|Guidobaldo del Monte Mechanicorum liber 1969, tr. Stillman Drake|
With the help of mechanics, too, those who work with wood, stone and marble, wines, oils and unguents, iron, gold, and other metals, as well as surgeons, barbers, bakers, tailors, and all workers in the useful arts, make many important contributions to human life.
And as for certain recent manipulators of words who deprecate mechanics, let them go and wipe away their shame, if they have any, and stop falsely charging [mechanics with] lack of nobility and lack of usefulness. If they still do not wish to do so, let us leave them, I say, in their ignorance; and let us rather follow Aristotle, the leader of the philosophers, whose burning love for mechanics is sufficiently proved by the acute Questions of Mechanics which he gave to posterity. In this achievement he greatly surpassed Plato. For, when Archytas and Eudoxus were keenly exploring the usefulness of mechanics, Plato (as Plutarch tells us) discouraged them from this course, on the ground that they were revealing to the masses and making public the noblest possession of philosophers and betraying, as it were, the secret mysteries of philosophy. But surely, at least in my judgment, such a view [that is, Plato's] is to be completely rejected, unless perhaps we wish to praise the detached contemplation of so noble a subject yet to impugn the fruits, the usefulness, and the goal of the art.
But in comparison with all other mathematicians Archimedes alone is to be praised most eloquently, for God willed that in mechanics he should be a unique ideal which all students of that subject might keep before them as a model for imitation. For he made a model of the universe all enclosed in a quite small and fragile glass sphere, with stars that imitated the actual work of nature and so accurately exhibited the laws of the heavens by their precise motions that the hand that rivaled nature deserved the following encomium: "So does his hand imitate nature that nature herself is thought to have imitated his hand." Archimedes, with the help of a block and tackle, pulled a load of 5000 pecks with one hand. Alone with his machines he pulled a heavily loaded ship onto the shore and then pulled it toward himself as if it were being moved in the sea by oars or sails. And then he pulled it from the shore back into the sea (something that all the [human] strength of Sicily could not have accomplished). His too are those engines of war with which Syracuse was so defended against Marcellus that the operator of those engines was always called a hundred-handed Briareus by the Romans. Finally, relying on this art he made so bold as to give utterance to a statement in such [apparent] conflict with the laws of nature: "Give me a place to stand, and I shall move the earth. " And not only do we show in the present book that this could have been done with a lever, but, in fact, all antiquity seems to me to have been completely convinced of this (though possibly this will appear remarkable to many). For antiquity attributed to Neptune a trident, like a lever; and by virtue of it he is everywhere called Earth-shaker by the poets. Indeed, it is with this in mind that our most celebrated poet introduces Neptune raising the shoals with that device so that they may be visible to the Trojans, "with his trident he raises and opens up the vast shoals".
Other mechanicians were Hero, Ctesibius, and Pappus. And though they did not perhaps reach the pinnacle of mechanics, as did Archimedes, still they had remarkable understanding of the subject of mechanics and were all great men. Indeed this is especially true of Pappus, so that no one could, I believe, blame me for following him as my leader. I have more readily done so for the reason that Pappus does not depart even a nail's breadth from the principles of Archimedes. For I have always wished in this branch of science to follow in the footsteps of Archimedes. And though his thoughts on the subject of mechanics have for some years been widely sought by scholars, still his very learned book On [Plane] Equilibrium is extant; in that book I believe that practically all the teachings of mechanics are gathered together, as in an abundant store. Surely, if the mathematicians of our time had a better knowledge of this book, they would have found that many ideas, which they themselves now declare valid and correct, are there very acutely and properly shaken and overturned. But let them see for themselves. I return to Pappus, who, deeply devoted to a richer application of mathematics and to increasing the profits to be derived from such application, made a thorough and brilliant investigation of the five primary machines, that is, the lever, pulley, wheel and axle, wedge, and screw. And he proved that, in the case of machines, everything that could properly be considered as sharply defined or definitely established was reducible to those machines which [potentially] are capable of unlimited force. I wish that the ravages of time had not caused any loss in the writings of so great a man. For such a thick mist of ignorance would not have covered almost all the earth, nor would there have been such ignorance of the subject of mechanics that men are thought of as leading mathematicians who, by their inept distinctions, remove some difficulties, but not those that are very arduous or obscure.
Thus, there are found some keen mathematicians of our time who assert that mechanics may be considered either mathematically, removed [from physical considerations], or else physically. As if, at any time, mechanics could be considered apart from either geometrical demonstrations or actual motion! Surely when that distinction is made, it seems to me (to deal gently with them) that all they accomplish by putting themselves forth alternately as physicists and as mathematicians is simply that they fall between two stools, as the saying goes. For mechanics can no longer be called mechanics when it is abstracted and separated from machines.
Yet in the midst of that darkness (though there were also some other famous names), Federico Commandino shone like the sun; he, by his many learned studies, not only restored the lost heritage of mathematics, but actually increased and enriched it. For that great man was so endowed with all mathematical talents that Archytas, Eudoxus, Hero, Euclid, Theon, Aristarchus, Diophantus, Theodosius, Ptolemy, Apollonius, Serenus, Pappus, and even Archimedes himself (for his commentaries on Archimedes smell of Archimedes' own lamp) seem to have lived again in him. And, lo, just as he had been suddenly thrust from the darkness and prison of the body (as we believe) into the light and liberty of mathematics, so at the most inopportune time he left mathematics bereft of its fine and noble father and left us so prostrate that we scarcely seem able even by a long discourse to console ourselves for his loss. And yet in his endless concern with the elucidation of other parts of mathematics, he either left mechanics completely untreated or touched on it just casually.