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A New Edition of the Metrica of Heron of Alexandria JENS HØYRUP A NEW EDITION OF THE METRICA OF HERON OF ALEXANDRIA ESTRATTO da PHYSIS Rivista Internazionale di Storia della Scienza 2018/1-2 ~ a. 53 ISSN 0031-9414 Vol. LIII (2018) Nuova Serie Fasc. 1-2 INDICE G. Cimino, La seconda serie di «Physis» (1991-2018): un breve rapporto/ * The second series of «Physis» (1991-2018): a short report........... pag. 1 M. Di Giandomenico, Cinquant’anni del Seminario di Storia della Scien- PHYSIS za dell’Ateneo barese (1967-2017) ............................. » 23 RIVISTA INTERNAZIONALE DI STORIA DELLA SCIENZA Studi e ricerche 1-2 Fasc. A. Ciocci, Le proporzioni e il moto dei corpi: l’eco della scuola francesca- * na di Oxford in tre problemi di cinematica della Summa di Pacioli ... » 37 F.A. Meschini, Esitazioni cartesiane: embriologia e anti-finalismo ...... » 59 F. Baldassarri, I moti circolari nella meccanica della vita in Descartes: embriologia e nutrizione nella medicina e nella botanica .......... » 77 E. Giannetto, Pascal’s Physics, Mathematics and Cosmology........... » 95 G. Pareti, L’impegnativa eredità della metafisica del calcolo infinitesimale » 111 S. Veneroni, Osservazioni fisico-teoriche attorno al primo scritto di Kant sulle forze vive del 1746 (1749)................................ » 143 E. Luciano, I contributi di Giovanni Vacca alla storia della logica matema- tica fra erudizione e critica storiografica........................ » 175 A. Volpone, Paolo Della Valle ed Edmund B. Wilson sulla natura dei cro- mosomi: concezioni a confronto.............................. » 201 E. Cicciola, Scienza e massoneria: storia e storiografia ............... » 221 Serie LIII (2018) Nuova Vol. N. Allocca, E. De Caroli, Introspezione e metodi psicologici. Il contri- buto di Francesco De Sarlo in «Psiche» ......................... » 251 * S. Degni, Il contributo di Renata Calabresi allo studio sperimentale del ‘presente psichico’.......................................... » 281 R. Passione, Psichiatria e condizione umana: il contributo di Silvano Arieti » 309 A. Molaro, Il corpo e l’istituzione: Franco Basaglia dalla fenomenologia alla psichiatria radicale ...................................... » 331 PHYSIS PHYSIS Note e discussioni * M.A. Rancadore, La parola chiave «infinito» nello studio della natura svi- luppato dai presocratici ..................................... » 361 C. Genna, Il concetto di infinito nel contesto del ‘Rinascimento scientifico’ » 371 R. Cesareo, Il progetto dei servizi segreti americani di assassinare Werner Heisenberg ............................................... » 381 Essay Reviews J. Høyrup, A New Edition of the Metrica of Heron of Alexandria......... » 391 LEO S. OLSCHKI EDITORE M. Innamorati, Recenti edizioni italiane di opere di Carl Gustav Jung... » 411 FIRENZE PHYSIS RIVISTA INTERNAZIONALE DI STORIA DELLA SCIENZA Vol. LIII Nuova Serie 2018 LEO S. OLSCHKI EDITORE FIRENZE PHYSIS RIVISTA INTERNAZIONALE DI STORIA DELLA SCIENZA pubblicata dalla domus galilæana di pisa in collaborazione con società italiana di storia della scienza seminario di storia della scienza dell’università di bari DIREZIONE E REDAZIONE (EDITORS) Direttore responsabile (Senior Editor): Vincenzo Cappelletti. Direttore (Editor): Guido Cimino. Comitato direttivo (Editorial Board): Nino Dazzi, Mauro Di Giandomenico, Paolo Fre- guglia, Carlo Maccagni, Giuliano Pancaldi, Raffaella Simili. Responsabile delle recensioni (Book Reviews Editor): Antonino Trizzino. Redazione (Editorial Office): Silvia Degni, Antonino Trizzino. CONSIGLIO SCIENTIFICO (ADVISORY EDITORS) Evandro Agazzi, Giulio Barsanti, Enrico Berti, Jed Buchwald, Paolo Casini, Catherine Chevalley, Salvo D’Agostino, Jean Dhombres, François Duchesneau, Dietrich von Engelhardt, Paolo Galluzzi, Enrico Giusti, Robert Halleux, John L. Heilbron, Eberhard Knobloch, Sandra Linguerri, Geoffrey Lloyd, Renato Mazzolini, Luigi Pepe, Marcello Pera, William R. Shea, Maurizio Torrini. Direzione: Domus Galilaeana - via S. Maria 26 - 56100 Pisa - Tel. +39.050.23726 Redazione: Dipartimento di Psicologia dei Processi di Sviluppo e Socializzazione - Università di Roma «La Sapienza» - Via dei Marsi, 78 - 00185 Roma - Italy e-mail: [email protected] Ogni articolo è sottoposto alla valutazione anonima di due esperti. Each article is submitted to a double-blind scholarly peer review. SOMMARIO G. Cimino, La seconda serie di «Physis» (1991-2018): un breve rapporto/The second series of «Physis» (1991-2018): a short report ............................................. pag. 1 M. Di Giandomenico, Cinquant’anni del Seminario di Storia del- la Scienza dell’Ateneo barese (1967-2017) ................ » 23 Studi e ricerche A. Ciocci, Le proporzioni e il moto dei corpi: l’eco della scuo- la francescana di Oxford in tre problemi di cinematica della Summa di Pacioli .................................... » 37 F.A. Meschini, Esitazioni cartesiane: embriologia e anti-finalismo » 59 F. Baldassarri, I moti circolari nella meccanica della vita in Des- cartes: embriologia e nutrizione nella medicina e nella bota- nica ............................................... » 77 E. Giannetto, Pascal’s Physics, Mathematics and Cosmology ... » 95 G. Pareti, L’impegnativa eredità della metafisica del calcolo infi- nitesimale .......................................... » 111 S. Veneroni, Osservazioni fisico-teoriche attorno al primo scrit- to di Kant sulle forze vive del 1746 (1749) ................ » 143 E. Luciano, I contributi di Giovanni Vacca alla storia della logica matematica fra erudizione e critica storiografica .......... » 175 A. Volpone, Paolo Della Valle ed Edmund B. Wilson sulla natura dei cromosomi: concezioni a confronto ................. » 201 E. Cicciola, Scienza e massoneria: storia e storiografia ........ » 221 N. Allocca, E. De Caroli, Introspezione e metodi psicologici. Il contributo di Francesco De Sarlo in «Psiche» ............ » 251 VI SOMMARIO S. Degni, Il contributo di Renata Calabresi allo studio sperimen- tale del ‘presente psichico’ ............................. pag. 281 R. Passione, Psichiatria e condizione umana: il contributo di Sil- vano Arieti ......................................... » 309 A. Molaro, Il corpo e l’istituzione: Franco Basaglia dalla feno- menologia alla psichiatria radicale ...................... » 331 Note e discussioni M.A. Rancadore, La parola chiave «infinito» nello studio della natura sviluppato dai presocratici ....................... » 361 C. Genna, Il concetto di infinito nel contesto del ‘Rinascimento scientifico’ .......................................... » 371 R. Cesareo, Il progetto dei servizi segreti americani di assassina- re Werner Heisenberg ................................ » 381 Essay Reviews J. Høyrup, A New Edition of the Metrica of Heron of Alexandria » 391 M. Innamorati, Recenti edizioni italiane di opere di Carl Gustav Jung ............................................... » 411 Recensioni M.J. Ratcliff, Genèse d’une découverte. La division des infusoires: 1765-1766 (M.T. Monti) ‒ R. Rashed, Fermat et les débuts mo- dernes de la géométrie (P. Freguglia) ‒ A. Becchi, Arlecchino e il microscopio. Saggio sulla filosofia naturale di Leibniz (O. Ottavia- ni) ‒ G. Cosmacini, La medicina dei papi (E. Giora) ‒ A. Civita, Psicoanalisi e psichiatria: storia ed epistemologia (M. Fornaro) .. » 429 ESSAY REVIEWS A NEW EDITION OF THE METRICA OF HERON OF ALEXANDRIA * Jens Høyrup ** Roskilde University – Denmark Quoting a letter to the Emperor from February 1865,1 Emmanuel Miller an- nounced in 1868 2 to have been shown in the library of the Old Serail of Constan- tinople “a very beautiful manuscript from the 11th century, containing the writings of Heron of Alexandria,” which it “would be very important to compare with an edition of this famous mathematician, and in particular with the excellent mem- oir of M. Henri Martin, of Rennes, about the writers that have carried the name of Heron.”3 The Old Serail library was not easily accessible – visit to the Serail was grant- ed to foreign ambassadors taking their leave and normally to nobody else.4 A few years after Miller’s announcement, however, Anton Dethir, director of the Impe- rial Ottoman Museum, included a (fairly complete) list of the titles contained in the same manuscript in an inventory of such manuscripts as had already seen by foreign scholars – ascribing it now to the 12th century.5 Then, in 1887, Friedrich Blass was admitted, and in the next year 6 he first said about the manuscript in * Essay review of Fabio Acerbi, Bernard Vitrac (eds., trans.), Héron d’Alexandrie, Metrica, Pisa-Roma, Fabrizio Serra, 2014. ** Jens Høyrup, Section for Philosophy and Science Studies, Roskilde University, Box 260, DK-4000 Roskilde, Denmark ‒ [email protected]. 1 Published according to Miller (p. I, n. 1) in Le Moniteur (probably Le Moniteur Universel), 13 March 1865. 2 Miller, 1868, p. v. 3 That is, Martin, 1854. My translation into English, as everywhere in the following where nothing else is stated. 4 Abel, 1878, p. 564. 5 Ibid., p. 565. 6 Blass, 1888, pp. 220, 222. 392 JENS HØYRUP question that it contains “The Geometry of Euclid – Heron of Alexandria on Mea- sures,” dating it again to the 12th century; next he quoted Dethir’s more complete description via Abel. Only Richard Schöne was competent and interested enough in such matters to discover in 1896 that the manuscript contains Heron’s Metrica, so far only known from a reference in Eutocios and from a fragment which Paul Tannery had identified in 1894.7 In 1903, finally, Hermann Schöne (son of Rich- ard) published the first critical
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  • Hipparchus's Table of Chords
    ApPENDIX 1 Hipparchus's Table of Chords The construction of this table is based on the facts that the chords of 60° and 90° are known, that starting from chd 8 we can calculate chd(180° - 8) as shown by Figure Al.1, and that from chd S we can calculate chd ~8. The calculation of chd is goes as follows; see Figure Al.2. Let the angle AOB be 8. Place F so that CF = CB, place D so that DOA = i8, and place E so that DE is perpendicular to AC. Then ACD = iAOD = iBOD = DCB making the triangles BCD and DCF congruent. Therefore DF = BD = DA, and so EA = iAF. But CF = CB = chd(180° - 8), so we can calculate CF, which gives us AF and EA. Triangles AED and ADC are similar; therefore ADIAE = ACIDA, which implies that AD2 = AE·AC and enables us to calculate AD. AD is chd i8. We can now find the chords of 30°, 15°, 7~0, 45°, and 22~0. This gives us the chords of 150°, 165°, etc., and eventually we have the chords of all R P chord 8 = PQ, C chord (180 - 8) = QR, QR2 = PR2 _ PQ2. FIGURE A1.l. 235 236 Appendix 1. Hipparchus's Table of Chords Ci"=:...-----""----...........~A FIGURE A1.2. multiples of 71°. The table starts: 2210 10 8 2 30° 45° 522 chd 8 1,341 1,779 2,631 3,041 We find the chords of angles not listed and angles whose chords are not listed by linear interpolation. For example, the angle whose chord is 2,852 is ( 2,852 - 2,631 1)0 .
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