105.
The smallest natural point is larger than all mathematical points, and the proof of this is that the natural point has continuity, and everything which has continuity is infinitely divisible; but the mathematical point is indivisible because it is not a quantity. Every continuous quantity is mentally infinitely divisible. Among the magnitude of things which are among us, the chief of all is nothingness; and its function extends to matter that does not exist, and its essence is in time in the past or in the future, and it has nothing of the present. This nothingness has its part equal to the whole and the whole to the part, and the divisible to the indivisible, and produces the same result by addition or subtraction, or if it be divided or multiplied,—as is proved by arithmeticians by their tenth character, which represents nothing. And its power does not extend to the things of nature.
That which is called nothingness is found only in time and in words: in time it is found in the past and future, and not in the present; and thus in words among things which are said to be nonexistent or impossible. In time nothingness dwells in the past and the future, and not at all in the present, and in nature it resides among the things which are impossible. Whence from that which has been said, it has no being, because where there is nothingness there would be a vacuum.
106.
With regard to this matter, we have said on the previous page that the definition of a spirit is a power united with a body, because it cannot move of its own accord nor acquire any kind of motion. And if you say that it moves itself, this cannot be within the elements, because if the spirit is an incorporate quantity this quantity is a vacuum and the vacuum does not exist in nature, and if it did exist it would be immediately filled by the rushing in of the element in which the vacuum was formed. So according to the definition of weight which runs: "Gravity is an accidental power created by one element attracted to or suspended in another," it follows that no element, weighing nothing in its own element, can have weight in the element which is above it and lighter than it; for instance, no one part of water has no more gravity or lightness than any other part, but if you were to draw it up into the air, it would acquire weight, and this weight cannot sustain itself by itself; and it must therefore inevitably fall, and thus wherever there is a vacuum in water it will fall in. The same thing would happen with a spirit among the elements where it would continuously generate a vacuum in whatever element it might find itself, for which reason it is inevitable that it would move in a constant flight to the sky until it had quitted these elements.
107.
We have proved that a spirit cannot exist in the elements without a body, nor move of itself by voluntary motion unless it be to rise upwards. But now we will say that if such a spirit took a body made of air it would inevitably melt into air, because if it remained united it would be separated and fall and form a vacuum, as we have described above. Therefore if it desired to remain in the air it is necessary that it should blend with a quantity of air, and if it were united with the air, two difficulties arise: that is, that it will rarefy that portion of air with which it is mingled, and this rarefied air will fly upwards and will not remain in the air which is heavier than itself; and besides this the ethereal spiritual essence is disunited, and its nature is changed, for which reason that nature loses some of its first virtue. There is in addition to these a third difficulty, and this is that a body of this kind, made of air and assumed by the spirits, is exposed to the penetrating winds which continually sunder and scatter the united portions of the air, eddying and whirling amidst the rest of the atmosphere; therefore the spirit who would pervade this air would be dismembered or rent and broken up with the rending of the air of which it formed part.
108.
It is impossible that the spirit, incorporated with a certain quantity of air, should move this air; and this is proved by the passage where it is said that "the spirit rarefies that portion of the air with which it is mingled." This air therefore will rise high above the other air, and the air will be set in motion by its own lightness and not by the volition of the spirit, and if this air encounters a wind, the air will be moved by the wind and not by the spirit which is incorporated in it.
109.
In order to show whether the spirit can speak or not it is first necessary to define the voice and the manner of its origin. The following will be our definition: The voice is the movement of air in friction against a dense body, or a dense body in friction against the air (which is the same idea), and by this friction of the dense and the rare what is rare is condensed, and resistance is caused; and again, when the rare in swift motion and the rare in slow motion come into contact, they condense one another and produce sound, and a great noise is made. The sound or murmur made by the rare moving through the rare with slow motion is like the great flame whence sounds issue in the air; the exceedingly great noise made by the rare, when the air which is rare and swift mingles with that which is rare and in [slow] motion, is like the flame of fire issuing from a great gun and striking against the air; likewise the flame when it issues from a cloud strikes the air as it begets the thunderbolt. Therefore we will say that the spirit cannot produce a voice unless the air be set in motion, but since there is no air within, it cannot discharge what it does not possess; and if it wishes to move that air in which it is incorporated, it is necessary that the spirit should multiply itself; but that which has no quantity cannot be multiplied. In the fourth place it is said, that no rare body can move if it has not a stable spot whence it may take its motion, and more especially is this the case when an element must move in its own element, which does not move of itself, excepting by uniform evaporation at the centre of the thing evaporated; as occurs in the case of the sponge squeezed in the hand under water, whence the water escapes in every direction with equal motion through the spaces between the fingers of the hand which squeezes it. As to whether the spirit has an articulate voice and can be heard, and as to what are hearing and sight—the wave of the voice travels through the air as the images of objects travel to the eye.
110.
O mathematicians, clear up this error! The spirit cannot have a voice, for where there is a voice there is a body, and where there is a body there is occupation of space, which prevents the eye seeing what is behind that space; therefore a body fills all the surrounding air, that is to say, with its own image.
111.
There can be no voice where there is no motion or percussion of the air, there can be no percussion of the air where there is no instrument, there can be no such thing as an immaterial instrument; and this being so, a spirit can have neither voice, nor shape, nor force; and if it assumes a shape it can neither penetrate nor enter where the issues are closed. If any one were to say that a spirit may take bodies of various shapes by means of concentrated and compressed air, and by means of this instrument speak and move with force—I reply to this argument that where there are no nerves or bones, no force can be expended in any movement made by these imaginary spirits.
BIBLIOGRAPHICAL NOTE
AND
TABLE OF REFERENCES
BIBLIOGRAPHICAL NOTE
* *
*
Only of late years have the manuscripts of Leonardo da Vinci seen the light and the many difficulties been overcome which long proved an obstacle to their publication. The labour of editing, deciphering and translating his many scattered and fragmentary codices was beyond the efforts of any single man. The gratitude of the cultivated world is therefore due to those who, like J. P. Richter, C. Kavaisson-Mollien, Luca Beltrami, Piumati, Sabachnikoff, and, last but not least, the scholars of the Academia del Lincei, have so faithfully devoted themselves to this task, which alone has made possible the present little work.
It was unavoidable that the form in which these manuscripts have been published should practically restrict their possession to the great libraries. But an excellent volume of selections from the writings of Leonardo, which are found in so haphazard a manner scattered through his codices and intermingled with his drawings and diagrams, has been published in Italy (Leonardo da Vinci: Frammenti Letterari e Storici, Florence, 1900). By kind permission of its editor, Dr. Solmi, this has served as a basis for the text of the present translation. The references, however, have been verified with the complete editions of Leonardo's works, while a different arrangement has been made of the text.
L. E.
TABLE OF REFERENCES
[A] Les manuscrits de Léonard de Vinci. Le manuscrit A de la Bibliothèque de l'Institut. Edit. Ravaisson-Mollien, vol. i. Paris, 1880.
[ASH I] Les manuscrits de Léonard de Vinci. Les manuscrits H de la Bibliothèque de l'Institut; 2038 (Ash I) et 2037 (Ash II) de la Bibliotheque Nationale. Edit. Ravaisson-Mollien, vol. vi. Paris, 1891.
[ASH II] Idem.
[B] Les manuscrits de Léonard de Vinci. Les manuscrits B et D de la Bibliothèque de l'Institut. Edit. Ravaisson-Mollien, vol. ii. Paris, 1883.
[C] Les manuscrits de Leonard de Vinci. Les manuscrits C, E et K de la Bibliothèque de l'Institut. Edit. Ravaisson-Mollien, vol. iii. Paris, 1888.
[C A] Il Codice Atlantico di Léonardo da Vinci nella Biblioteca Ambrosiana di Milano. Rome; Milan, 1891. (Still in course of publication.)
[D] See B.
[E] See C.
[F] Les manuscrits de Léonard de Vinci. Les manuscrits F et I de la Bibliothèque de l'Institut. Edit. Ravaisson-Mollien, vol. iv. Paris, 1889.
[G] Les manuscrits de Léonard de Vinci. Les manuscrits G, L et M de la Bibliothèque de l'Institut. Edit. Ravaisson-Mollien, vol. v. Paris, 1890.
[H] See Ash I.
[I] See F.
[L] See G.
[Lu] Léonardo da Vinci: Das Buch vom Malerei. Herausgegeben v. H. Ludwig. 3 vols. Berlin, 1882.
[M] See G.
[R] The Literary Works of Leonardo da Vinci. Compiled and edited from the original manuscripts by J. P. Richter. 2 vols. London, 1883.
[S] Leonardo da Vinci: Frammenti Letterari e Filosofici. Trasceiti dal Dr. Edmondo Solmi. Florence, 1900.
[T] Il codice di Léonardo da Vinci nella Biblioteca del Principe Trivulzio. Edit. L. Beltrami. Milan, 1892.
[V U] Leonardo da Vinci. Il codice del volo degli uccelli ed altre materie. Edit. Sabachnikoff e Piumati. Paris, 1893.
THOUGHTS ON LIFE
3 1 R 4 4 4 CA 119 r
3 2 R 1339 5 5 Lu 9
4 3 R 841 5 6 R 1169
5 7 S 69 14 36 R 838
6 8 C A 119 r 14 37 Lu 16
6 9 C A 91 v 15 38 Lu 65
6 10 C A 119 r 15 39 S 96
6 11 S 71 15 40 B 4 v
7 12 R 1178 15 41 F 96 v
7 13 S 72 15 42 C A 79 r
7 14 T 2 v 15 43 S 98
8 15 C A 112 r 15 44 S 99
8 l6 Lu 65 16 45 G 47 r
9 17 S 74 16 46 C A 119 v
9 l8 S 336 l6 47 R 837
9 19 S 74 17 48 R 1210
9 20 R ll75 19 49 I 18 r
9 21 M 58 v 19 50 S 67
10 22 V U 12 r 19 51 R 1135
10 23 S 76 19 52 C A 169 v
10 24 C A 119 r 20 53 S 114
11 25 C A 117 r 20 54 S 115
11 26 C A 76 r 21 55 Ash II 4 r
11 27 C A 117 r 21 56 C A 59 r
12 28 C A 76 r 21 57 T 6 r
12 29 F 27 v 21 58 G 74 v
12 30 S 83 22 58 S 121
12 31 R 1150 22 60 S 122
12 32 C A 154 r 22 61 S 123
13 33 C A 154 r 23 62 H 89 v
13 34 C A 86 r 23 63 S 168
13 35 T 20 v 23 64 F 49 v
24 65 S 169 36 94 C A 29 v
24 66 R 846 36 95 C A 12 r
24 67 R 1219 36 96 C A 71 v
25 68 R 1187 37 97 S 205
25 69 R 838 37 98 T 34 R
27 70 C A 90 r 37 99 T 34 r
28 71 C A 119 v 37 100 T 27 r
29 72 R 839 37 101 C A 71 r
29 73 Lu 499 38 102 Lu 77
30 74 T 7 v 38 103 R 1132
30 75 S 180 39 104 R 1133
30 76 R 916 39 105 S 208
31 77 R 798 39 106 T 340
31 78 S 187 39 l07 T 14 v
32 79 C A 119 r 39 108 C 117 v
32 80 R 1 39 109 G 49 r
32 81 Lu 292 40 110 S 209
33 82 S 201 41 111 H passim
34 83 H 60 r 44 ll2 S 214
34 84 H 32 r 45 113 H 48 v
34 85 S 202 45 114 S 2l6
34 86 C A 76 r 45 115 R 827
35 87 S 202 46 116 R 844
35 88 H 33 v 47 117 R 8l6
35 89 S 203 47 118 S 221
35 90 T 33 v 48 119 S 221
35 91 T 23 v 48 120 S 229
35 92 Ash i 34 v 48 121 C 15 v
36 93 C A 76 r 50 122 R 1358
51 123 S 217 54 127 R 300
52 124 R 1355 55 128 S 382
52 125 Lu 24 55 129 S 199
53 126 Lu 16
THOUGHTS ON ART
60 2 S 274 85 25 Lu 31
60 3 Lu 438 87 26 Lu 30
60 4 Lu 27 88 27 Lu 32
60 5 Lu 34 90 28 S 276
61 6 Lu 7 90 29 Lu 9
62 7 Lu 8 90 30 Lu 13
64 8 Ash II 19 v 91 31 S 275
65 9 Lu 2 92 32 Ash II 20 r
66 10 Lu 7 92 33 Ash II 26 r
66 11 Lu 14 93 34 Ash II 25 r 24 v
68 12 Lu 10
68 13 Lu 46 95 35 Lu 35
68 14 Lu 18 96 36 Lu 36
69 15 Lu 20 97 37 Lu 38
71 16 Lu 21 98 38 Lu 40
72 17 Lu 22 99 39 Lu 41
73 18 S 251 100 40 Lu 405
77 19 S 257 100 41 Lu 62
80 20 Lu 27 100 42 R 498
82 21 Lu 27 100 43 Lu 57
82 22 Lu 26 101 44 Ash II 16 v
83 23 Lu 28 101 45 Lu 58
101 46 R 103 116 70 Lu 107
102 47 R 104 116 71 S 337
103 48 Lu 404 117 72 S 338
104 49 Ash II 22v 117 73 S 336
105 50 Lu 54 117 74 S 337
105 51 I 130 v 118 75 Lu 108
105 52 C A 76 v 119 76 Lu 109
106 53 C A 119 v 120 77 A 23 r
106 54 G 8 v 120 78 K 110 v
106 55 Ash II 17 v 120 79 S 338
107 56 C A 181 v 121 80 Lu 15, 25
107 57 S 200 125 81 R 1021
108 58 S 284 125 82 Lu 806
109 59 S 78 127 83 Ash I 18 v
111 60 S 283 128 84 Ash I 21 r
111 61 G 33 r v 129 85 Ash I 30 v
111 62 R 796 133 86 S 2l6
112 63 Ash II 26 r 134 87 Ash II 22 v
113 64 Ash II 28 r 134 88 S 335
113 65 Ash II 26 r 135 89 S 338
114 66 Ash II 25 r 136 90 S 339
114 67 Ash II 24 v 137 91 S 341
115 68 Lu 53 137 92 S 342
116 69 S 122 137 93 S 340
THOUGHTS ON SCIENCE
141 2 R 110 141 4 R 6
142 5 R 1157 154 34 F 6 r
142 6 G 96 v 155 35 F 8 r
142 7 T 12 r 155 36 F 34 v
142 8 Lu 1 155 37 G 34 r
143 9 Lu 33 156 38 F 85 v
146 10 E 8 v 156 39 S 136
146 11 R 1156 158 40 S 141
146 12 K 49 r 158 41 S 139
146 13 I 102 r, v 158 42 S 140
147 14 A 24 r 159 43 S 128
148 15 S 124 160 44 R 902
148 l6 T 36 v 161 45 S 138
148 17 T 36 v 161 46 S 137
148 18 H 141 r 161 47 S 137
148 19 E 22 r 161 48 S 138
149 20 I 68 r 162 49 S 139
149 21 R 859 162 50 S 139
149 22 F 52 r 162 51 S 142
150 23 S 126 163 52 C A 80 r
150 24 S l27 164 53 H 95 r
151 25 B 63 r 164 54 H 90 r
151 26 S 125 164 55 S 88
151 27 C 26 v 164 56 F 30 v
151 28 A 60 r 164 57 R 1000
151 29 S 124 165 58 R 970
152 30 C 28 v 165 59 H 77 r
152 31 R 860 165 60 R 965
153 32 S 131 166 61 R 953
154 33 S 132 166 62 F 52 v
167 63 G 49 v 176 88 S 118
167 64 K 22 177 89 E 54 r
168 65 S 113 177 90 C A 66 v
168 66 S 113 177 91 E 52 v
168 67 C A 147 v 178 92 S 148
168 68 E 55 v 178 93 S 167
168 69 S 88 178 94 S 200
169 70 M 57 r 178 95 S 200
169 71 R 107 179 96 S 200
170 72 C A 337 v 179 97 R 1206
170 73 T 39 r 179 98 K 101 v
171 74 I 202 179 99 R 796
171 75 D 5 r 180 100 Lu 17
172 76 F 2 v 180 101 S 66
172 77 C A 75 v 181 102 S 122
172 78 H 67 v 181 103 R 1213
173 79 F 2 v 183 104 S 181
173 80 F 69 v 184 105 Ash III 27 v
174 81 S 129 185 106 S 192
174 82 C A 153 v 186 107 R 1214
174 83 V U 3 v 187 108 R 1215
175 84 R 984 187 109 C A 187 v
175 85 S 142 189 110 S 196
175 86 C A 76 r 189 111 B 4 V
176 87 C A 76 r