Kaspar Schott on Marin Getaldić’s Promotus Archimedes

Kaspar Schott, prvo rimski urednik Kircherovih izdanja (1652–1655), a potom profesor matematike na isusovačkoj akademiji u Würzburgu (1655–1666), u trima je svojim djelima uputio na Getaldića. Radi dovršetka svojih rukopisa on je na frankfurtskom sajmu knjiga u jesen 1655. godine, u glasovitoga amsterdamskoga izdavača i knjižara Jana Jansona, nabavio dva djela koja je po Kircherovu nalogu ostavio u Rimu, a oba su upućivala na Getaldićeve znanstvene doprinose: Ricciolijev Almagestum novum i Delitiae mathematicae et physicae (1651) Georga Philippa Harsdörffera. U predgovoru svoga prvijenca Mechanica hydraulico-pneumatica (1657) Schott je Getaldića uvrstio u poduži popis pisaca iz hidrostatike i pneumatike: između starijih suvremenika i istaknutih znanstvenika iz sljedećega naraštaja. Osim toga smatrao je da četvorica autora iscrpljuju sadržaj ondašnje hidrostatike: Stevin, Getaldić, Galilei i Giovanni Battista Odierna, ali Getaldića nije izrijekom uvrstio među autore koji uspješno povezuju teoriju s praksom. U svojoj je vlastitoj knjižnici Schott imao djela petorice autora koji su u svojim djelima upućivali na Getaldića: Marina Mersennea, Marija Bettinija, Giovannija Battiste Odierne, Niccolòa Cabea i Georga Philippa Harsdörffera. Njemački je isusovac u svoju Mehaniku uključio poglavlje o Stevinovoj »čudesnoj« hidrostatičkoj vagi, a taj se kontekst ne može smisleno povezati s Getaldićevom vagom i metodologijom vaganja. U svom drugom djelu pod neobičnim naslovima Magia universalis naturae et artis (1657–1658) i Thaumaturgus mathematicus Schott je sustavno izložio osam matematičkih i fizičkih disciplina, a u trećem svesku, koji sadrži treći dio, prikazao je hidrostatiku pod naslovom »Magia hydrostatica«, pri čem je čak jedanaest puta izravno spomenuo Getaldića. Na početku svoje hidrostatike Schott je izrekao deset postulata ili, kako ih je on nazvao, »hipoteza«, a u njihovim se obrazloženjima dvaput pozvao na Getaldića. Uz drugu je hipotezu uputio na Getaldićeve podatke za različite relativne težine tekućina da bi potkrijepio da se tekućine razlikuju po svojoj relativnoj težini, a uz desetu hipotezu upozorio na to da je Getaldić u drugom i trećem stavku svoga Unaprijeđenoga Arhimeda dokazao tvrdnju: čvrsta i tekuća tijela međusobno su razmjerna po težini i obujmu. S pravom je prigovorio Getaldićevim podacima za relativne težine tekućina, »jer tekućine iste vrste nemaju na svim mjestima jednaku težinu«, misleći prije svega na vino i ulje. S druge strane, osobito je pohvalio Getaldićevo tumačenje Vitruvijeva izvješća o Arhimedovu otkriću, čak ga je u rješavanju poteškoća u Vitruvijevu tekstu stavio ispred Galileia, Odierne i Cabea. Njemački je isusovac najopsežnije prikazao Getaldićevu metodu za otkrivanje udjela zlata u Hieronovu zavjetnom vijencu – s pomoću pravila trojnog, pridodavši čak i Getaldićev primjer. U »Magia hydrostatica« (1658) Schott je dakle referirao ili komentirao sve bitne sastavnice Getaldićeve metodologije u Unaprijeđenom Arhimedu: dokaze u prvom, teorijskom dijelu rasprave; podatke u tablicama; dokaze i primjere uz problem Hieronova zavjetnoga vijenca s najznatnijim primjenama. Napokon, u svojoj »potpunoj enciklopediji svih matematičkih disciplina«, što ju je naslovio Cursus mathematicus (1661), Schott je na početku hidrostatike uputio na Getaldića kao na jednoga od triju glavnih pisaca u tom području – uz Arhimeda i Stevina. Skratio je svoja obrazloženja uz drugu i šestu ‘hipotezu’ pa stoga nije spomenuo Getaldića. Ponovio je i prigovor Getaldiću da relativna težina nekih tekućina ovisi o mjestu njihove proizvodnje. Ipak, u usporedbi s »Magia hydrostatica« broj uputnica na Getaldića smanjen je s jednaest na dvije, jer je, protivno očekivanjima, argumentativni sloj, naglašeno prisutan u Magia universalis naturae et artis, posve izostao u Schottovu djelu Cursus mathematicus, uključujući i dokaze.Kaspar Schott, first the editor of Kircher’s works in Rome (1652–1655), and later professor of the Jesuit Academia Herbipolitana in Würzburg (1655–1666), referred to Getaldić in three of his works. In order to complete his manuscripts, at the Frankfurt Book Fair in autumn 1655, from a renowned Amsterdam publisher and bookseller Jan Jansson, he acquired two works which, upon Kircher’s instructions, he left in Rome, both of which were related to Getaldić’s scientific contributions: Riccioli’s Almagestum novum and Delitiae mathematicae et physicae (1651) by Georg Philipp Harsdörffer. In the preface of his first published work Mechanica hydraulico-pneumatica (1657), Schott included Getaldić into a long list of authors in hydrostatics and pneumatics: among older contemporaries (della Porta, Stevin, Galileo, and Benedetto Castelli) and prominent scientists from the next generation (Mersenne, Mario Bettini, and Niccolò Cabeo). Further, in his opinion four authors exhaust the content of contemporary hydrostatics: Stevin, Getaldić, Galileo, and Giovanni Battista Odierna. Yet he did not include Getaldić by name among the authors who successfully combined theory with practice. In his private library Schott had the books of five authors who referred to Getaldić in their works: Marin Mersenne, Mario Bettini, Giovanni Battista Odierna, Niccolò Cabeo, and Georg Philipp Harsdörffer. Into his Mechanics, the German Jesuit included a chapter on Stevin’s »admirable« hydrostatic balance, yet the mentioned context cannot be associated with Getaldić’s balance and the methodology of measuring. Under unusual titles Magia universalis naturae et artis (1657–1658) and Thaumaturgus mathematicus, Schott systematically explicated eight mathematical and physical disciplines, while in the third volume containing the third part he expounded hydrostatics, where he mentioned Getaldić exactly 11 times. At the beginning of his “Magia hydrostatica,” Schott formulated ten postulates or ‘hypotheses,’ as he called them, in which he twice referred to Getaldić. In the second hypothesis he drew attention to Getaldić’s data on different relative weights of liquids in order to prove that liquids differ in relative weight, while in the tenth hypothesis he warned that Getaldić in the second and third propositions of his Promotus Archimedes proved the following: solid and liquid bodies are proportional to each other by weight and volume. He rightly objected to Getaldić’s results on the relative weights of liquids, “because liquids of the same kind do not have equal weight in all places,” having primarily wine and oil in mind. On the other hand, he especially commended Getaldić’s interpretation of Vitruvius’s description of Archimedes’s discovery, whereby in solving difficulties in Vitruvius’s text he placed Getaldić before Galileo, Cabeo, and Odierna. German Jesuit most thoroughly elaborated Getaldić’s method for determining the portion of gold in Hiero’s wreath – with the help of the rule of three, and even added Getaldić’s example. Therefore, in “Magia hydrostatica” (1658) Schott referred to or commented all the essential components of Getaldić’s methodology in his Promotus Archimedes: proofs in the first, theoretical part of the treatise, along with the data in the tables, but also the demonstrations and examples related to the problem of Hiero’s wreath with the most significant applications. Finally, in his “comprehensive encyclopaedia of all mathematical disciplines,” which he entitled Cursus mathematicus (1661), Schott opened his hydrostatics with a reference to Getaldić as one of the three major authors in this field – alongside Archimedes and Stevin. He shortened the explanations of his second and sixth hypothesis, therefore he did not mention Getaldić. He repeated his objection that relative weight of some liquids depended on the place of production. In comparison with “Magia hydrostatica,” the number of references to Getaldić is being reduced from 11 to 2 because, contrary to expectations, the argumentative layer, very extensive in Magia universalis naturae et artis, has been fully omitted in Schott’s Cursus mathematicus, including the proofs