Il Compasso geometrico e militare di Galileo: Note
1. As there is no danger of mistaking, the titles of the works mentioned in this paper are always synthesised in the following way: Compasso, Annotazioni, Usus et fabrica circini and Difesa. As for critical essays, except for the Annotazioni, which had never been re-printed, see the second volume of the National Edition Le Opere di Galileo Galilei, Barbera, Florence 1968, which will be referred to as G.G.
2. "440 of them were found at the bookseller's and 13 in the author's house, since 30 of them were already widespread in different parts of Europe. () These copies handed out, since the ignominy imposed on me had already been spread around the world, I needed to () publish this writing". Difesa, 162; G.G. II, 561. (Works quotations are extracted from are always reported by their shortened title followed by the page number. The volume is shown in Roman numbers).
3. G.G., X, 296. Giovan Battista Manso (March 18th, 1610): "God wanted him to dedicate himself to the discovery of new skies by a new method () and lead him through ways not covered by the human intellect anymore, as a second Colombo". On April 19th, the great Giovanni Kleper writes something important to him: "Scio quantum intersit inter rationales coniecturas, et ocularem experimentiam; inter Ptolomei disputationem de Antipodibus, et Columbi detectionem novi orbis" G.G. X, 324. Orazio Del Monte on 16th June: "Your Highness can easily compete in glory with Colombo".
4. "Sidereus Nuncius",G.G. III, part I, 60.
5. This passage is at the beginning of " Il Saggiatore", G.G. VI, 214-215, where Galileo is about to accuse Simon Mayr of trying to steal his antecedence in the discovery of Jupiter's satellites. This claim was included in Mundus Jovialis anno 1609 detectus ope perspicilli belgici. Hoc est quatuor jovialium planetarum cum theoria, tum tabulae propriis observationibus maxime fundatae, published only in 1614 by Mayr. Mayr has been considered a plagiarist for ages, but, after deeper studies, he is considered an independent discoverer. As for his role in the Compasso, it will be very difficult to reach the truth, because Galileo's claims seem to be grounded only on his suspicions.
6. Compasso was printed in his house. The printed received 85 Italian Lira and the picture engraver received 16.5 Italian Lira. G.G. XIX, 167.
7. "Neither any instrument's description nor any explanation of how to build it " was included in the treatise and, in order to follow its instructions, it was necessary to have the compass: that is why publishing a greater number of copies would have been totally useless.
8. G.G. X,171-172.
9. In fact,Galileo made a mistake about his name and most of all his nationality, by calling him Giovanni Eutel Zieckmeser, a Flemish man.
10. As for Hasdale, see his letters in G.G. X, 366, 370, and 417, 492.
11. G.G. X,370.
12. As for Pompeo Panico's signature of Cornaro's declaration, see Difesa, 152-153; G.G. II, 546.
13. Difesa, 163-164; G.G. II,562.
14. Zugmesser's writings were deposited in the Cancelleria Pretoria of Padova: "in order to confirm the truth and for a public knowledge, the original manuscripts are reserved by the Coadjutor Notary of our Chancellery" Difesa, 187; G.G. II, 600. Favaro was asked to look for them, but they have not been found yet. However, it is known from Galileo as well that the writings left in Padua included just a few things more than some instructions more or less similar to his ones. These are the table of the quadrant's regular polygons and the quadrant's use. For example, he could teach how to find the degrees of any suggested arc and the angles of triangles: in order to do these, it was provided with a table of sines. The astronomical quadrant's divisions were shown by Galileo's instrument as well but as it was a trivial addition that let the compass to be used as a quadrant, he observed that "its use will not be described, as it has already been revealed by others". Compasso, 25; G.G. II, 412.
15. Difesa,153; G.G. II, 547.
16. G.G. X, 174. At the end of Difesa, Galileo speaks about Capra's wrong use of Magini's books (Difesa, 184-87; G.G. II, 595-97).
17. Difesa,184; G.G. II, 594.
18. Giovanni Camillo Gloriosi wrote to Giovanni Terrenzio (May 29th, 1610): "Quo in crimine Galileaus suspectus est, cum auctorem quoque se faciat instrumenti quod Circinum Militare et Geometricum Appellavit. Magnoque Hetruriae Principi dedicavit; vetus quippe adinventum, et ab omnibus una voce Michaeli Coigneto Antuerpiensi, ut primo inventori, attributum". In this letter Gloriosi is presented hostile to Galileo and moved by envy.
19. G. B. Venturi, Memorie e lettere inedite finora o disperse di Galileo Galilei ordinate e illustrate con annotazioni(), Vincenzi, Modena 1818-1821, part I, 77-80.
20. The attribution of the compass to Guidobaldo is claimed, using many details, in Fabrica et Uso del Compasso Polimetro, by Muzio Oddi of Urbino, in a book published in 1633, after Galileo's condemnation. Oddi met Giovannantonio Magini, who he esteemed very much and kept a frequent correspondence with. Thinking of Magini's well-known feelings of envy for Galileo, it is likely that, as happened to other correspondents of Magini, Oddi as well was infected by his hostility. Accordingly, the attribution of the compass to Guidobaldo cannot be accepted without any reservation, dating however back to a long time before the book's publication: as early as September 1622, Oddi wrote to Piermatteo Giordani: "I need to publish two short leaflets, one concerning a square instrument (which was published in 1625 under the title Dello Squadro) and another one about a polymetric compass, which was attributed to themselves respectively by Galileo, Coignet, Capra as well as other people, and I'm demonstrating how Sir Guidobaldo's memory has been so happy". G.G. XIII, 97.
21. A. Favaro, "Per la Storia del Compasso di Proporzione", in Atti del R. Istituto Veneto di Scienze, Lettere ed Arti, Vol. LXVII, part II, 724.
22. Alessandro Sertini said to Galileo (April 16, 1605): "a few of the geometrical instruments invented by Your Lordship have been seen, and Orazio del Monte had one of them". G.G. X, 143. Orazio had probably received the compass in 1597, when he was entrusted to Galileo in order to complete his-most of all military- education by his father, who wrote: "I have introduced him into mathematics and I wish Your Lordship to convince him to follow us, () and I told him to come to Your Lordship if he found any difficulty, who I am sure will be so kind as to be his teacher ". G.G., X, 71-72.
23. G.G. X,166-167.
24. G.G. X,371-372.
25. A. Favaro, Galileo Galilei e lo studio di Padova, Le Monnier, Florence 1883, vol. I, 166.
26. G.G. X, 171.
27. M.C. Cantù, M. L. Righini Borelli, Gli strumenti Antichi al Museo di Storia della Scienza di Firenze, Arnaud, Florence 1980; and M. Miniati (ed) L'età di Galileo. Il Secolo d'Oro della Scienza in Toscana, Istituto e Museo di Storia della Scienza di Firenze, Florence 1987.
28. Girolamo Mercuriale of Pisa to Galileo in Padua, on 29 May 1601, G. G. X, 83-84.
29. G.G. II, 31.
30. It can be interesting to know that "in the fifth and last book the Scienze Meccaniche are taught, consisting in constructing several machines and instruments helping to raise very heavy weights using a little strength in order to do easily all the necessary services during war and peace". Guidobaldo del Monte is the only one mentioned in this book. Lorini, during the few years he spent in Flanders perhaps had knowledge of Stevin's mathematical works (which deal with fortifications as well) because his book mentions the discussion of one of Aristotle's problems in a very similar way to Stevin's book. It is interesting to focus on some points in Lorini's book, even biographical, which are in common with Galileo. In Le Mecaniche, written before 1599, Galileo is angry against macanici because they believe "They are able o move and raise very heavy weights using a little strength, believing that their machines can betray nature, whose very instinct is that no resistance can be won by any force more powerful than this one". Galileo seems to be referring to Lorini.: "These are the tasks that can be performed by mechanical instruments, and not the uses dreamed by green engineers in pursuit of impossible enterprises, which are shamefully deceived by principles".. About the lever, he adds: "That instrument's utility is not the utility believed by mechanics, that is overtake and in a certain way, betray nature, winning a very big resistance with a very little strength". And , talking about the argano: " the utility of these machines is not the one that mechanics believe, that is one can betray nature, winning its powerful resistance with a very little strength." G. G. II, 155, 156, 157, 158, 166, 170.
31. Letting the author to talk with a Florentine friend.
32. It has been partially reproduced by Stillmann Drake in "Galileo's Notes on motion", a supplement to Annali dell'Istituto e Museo di Storia della Scienza, 1979.
33. For instance, on the 187r paper there is 317x75=24675 and the mistake is done when the partial products are added, forgetting to add a unity. On the 154r paper, another mistake is: 17689x16=282624. On 189v paper is: 48143x4=192472.- Another mistake of the same kind is on paper 114r: 69x69=4661.
34. this number 254 gives the occasion for a new way of dividing the line into two equal parts, in order to construct the arithmetical line, which is different from Bernegger's. The 1640 edition of Compasso, printed in Padua by Paolo Frambotto, the first one after the 1606 edition, shows a picture of the compass that was later copied in the following edition. In this figure, the arithmetical lines are divided into 254 parts. Perhaps this is the explanation: as 256 is the eighth power of 2, accordingly a correct division is obtained by dividing into two equal parts eight times the segments obtained each time. The last two points can be deleted from the two framing lines. See the picture of the compass reprinted in this edition.
35. P. Casati, Fabrica, et Uso del Compasso di Proporzione, dove Insegna a gli Artifici il Modo di Fare in Esso le Necessarie Divisioni, e con Varj Problemi Usuali mostra L'Utilità di Questo Stromento, del molto Rev. Paolo Casati, Dando le Ragioni & Apportando le Dimostrazioni di Tutte le Operazioni nella Fabrica, e nell'Uso, Ferroni, Bologna 1664.
36. F.M. Gaudio, Insitutiones Mathematicae ad Usum Scholarum Piarum, Puccinelli, Rome 1772-1779, Vol. II, 77-78.
37. P.Petit, L'usage ou le moyen de pratiquer par une règle toutes les operations du compas de proportion.. Avec une emple consruction du l'une et de l'autre augmentée des tables de la pesanteur et grandeur des metaux et de tous les poids d'Europe, d'Afrique et d'Asie, a la mésure et aux poids de Paris. Comme aussi la construction et l'usage du Talftoc ou Calibre d'Artillerie. Par P.P.B. A Paris chez Melchior Mondiere MDCXXXIIII..
38. Didier or Denis Henrion, the pseudonym of clement Cyriaque de Mangin, is the author of the work whose passage where Galileo's error on the measurement of the alloy's size is mentioned by Petit. Its title is L'usage du compas de proportion, whose first two editions were printed in Paris in 1618 and 1624.
39. Henrion is a well-known translator of mathematics texts from Latin into French, which he sometimes improved by means of additions. In the introduction to the 1624 edition of his book about the compass, Henrion declares: "after seeing seventeen or eighteen years ago a small proportional compass with points and only two divisions son it in Mister (Jacques) Alleaume, the king's engineer's hands, I spent some time looking for its construction and use, but seeing that its.
40. M Oddiis another person who knows how to do the exact calculation, but he does it in a very complicated way in his Fabrica e uso del compasso polimetro. First, he solves the XIV problem: "given two balls, A and B, try to find the diameter of a ball which is equal to both of these two"; and then the XVIII problem: "if one should make a ball of bronze of sixty-eight Pounds, whose mixture is 24%, try to find its diameter".
41. Venturi G. B. Memorie e Lettere inedite finora o disperse di Galileo Galilei ordinate e illustrate con annotazioni(), Vincenzi, Modena, 1818-1821, part I, 77-80.
42. Ferdinand I, who had married Christine of Lorena in 1589. At his death, on February 3rd, 1609, his son Cosimo became grand Duke.
43. "Yet, as I decided to return, I would like to receive from Your Lordship some rest and freedom from my lectures in order to carry out my works" G.G. X, 350.
44. Letter to Galileo in Padua, July 10, 1610. G. G. X, 400.
45. Letter to Galileo in Padua, July 10, 1610. G. G. X, 400.
46. July 2nd, 1591.
47. A. Favaro, Galileo Galilei e lo Studio di Padova, Le Monnier, Florence 1883, Vol. I, 36-50. His article is very important: "Sulla veridicità del "Racconto Isterico della Vita di Galileo" dettato da Vincenzio Viviani" in Archivio Storico Italiano, 1915, 323-380.
48. G.G. XIX, 39, 41 and 43.
49. Giuliano de Ricci's 1571 chronicle says: "in important writings the value of the piastrone or ducat in silver called Florin is still 7 Lira". The passage is from C. M. Cipolla, La moneta a Firenze nel Cinquecento, Il Mulino, Bologna 1987, p. 131.
50. "D.Galileo Galilei, lecturer on Mathematics from September 26, 1592, receiving a salary of 180 florins900 Lira". G. G: , XIX, 124.
51. In the period taken into consideration, the Venetian Lira had the value of 4.31 grams of pure silver, whereas the Florentine Lira was valued 4.46 grams , with a difference of 3%.
52. G.G. XIX, 606 and 638. Nicolò Gherardini mentions Giovanni de' Medici, Cosimo I's natural son, and tells that the difference from that person appeared when some machines need inventing "for a certain factory, i don't know whether it was a fortification or another building" . He tells that "Mr D. Giovanni didn't like the criticism, and showed his grudge through angry words, which scared Galileo so that, after not too much time, he thought it better to apologise for his behaviour".
53. As for Guidubaldo's letters, see G.G. X, 42, 45 and 47.
54. Had his family been more prestigious and had more influential relations and economic resources, Galileo would not have been involved in Giovanbattista Ricasoli's strange events and as a witness in two inquiries for his testament's cancellation when, after his death, someone wanted to prove Ricasoli's insanity. In the inquiry's papers, his name always appears together with offensive words,. Contumelies cast on several witnesses and Galileo as well are shown in the marginal notes: sad rude unfrocked friar, because you were promised 150 florins for your sister, lute musician's son, poor unfrocked friar.." G.G. XIX, 45-46.
55. In 1577 Moletti was a lecturer at Padua earning 200 florins, and in 1584 earning 390 florins.
56. G.G., X, 58.
57. "In his speech in front of the Senate in May 1577, after his role as podestà at Padua Pasquale Cicogna tells that in 1576 the students were reduced to eighteen and even fewer because of the pestilence". A Favaro, "Amici e Corrispondenti Di GalileoGalilei XL. Giuseppe Moletti," in Atti del Reale Istituto Venento di Scienze, Lettere ed Arti, 1918, vol. LXXVII, part II, 61.
58. In his letter about Galileo's negotiations for a good increase in salary on the occasion of the conferring of his professorship-which was late as usual- Giovanfrancesco Sagredo reminded him that the opinion of the Riformatori dello Studio was that "it was nearly impossible to live on the sole professorship, and one need to give private lessons". G. G: X, 77.
59. Mercuriale wrote from Pisa (March 3, 1593)
60. Galileo himself shows great dissatisfaction as one can read in his letter of a few years later, in February 1609 in the same letter: "My public salary consist of 520 florins, which will be transformed in a few months into many scuds thanks to the confirmations of my nomination, and these will be surely more than enough, having a big help from the keeping of pupils and private lessons, which is what I want. I say this because I easily escape many of them, wishing infinitely more free time than gold, because I know that it is more difficult to obtain a sum of gold enough to be famous among other people than to receive honours from my studies". G.G. X, 105.
61. In the letter which was mentioned in the previous note.
62. Giovanfrancesco Sagredo wrote to Galileo(April 12, 1604): "Your Excellency's conferring of the professorship and increase of salary has been solicited by the very effective offices of myself and Mister Veniero, but they say they have little money and do not want to send this negotiation to their judge, so our hope is over". G: G. X, 105.
63. G.G. X, 106-107.
64. G.G.XIX, 155. Galileo, noting the gift, valued it 900 lira, that is nearly 130 scuds.
65. G. G. X, 109.
66. A. Favaro, Galileo e lo studio di Padova, Le Monnier, Florence 1883, Vol II, 99.
67. In October 1605, as Ferdinand I had ordered, the Resident of Tuscany at Venice had put in a good word for Galileo's interests to the Procuratore Leonardo Donato and to the other riformatore dello Studio di Padova, Girolamo Capello.
68. Cosimo de' Medici.
69. GirolamoMercuriale, from Pisa, on May 29th 1601 to Galileo in Padua. G. G. X, 83-84.
70. Letter already mentioned in note 58. G. G: X, 233.
71. May 7, 1610. Letter written in Padua to Belisario Vinta, the grand duke's secretary. G. G: X, 348-353.
72. G. G. X, 144. Letter dated June 4, 05. Vincenzo Giugni was then Ferdinand I's guardaroba maggiore. The grand Duchess is Cristina di Lorena.
73. G.G. X, 146.
74. G.G. X, 151, December 5, 1605.
75. Asdrubale Barbolani da Montalto, resident at Venice for the grand Duke, wrote to Belisario Vinta (August 12th, 1606: "Mister Galileo Galilei' sconferring has been positively received, as he wished, thanks to Mr Girolamo Capello, who
76. G.G. X, 148, November 5, 1605.
77. G. G. X, 214, June 11, 1608.
78. In the letter to Vinta mentioned in note 17, a few ready works are mentioned by Galileo: I have several leaflets about natural subjects as well, such as De sono et voce, De visu et coloribus, De maris estu, De compositione continui, De animalium motibus and so further.
79. These works' manuscripts are not autograph. Breve Architettura all'Architettura Militare uis a summary of public lessons given by Galileo during his first year in Padua (1592-1593), as Favaro declares whereas Trattato di Fortificazione reports a draft probably written by himself for private teaching. Galileo usually asked a scribe to copy the text of his lessons for the students who were living with him. They were taught fortification as well as the use of the geometrical and military compass, Euclid, mechanics, cosmography, geodesy, arithmetic and the sphere. See: G. G. II, 9. Le Mecaniche was published in 1634, in a (re-organised) translation of Marin Mersenne: Les Méchaniques de Galilée, Mathématicien et Ingénieur du Duc de Florence.
80. We can mention, just as an example: Delle fortificazioni delle città di Girolamo Maggi e del Capitano Iacomo Castriotto, Venice, 1583, and Le fortificazioni di Buonaiuto Lorini, nobile fiorentino, Venice 1597 and 1609.
81. G. G. XIX, 116-117.
82. G. G. X, 369.
83. Sagredo wrote him in December 1612: "it is said that, because of bad air and something else, Your Excellency will go back to Padua againbut, even if I know friends who praise and esteem you, men are disgusted at your departure, because of the conferring of your professorship and most of all because of your behaviour during your departure". G. G: XI, 447.
84. For information on the subject, see the important chapter "Galileo, Sarpi e la Società Veneziana", in G. Gozzi, Paolo Sarpi tra Venezia e l'Europa, Einaudi, Torino 1979.
* tratto da
" IL COMPASSO GEOMETRICO E MILITARE DI GALILEO GALILEI "
Testi, annotazioni e disputa negli scritti di G. Galilei, M. Bernegger
e B. Capra
a cura di Roberto Vergara Caffarelli, Pisa, 1992.