On the Conception of Nothingness
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 thingswhich are impossible. Whence from that which has been said, it has no being, because where there is nothingness there would be a vacuum.
On Spirits
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 vacuumin 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.
Has the Spirit a Body?
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 pervadethis 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.
Can the Spirit speak?
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 rarewith 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.
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, havebeen 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.
On Life
Page. No. Reference. Page. No. Reference.3 1 R 4 4 4 CA 119 r3 2 R 1339 5 5 Lu 94 3 R 841 5 6 R 1169
Page. No. Reference. Page. No. Reference.5 7 S 69 14 36 R 8386 8 C A 119 r 14 37 Lu 166 9 C A 91 v 15 38 Lu 656 10 C A 119 r 15 39 S 966 11 S 71 15 40 B 4 v7 12 R 1178 15 41 F 96 v7 13 S 72 15 42 C A 79 r7 14 T 2 v 15 43 S 988 15 C A 112 r 15 44 S 998 l6 Lu 65 16 45 G 47 r9 17 S 74 16 46 C A 119 v9 l8 S 336 l6 47 R 8379 19 S 74 17 48 R 12109 20 R ll75 19 49 I 18 r9 21 M 58 v 19 50 S 6710 22 V U 12 r 19 51 R 113510 23 S 76 19 52 C A 169 v10 24 C A 119 r 20 53 S 11411 25 C A 117 r 20 54 S 11511 26 C A 76 r 21 55 Ash II 4 r11 27 C A 117 r 21 56 C A 59 r12 28 C A 76 r 21 57 T 6 r12 29 F 27 v 21 58 G 74 v12 30 S 83 22 58 S 12112 31 R 1150 22 60 S 12212 32 C A 154 r 22 61 S 12313 33 C A 154 r 23 62 H 89 v13 34 C A 86 r 23 63 S 16813 35 T 20 v 23 64 F 49 v
Page. No. Reference. Page. No. Reference.24 65 S 169 36 94 C A 29 v24 66 R 846 36 95 C A 12 r24 67 R 1219 36 96 C A 71 v25 68 R 1187 37 97 S 20525 69 R 838 37 98 T 34 R27 70 C A 90 r 37 99 T 34 r28 71 C A 119 v 37 100 T 27 r29 72 R 839 37 101 C A 71 r29 73 Lu 499 38 102 Lu 7730 74 T 7 v 38 103 R 113230 75 S 180 39 104 R 113330 76 R 916 39 105 S 20831 77 R 798 39 106 T 34031 78 S 187 39 l07 T 14 v32 79 C A 119 r 39 108 C 117 v32 80 R 1 39 109 G 49 r32 81 Lu 292 40 110 S 20933 82 S 201 41 111 H passim34 83 H 60 r 44 ll2 S 21434 84 H 32 r 45 113 H 48 v34 85 S 202 45 114 S 2l634 86 C A 76 r 45 115 R 82735 87 S 202 46 116 R 84435 88 H 33 v 47 117 R 8l635 89 S 203 47 118 S 22135 90 T 33 v 48 119 S 22135 91 T 23 v 48 120 S 22935 92 Ash i 34 v 48 121 C 15 v36 93 C A 76 r 50 122 R 1358
Page. No. Reference. Page. No. Reference.51 123 S 217 54 127 R 30052 124 R 1355 55 128 S 38252 125 Lu 24 55 129 S 19953 126 Lu 16
On Art
59 1 C A 141 v 85 24 Lu 2960 2 S 274 85 25 Lu 3160 3 Lu 438 87 26 Lu 3060 4 Lu 27 88 27 Lu 3260 5 Lu 34 90 28 S 27661 6 Lu 7 90 29 Lu 962 7 Lu 8 90 30 Lu 1364 8 Ash II 19 v 91 31 S 27565 9 Lu 2 92 32 Ash II 20 r66 10 Lu 7 92 33 Ash II 26 r66 11 Lu 14 93 34 Ash II 25 r 24 v68 12 Lu 1068 13 Lu 46 95 35 Lu 3568 14 Lu 18 96 36 Lu 3669 15 Lu 20 97 37 Lu 3871 16 Lu 21 98 38 Lu 4072 17 Lu 22 99 39 Lu 4173 18 S 251 100 40 Lu 40577 19 S 257 100 41 Lu 6280 20 Lu 27 100 42 R 49882 21 Lu 27 100 43 Lu 5782 22 Lu 26 101 44 Ash II 16 v83 23 Lu 28 101 45 Lu 58
Page. No. Reference. Page. No. Reference.101 46 R 103 116 70 Lu 107102 47 R 104 116 71 S 337103 48 Lu 404 117 72 S 338104 49 Ash II 22v 117 73 S 336105 50 Lu 54 117 74 S 337105 51 I 130 v 118 75 Lu 108105 52 C A 76 v 119 76 Lu 109106 53 C A 119 v 120 77 A 23 r106 54 G 8 v 120 78 K 110 v106 55 Ash II 17 v 120 79 S 338107 56 C A 181 v 121 80 Lu 15, 25107 57 S 200 125 81 R 1021108 58 S 284 125 82 Lu 806109 59 S 78 127 83 Ash I 18 v111 60 S 283 128 84 Ash I 21 r111 61 G 33 r v 129 85 Ash I 30 v111 62 R 796 133 86 S 2l6112 63 Ash II 26 r 134 87 Ash II 22 v113 64 Ash II 28 r 134 88 S 335113 65 Ash II 26 r 135 89 S 338114 66 Ash II 25 r 136 90 S 339114 67 Ash II 24 v 137 91 S 341115 68 Lu 53 137 92 S 342116 69 S 122 137 93 S 340
On Science
141 1 Lu 1 141 3 R 3141 2 R 110 141 4 R 6
Page. No. Reference. Page. No. Reference.142 5 R 1157 154 34 F 6 r142 6 G 96 v 155 35 F 8 r142 7 T 12 r 155 36 F 34 v142 8 Lu 1 155 37 G 34 r143 9 Lu 33 156 38 F 85 v146 10 E 8 v 156 39 S 136146 11 R 1156 158 40 S 141146 12 K 49 r 158 41 S 139146 13 I 102 r, v 158 42 S 140147 14 A 24 r 159 43 S 128148 15 S 124 160 44 R 902148 l6 T 36 v 161 45 S 138148 17 T 36 v 161 46 S 137148 18 H 141 r 161 47 S 137148 19 E 22 r 161 48 S 138149 20 I 68 r 162 49 S 139149 21 R 859 162 50 S 139149 22 F 52 r 162 51 S 142150 23 S 126 163 52 C A 80 r150 24 S l27 164 53 H 95 r151 25 B 63 r 164 54 H 90 r151 26 S 125 164 55 S 88151 27 C 26 v 164 56 F 30 v151 28 A 60 r 164 57 R 1000151 29 S 124 165 58 R 970152 30 C 28 v 165 59 H 77 r152 31 R 860 165 60 R 965153 32 S 131 166 61 R 953154 33 S 132 166 62 F 52 v
Page. No. Reference. Page. No. Reference.167 63 G 49 v 176 88 S 118167 64 K 22 177 89 E 54 r168 65 S 113 177 90 C A 66 v168 66 S 113 177 91 E 52 v168 67 C A 147 v 178 92 S 148168 68 E 55 v 178 93 S 167168 69 S 88 178 94 S 200169 70 M 57 r 178 95 S 200169 71 R 107 179 96 S 200170 72 C A 337 v 179 97 R 1206170 73 T 39 r 179 98 K 101 v171 74 I 202 179 99 R 796171 75 D 5 r 180 100 Lu 17172 76 F 2 v 180 101 S 66172 77 C A 75 v 181 102 S 122172 78 H 67 v 181 103 R 1213173 79 F 2 v 183 104 S 181173 80 F 69 v 184 105 Ash III 27 v174 81 S 129 185 106 S 192174 82 C A 153 v 186 107 R 1214174 83 V U 3 v 187 108 R 1215175 84 R 984 187 109 C A 187 v175 85 S 142 189 110 S 196175 86 C A 76 r 189 111 B 4 V176 87 C A 76 r
Publisher logo
Publisher logo