and partly with practical questions. Some of his theoretical views of the motion of water were collected in a copied manuscript volume by an early transcriber, but without any acknowledgment of the source whence they were derived. This copy is now in the Library of the Barberini palace at Rome and was published under the title: "De moto e misura dell'acqua," by FRANCESCO CARDINALI, Bologna_ 1828. In this work the texts are arranged under the following titles: Libr. I. Della spera dell'acqua; Libr. II. Del moto dell'acqua; Libr. III. Dell'onda dell'acqua; Libr. IV. Dei retrosi d'acqua; Libr. V. Dell'acqua cadente; Libr. VI. Delle rotture fatte dall'acqua; Libr. VII Delle cose portate dall'acqua; Libr. VIII. Dell'oncia dell'acqua e delle canne; Libr. IX. De molini e d'altri ordigni d'acqua. The large number of isolated observations scattered through the manuscripts, accounts for our so frequently finding notes of new schemes for the arrangement of those relating to water and its motions, particularly in the Codex Atlanticus: I have printed several of these plans as an introduction to the Physical Geography, and I have actually arranged the texts in accordance with the clue afforded by one of them which is undoubtedly one of the latest notes referring to the subject (No. 920_). The text given as No._ 930 which is also taken from a late note-book of Leonardo's, served as a basis for the arrangement of the first of the seven books—or sections—, bearing the title: Of the Nature of Water (Dell'acque in se). As I have not made it any part of this undertaking to print the passages which refer to purely physical principles, it has also been necessary to exclude those practical researches which, in accordance with indications given in 920, ought to come in as Books 13, 14 and 15. I can only incidentally mention here that Leonardo—as it seems to me, especially in his youth—devoted a great deal of attention to the construction of mills. This is proved by a number of drawings of very careful and minute execution, which are to be found in the Codex Atlanticus. Nor was it possible to include his considerations on the regulation of rivers, the making of canals and so forth (No. 920, Books 10, 11 and 12_); but those passages in which the structure of a canal is directly connected with notices of particular places will be found duly inserted under section XVII (Topographical notes). In Vol. I, No._ 5 the text refers to canal-making in general. On one point only can the collection of passages included under the general heading of Physical Geography claim to be complete. When comparing and sorting the materials for this work I took particular care not to exclude or omit any text in which a geographical name was mentioned even incidentally, since in all such researches the chief interest, as it appeared to me, attached to the question whether these acute observations on the various local characteristics of mountains, rivers or seas, had been made by Leonardo himself, and on the spot. It is self-evident that the few general and somewhat superficial observations on the Rhine and the Danube, on England and Flanders, must have been obtained from maps or from some informants, and in the case of Flanders Leonardo himself acknowledges this (see No. 1008_). But that most of the other and more exact observations were made, on the spot, by Leonardo himself, may be safely assumed from their method and the style in which he writes of them; and we should bear it in mind that in all investigations, of whatever kind, experience is always spoken of as the only basis on which he relies. Incidentally, as in No._ 984, he thinks it necessary to allude to the total absence of all recorded observations. I. INTRODUCTION. Schemes for the arrangement of the materials (919-928). 919. These books contain in the beginning: Of the nature of water itself in its motions; the others treat of the effects of its currents, which change the world in its centre and its shape. 920. DIVISIONS OF THE BOOK. Book 1 of water in itself. Book 2 of the sea. Book 3 of subterranean rivers. Book 4 of rivers. Book 5 of the nature of the abyss. Book 6 of the obstacles. Book 7 of gravels. Book 8 of the surface of water. Book 9 of the things placed therein. Book 10 of the repairing of rivers. Book 11 of conduits. Book 12 of canals. Book 13 of machines turned by water. Book 14 of raising water. Book 15 of matters worn away by water. 921. First you shall make a book treating of places occupied by fresh waters, and the second by salt waters, and the third, how by the disappearance of these, our parts of the world were made lighter and in consequence more remote from the centre of the world. 922. First write of all water, in each of its motions; then describe all its bottoms and their various materials, always referring to the propositions concerning the said waters; and let the order be good, for otherwise the work will be confused. Describe all the forms taken by water from its greatest to its smallest wave, and their causes. 923. Book 9, of accidental risings of water. 924. THE ORDER OF THE BOOK. Place at the beginning what a river can effect. 925. A book of driving back armies by the force of a flood made by releasing waters. A book showing how the waters safely bring down timber cut in the mountains. A book of boats driven against the impetus of rivers. A book of raising large bridges higher. Simply by the swelling of the waters. A book of guarding against the impetus of rivers so that towns may not be damaged by them. 926. A book of the ordering of rivers so as to preserve their banks. A book of the mountains, which would stand forth and become land, if our hemisphere were to be uncovered by the water. A book of the earth carried down by the waters to fill up the great abyss of the seas. A book of the ways in which a tempest may of itself clear out filled up sea-ports. A book of the shores of rivers and of their permanency. A book of how to deal with rivers, so that they may keep their bottom scoured by their own flow near the cities they pass. A book of how to make or to repair the foundations for bridges over the rivers. A book of the repairs which ought to be made in walls and banks of rivers where the water strikes them. A book of the formation of hills of sand or gravel at great depths in water. 927. Water gives the first impetus to its motion. A book of the levelling of waters by various means, A book of diverting rivers from places where they do mischief. A book of guiding rivers which occupy too much ground. A book of parting rivers into several branches and making them fordable. A book of the waters which with various currents pass through seas. A book of deepening the beds of rivers by means of currents of water. A book of controlling rivers so that the little beginnings of mischief, caused by them, may not increase. A book of the various movements of waters passing through channels of different forms. A book of preventing small rivers from diverting the larger one into which their waters run. A book of the lowest level which can be found in the current of the surface of rivers. A book of the origin of rivers which flow from the high tops of mountains. A book of the various motions of waters in their rivers. 928. [1] Of inequality in the concavity of a ship. [Footnote 1: The first line of this passage was added subsequently, evidently as a correction of the following line.] [1] A book of the inequality in the curve of the sides of ships. [1] A book of the inequality in the position of the tiller. [1] A book of the inequality in the keel of ships. [2] A book of various forms of apertures by which water flows out. [3] A book of water contained in vessels with air, and of its movements. [4] A book of the motion of water through a syphon. [Footnote 7: cicognole, see No. 966, 11, 17.] [5] A book of the meetings and union of waters coming from different directions. [6] A book of the various forms of the banks through which rivers pass. [7] A book of the various forms of shoals formed under the sluices of rivers. [8] A book of the windings and meanderings of the currents of rivers. [9] A book of the various places whence the waters of rivers are derived. [10] A book of the configuration of the shores of rivers and of their permanency. [11] A book of the perpendicular fall of water on various objects. [12] Abook of the course of water when it is impeded in various places. [12] A book of the various forms of the obstacles which impede the course of waters. [13] A book of the concavity and globosity formed round various objects at the bottom. [14] Abook of conducting navigable canals above or beneath the rivers which intersect them. [15] A book of the soils which absorb water in canals and of repairing them. [16] Abook of creating currents for rivers, which quit their beds, [and] for rivers choked with soil. General introduction. 929. THE BEGINNING OF THE TREATISE ON WATER. By the ancients man has been called the world in miniature; and certainly this name is well bestowed, because, inasmuch as man is composed of earth, water, air and fire, his body resembles that of the earth; and as man has in him bones the supports and framework of his flesh, the world has its rocks the supports of the earth; as man has in him a