The Notebooks of Leonardo Da Vinci by Leonardo Da Vinci (moboreader txt) 📕

speaking is that which may be multiplied, that is when, being multiplied by a certain number, it forms exactly the whole. A common aggregate part …

Second definition. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less.

By the first we define the lesser [magnitude] and by the second the greater is defined. A part is spoken

 

1490.

 

of in relation to the whole; and all their relations lie between these two extremes, and are called multiples.

 

1491.

 

Hippocrates says that the origin of men’s sperm derives from the brain, and from the lungs and testicles of our parents, where the final decocture is made, and all the other limbs transmit their substance to this sperm by means of expiration, because there are no channels through which they might come to the sperm.

[Footnote: The works of Hippocrates were printed first after Leonardo’s death.]

 

1492.

 

Lucretius in his third [book] ‘De Rerum Natura’. The hands, nails and teeth were (165) the weapons of ancient man.

They also use for a standard a bunch of grass tied to a pole (167).

[Footnote: Lucretius, de rerum natura libri VI were printed first about 1473, at Verona in 1486, at Brescia in 1495, at Venice in 1500 and in 1515, and at Florence in 1515. The numbers 165 and 167 noted by Leonardo at the end of the two passages seem to indicate pages, but if so, none of the editions just mentioned can here be meant, nor do these numbers refer to the verses in the poems of Lucretius.]

 

1493.

 

Ammianus Marcellinus asserts that seven hundred thousand volumes of books were burnt in the siege of Alexandria in the time of Julius Cesar.

[Footnote: Ammiani Marcellini historiarum libri qui extant XIII, published at Rome in 1474.]

 

1494.

 

Mondino says that the muscles which raise the toes are in the outward side of the thigh, and he adds that there are no muscles in the back [upper side] of the feet, because nature desired to make them light, so as to move with ease; and if they had been fleshy they would be heavier; and here experience shows …

[Footnote: “Mundini anatomia. Mundinus, Anothomia (sic). Mundini praestantissimorum doctorum almi studii ticiensis (sic) cura diligentissime emendata. Impressa Papiae per magistrum Antonium de Carfano 1478,” in-fol.; ristampata: “Bononiae Johan. de Noerdlingen, 1482,” in-fol.; “Padova per Mattheum Cerdonis de Vuindischgretz, 1484,” in-40; “Lipsia, 1493,” in-40; “Venezia, 1494,” in-40 e ivi “1498,” con fig. Queste figure per altro non sono, come si e preteso, le prime che fossero introdotte in un trattato di Notamia. Nel ‘fasciculus Medicinae’ di Giovanni Ketham, che riproduce l”Anatomia’ del Mundinus, impresso pure a Venezia da J. e G. de Gregoriis, 1491, in-fol., contengonsi intagli in legno (si vogliono disegnati non gia incisi da Andrea Mantegna) di grande dimensione, e che furono piu volte riprodotti negli anni successivi. Quest’ edizione del “fasciculus” del 1491, sta fra nostri libri e potrebbe benissimo essere il volume d’Anatomia notato da Leonardo. (G. D’A.)]

 

1495.

 

Of the error of those who practice without knowledge;—[3] See first the ‘Ars poetica’ of Horace [5].

[Footnote: A 3-5 are written on the margin at the side of the title line of the text given, entire as No. 19]

 

1496.

 

The heirs of Maestro Giovanni Ghiringallo have the works of Pelacano.

 

1497.

 

The catapult, as we are told by Nonius and Pliny, is a machine devised by those &c.

[Footnote: Plinius, see No. 946.]

 

1498.

 

I have found in a history of the Spaniards that in their wars with the English Archimedes of Syracuse who at that time was living at the court of Ecliderides, King of the Cirodastri. And in maritime warfare he ordered that the ships should have tall masts, and that on their tops there should be a spar fixed [Footnote 6: Compare No. 1115.] of 40 feet long and one third of a foot thick. At one end of this was a small grappling iron and at the other a counterpoise; and there was also attached 12 feet of chain; and, at the end of this chain, as much rope as would reach from the chain to the base of the top, where it was fixed with a small rope; from this base it ran down to the bottom of the mast where a very strong spar was attached and to this was fastened the end of the rope. But to go on to the use of his machine; I say that below this grappling iron was a fire [Footnote 14: Compare No. 1128.] which, with tremendous noise, threw down its rays and a shower of burning pitch; which, pouring down on the [enemy’s] top, compelled the men who were in it to abandon the top to which the grappling-iron had clung. This was hooked on to the edges of the top and then suddenly the cord attached at the base of the top to support the cord which went from the grappling iron, was cut, giving way and drawing in the enemy’s ship; and if the anchor—was cast …

[Footnote: Archimedes never visited Spain, and the names here mentioned cannot be explained. Leonardo seems to quote here from a book, perhaps by some questionable mediaeval writer. Prof. C. Justi writes to me from Madrid, that Spanish savants have no knowledge of the sources from which this story may have been derived.]

 

1499.

 

Theophrastus on the ebb and flow of the tide, and of eddies, and on water. [Footnote: The Greek philosophers had no opportunity to study the phenomenon of the ebb and flow of the tide and none of them wrote about it. The movement of the waters in the Euripus however was to a few of them a puzzling problem.]

 

1500.

 

Tryphon of Alexandria, who spent his life at Apollonia, a city of Albania (163). [Footnote: Tryphon of Alexandria, a Greek Grammarian of the time of Augustus. His treatise TtaOY Aeijecu appeared first at Milan in 1476, in Constantin Laskaris’s Greek Grammar.]

 

1501.

 

Messer Vincenzio Aliprando, who lives near the Inn of the Bear, has Giacomo Andrea’s Vitruvius.

 

1502.

 

Vitruvius says that small models are of no avail for ascertaining the effects of large ones; and I here propose to prove that this conclusion is a false one. And chiefly by bringing forward the very same argument which led him to this conclusion; that is, by an experiment with an auger. For he proves that if a man, by a certain exertion of strength, makes a hole of a given diameter, and afterwards another hole of double the diameter, this cannot be made with only double the exertion of the man’s strength, but needs much more. To this it may very well be answered that an auger

 

1503.

 

of double the diameter cannot be moved by double the exertion, because the superficies of a body of the same form but twice as large has four times the extent of the superficies of the smaller, as is shown in the two figures a and n.

 

1504.

 

OF SQUARING THE CIRCLE, AND WHO IT WAS THAT FIRST DISCOVERED IT BY ACCIDENT.

Vitruvius, measuring miles by means of the repeated revolutions of the wheels which move vehicles, extended over many Stadia the lines of the circumferences of the circles of these wheels. He became aware of them by the animals that moved the vehicles. But he did not discern that this was a means of finding a square equal to a circle. This was first done by Archimedes of Syracuse, who by multiplying the second diameter of a circle by half its circumference produced a rectangular quadrilateral equal figure to the circle [Footnote 10: Compare No. 1475.].

[Footnote: Vitruvius, see also Nos. 1113 and 343.]

 

1505.

 

Virgil says that a blank shield is devoid of merit because among the people of Athens the true recognition confirmed by testimonies …

[Footnote: The end of the text cannot be deciphered.]

 

1506.

 

In Vitolone there are 805 conclusions [problems] in perspective.

[Footnote: _(Witelo, Vitellion, Vitellon) Vitellione. E da vedersi su questo ottico prospettico del secolo XIII Luca Pacioli, Paolo Lomazzo, Leonardo da Vinci, ecc. e fra i moderni il Graesse, il Libri, il Brunet, e le Memorie pubblicate dal principe Boncompagni, e ‘Sur l’ orthographe du nom et sur la patrie de Witelo (Vitellion) note de Maximilien Curtze, professeur a Thorn’, ove sono descritti i molti codici esistenti nelle biblioteche d’ Europa. Bernardino Baldi nelle sue ‘Vite de’matematici’, manoscritto presso il principe Boncompagni, ha una biografia del Vitellione. Questo scritto del Baldi reca la data 25 agosto 1588. Discorsero poi di lui Federigo Risnerio e Giovanni di Monteregio nella prefazione dell’ Alfagrano, Giovanni Boteone, Girolamo Cardano, ‘De subtilitate’, che nota gli errori di Vitellione. Visse, secondo il Baldi, intorno all’ anno 1269, ma secondo il Reinoldo fioriva nel 1299, avendo dedicata la sua opera ad un frate Guglielmo di Monteca, che visse di que’ tempi.

Intorno ad un manoscritto dell’ ottica di Vitellione, citato da Luca Pacioli v’ha un secondo esemplare del Kurlz, con aggiunte del principe Boncompagni, e le illustrazioni del cav. Enrico Narducci. Nel ‘Catalogo di manoscritti’ posseduti da D. Baldassare de’ principi Boncompagni, compilato da esso Narducci, Roma, 1862, sotto al n. 358, troviamo citato: Vitellio, ‘Perspectiva’, manoscritto del secolo XIV. La ‘Prospettiva di Vitelleone’ (sic) Thuringo-poloni e citata due volte da Paolo Lomazzo nel Trattato dell’ arte della pittura. Vitellio o Vitello o Witelo. Il suo libro fu impresso in foglio a Norimberga nel 1535; la secondo edizione e del 1551, sempre di Norimberga, ed una terza di Basilea, 1572._ (See Indagini Storiche … sulla Libreria-Visconteo-Sforzesca del Castello di Pavia … per cura di G. D’A., Milano 1879. P. I. Appendice p. 113. 114).]

 

1507.

 

Vitolone, at Saint Mark’s.

[Footnote: Altro codice di cotesta ‘Prospettiva’ del Vitolone troviamo notato nel ‘Canone bibliographico di Nicolo V’, conservato alla, Magliabecchiana, in copia dell’ originale verosimilmente inviato dal Parentucelli a Cosimo de’ Medici (Magliab. cod. segn. 1 VII, 30 carte da 193 a 198). Proviene dal Convento di San Marco e lo aveva trascritto frate Leonardo Scruberti fiorentino, dell’ ordine dei predicatori che fu anche bibliotecario della Medicea pubblica in San Marco (See Indagini Storiche … per cura di G. D’A. Parte I, p. 97).]

 

1508.

 

How this proposition of Xenophon is false.

If you take away unequal quantities from unequal quantities, but in the same proportion, &c. [Footnote: Xenophon’s works were published several times during Leonardo’s lifetime.]

Inventories and accounts (1509—1545).

 

1509.

 

On the 28th day of April I received from the Marchesino 103 lire and 12 dinari. [Footnote: Instead of the indication of the year there is a blank space after d’aprile.—Marchesino Stange was one of Lodovico il Moro’s officials.—Compare No. 1388.]

 

1510.

 

On the 10th day of July 1492 in 135 Rhenish florins 1. 445 in dinari of 6 soldi 1. 112 S 16 in dinari of 5 1/2 soldi 1. 29 S 13 9 in gold and 3 scudi 1. 53

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1. 811 in all

 

1511.

 

On the first day of February, lire 1200.

 

1512.

 

The hall towards the court is 126 paces long and 27 braccia wide.

 

1513.

 

The narrow cornice above the hall lire 30.

The cornice beneath that, being one for each picture, lire 7, and for the cost of blue, gold, white, plaster, indigo and glue 3 lire; time 3 days.

The pictures below these mouldings with their pilasters, 12 lire each.

I calculate the cost for smalt, blue and gold and other colours at 1 1/2 lire.

The days I calculate at 3, for the invention of the composition, pilasters