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Preface

to the Liber de triplici motu

Prohemium

Preclara Philonis in libro Sapientie extat sententia deum maximum optimumque rerum omnium natura constantium opificem, cunctorum substantiam atque compaginem numero, mensura, ac pondere procreasse atque disposuisse; cui applaudit illud prophete qui profert numero seculum. Cui etiamt [sic] astipulatur divus ille Plato in Thimeo, magna auctoritate commendans deum numeris mundum fabricasse. Quam sententiam Aurelius Augustinus libro De Civitate Dei commendat. Quapropter intima, secretioraque nature atque minerve penetralia, rerumque omnium naturalium reconditas passiones, ac motus qui numeris consistunt perscrutari atque rimari volentes, arithmeticam atque geometriam aut saltem harum scientiarum quedam requisita documenta necessum est anteponant. Et non abs re quidem, quoniam non solum elementaris hec regio et naturalia illa entia que in ea natura procreanda censuit his numeris et geometricis ponderibus constant, verumetiam ethereus ille celorum globus (ut inquit Plinius et Aristoteles) Pythagore sententia arithmeticis proportionibus, musicisque tonis circumvoluitur. Inquit enim saturnum dorio moveri, mercurium pthogo, iovem phrygio. Quantam videlicet arithmetica scientia habeat ad philosophiam universasque disciplinas, luculentur in libro De Legibus divus Plato ostendit inquiens Legislator civibus omnibus precipiat ne a numerorum ordine quo ad possunt discedant. Nam nulla alia disciplina ad rei familiaris gubernationem, ad rem publicam, ad artes denique universas, tantam habeat vim, quantam huiusmodi numerorum cognitio. Sonnolentos, etiam a natura rudes, excitat, et dociles, memores, solertesque facit, preter naturam suam divina arte proficientes. Inconcussa enim et inviolata est arithmetice atque geometrie scientia, cuius veritati sacratissime sanctiones auctoritatem prebent inquientes arithmeticam et geometriam in se veritatem continere et quamvis pietatis scientie non sint, sunt tamen maximo adminculo atque adiumento ipsi scientie pietatis ut preclare Aurelius ille Augustinus in libro De Doctrina Christiana sacris comprobat rationibus. Has enim sapiens ille Salomon dicit pedissequas, atque ancillas theologie, quas iubet vocari ad turrim, et ad menia civitatis. His enim prostergatis, qui ad theologisandum et philosophandum progreditur (si divo Severino Boetio credimus) superflue conatur. Ad philosophiam utique temere his mathemathicis omissis documentis accedentes, philosophia ipsa sacrilegos, suique numinis invasores vestem suam in frustra lacerantes (teste Boetio) appellat. Et ut verum fatear hinc est quod nostris temporibus ob harum disciplinarum defectum balbutiens atque concutiens visa est philosophia. Plurimum enim apud Grecos philosophia valuit primatumque obtinuit, quia (ut inquit Cicero) in summo honore apud illos geometria fuit nihilque apud eos mathematicis illustrius. Non immerito igitur speculationibus physicis triplicis motus tractaculum proportionum ex mathematicis codicibus depromptum duximus preponendum et quantum ingenioli nostri vires suppetunt absolvendum.[The transcription was made using the copy at the Biblioteca Nacional de Portugal, Lisbon. Typographic abbreviations were spelled out.]

[The translation is our own, it is still under construction – you are welcome to help!]

Foreword

There is a very famous sentence in Philo’s Liber Sapientiae saying that the highest and best God, the creator of all things existing in nature, had engendered and distributed the substance and fastenings of all [things] according to number, measure and weight; to which abides that prophet [saying] he who brings out the world by number. Divine Plato in the Thimaeus supports him, by asserting with great authority that God had made the world using numbers. To this very sentence points Aurelius Agustinus in the book De Civitate Dei. Hence for those who want to thoroughly scrutinize and probe the most secret and the innermost [aspects] of nature and science, and the hidden changes and movements of all natural things that are based on numbers, it is indispensable that they put first arithmetic and geometry, or at least some of those sciences required for the purpose. And this is certainly not beside the point, because not only this elemental region and those natural beings, which it counts in this reproducing Nature, consist of these numbers and geometric weights, but after a sentence by Pythagoras (as say Pliny and Aristotle) also the aetherial globe of the heavens revolves according to arithmetic ratios and musical tones. Actually he says that Saturn moves according to dorian mode, Mercury to the [pactolian=lydian?], and Jupiter according to the phrygian mode. How much arithmetic has to do with philosophy and all the disciplines, divine Plato has brilliantly shown in the book De Legibus, speaking as a law-maker, he warns all citizens not to depart from the order of the numbers as long as they can. In fact no other discipline [he says] has so much force, as does the knowledge of this kind of numbers, when it comes to direct family affairs, public affairs, and finally all the arts. It wakes up the dozing and even those disposed to be rude, and makes them, by divine art, docile, mindful and eager, and proficient beyond their character. Indeed, the science of arithmetic and geometry is invincible and inviolable, and its truth lends the holiest sanctions to the authority by saying that arithmetic and geometry contain truth in themselves although they are no sciences of piety, they are nevertheless of the greatest support and help to the sciences of piety as Aurelius Augustinus famously confirms by holy proofs in the book De Doctrina Christiana. Wise Salomon calls them handmaiden, also maid servants, whom he commands to be called to the tower and to the walls of the city. When these are erased[?], it is superfluous for someone to make any effort to advance working in theology or philosophy (if we believe divine Severinus Boetius). Certainly, those who blindly approach philosophy while omitting these mathematical instructions, Philosophy herself calls sacrilegious, and invaders of her divinity who tear up in vain her garment (as Boetius attests). And to say the truth, hence comes that in our times philosophy appears stammering and also agitating for lack of those [mathematical] disciplines. Among the Greeks, philosophy was worth more, and had got primacy, because (as says Cicero) among them, geometry stood in the highest honour, and nothing was more distinguished for them than mathematical [things]. Therefore it is with good reason that we have drawn up a small treatise on proportions extracted from mathematical manuscripts to precede the physical speculations about the threefold movement and to do as much the forces of our modest mind are capable of. […]

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