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This is the second volume of the first fully-fledged English translation of the works of Archimedes - antiquity's greatest scientist and one of the most important scientific figures in history. It covers On Spirals and is based on a reconsideration of the Greek text and diagrams, now made possible through new discoveries from the Archimedes Palimpsest. On Spirals is one of Archimedes' most dazzling geometrical tours de force, suggesting a manner of 'squaring the circle' and, along the way, introducing the attractive geometrical object of the spiral. The form of argument, no less than the results themselves, is striking, and Reviel Netz contributes extensive and insightful comments that focus on Archimedes' scientific style, making this volume indispensable for scholars of classics and the history of science, and of great interest for the scientists and mathematicians of today.
This book offers a resolution of the paradox posed by the pleasure of tragedy by returning to its earliest articulations in archaic Greek poetry and its subsequent emergence as a philosophical problem in Plato's Republic. Socrates' claim that tragic poetry satisfies our 'hunger for tears' hearkens back to archaic conceptions of both poetry and mourning that suggest a common source of pleasure in the human appetite for heightened forms of emotional distress. By unearthing a psychosomatic model of aesthetic engagement implicit in archaic poetry and philosophically elaborated by Plato, this volume not only sheds new light on the Republic's notorious indictment of poetry, but also identifies rationally and ethically disinterested sources of value in our pursuit of aesthetic states. In doing so the book resolves an intractable paradox in aesthetic theory and human psychology: the appeal of painful emotions.
Cicero's On the Commonwealth (De re publica) and On the Laws (De legibus) represent the most significant surviving contribution to political thought in the 700+ years between the death of Aristotle and Augustine's City of God. They are ambitious and complex works, difficult to interpret not merely because so little survives of the Hellenistic philosophy on which Cicero drew, but also because we possess only parts of them: On the Commonwealth is fragmentary, and perhaps a third of it is still extant, while On the Laws not only survives only in part (three books out of at least five), but was apparently left unfinished at Cicero's death. The goal of this Introduction is to offer some background for reading these texts and some explanation of their form, structure, and arguments.
Cicero's Public Career
Early in December 63 BCE, the consul Marcus Tullius Cicero, having unmasked the conspiracy of Catiline and supervised the execution of several of the leading conspirators, was hailed as Father of his Country and escorted home by a crowd of grateful Romans from all ranks of society; a public thanksgiving was decreed in his honor, the first such award ever made for non-military service to the state. That moment was the summit of a remarkable career: not only had Cicero's consulate been distinguished by signal success and acclaim, but the very fact that he had achieved that office – the chief magistracy in republican Rome – and had done so at the earliest legal age of forty-two was itself unusual. Cicero was born in 106 BCE in the town of Arpinum, some 115 km southeast of Rome. The town had had Roman citizenship since 188, and Cicero's family were among its leading citizens; however, not one of them had ever held public office at Rome. Cicero's family did have strong connections among the Roman aristocracy, though, and he came to Rome very early (before the age of fifteen) to learn the ways of politics and law under the guidance of the leading orator (Lucius Licinius Crassus) and jurists (Quintus Mucius Scaevola the Augur and his cousin Quintus Mucius Scaevola the Pontifex) of the 90s and 80s. Cicero began his career as an advocate at the end of Sulla's dictatorship, and he first held public office as quaestor in 75.
Augustine, City of God 2.21: The discussion of this topic was put off to the next day, when it was the subject of a heated debate in Book 3. Philus himself presented the argument of those who believe that the conduct of public affairs is impossible without injustice, making a strong plea not to be taken to believe this himself. He argued conscientiously on behalf of injustice against justice as if he were trying to prove, by plausible arguments and examples, that the former is useful to the state, while the latter is useless. Then Laelius at the request of everyone took up the defense of justice and asserted as strongly as he could that nothing is so dangerous to a state as injustice and that in fact a state cannot exist or be maintained without a high degree of justice.
When this subject had been discussed to everyone's satisfaction, Scipio returned to the previous topic; he recalled and commended his brief definition of the commonwealth, in which he had said that it was the concern of the people, and that the people was not any large assemblage, but an assemblage associated with one another by agreement on law and community of interest. He then showed how useful definitions are in argument, and from these definitions of his he drew the conclusion that a commonwealth (that is the concern of the people) then truly exists, when its affairs are conducted well and justly, whether by a single king, or by a few aristocrats, or by the people as a whole. But when there is an unjust king (whom in the manner of the Greeks he called a tyrant), or unjust aristocrats (whose conspiracy he called a faction), or when the people itself is unjust – and here he was not able to find any familiar name other than to call the people itself a tyrant – then there is not a flawed commonwealth, as had been argued on the previous day, but (the logical conclusion from his definitions) no commonwealth at all: there is no “concern of the people” when a tyrant or a faction has seized hold of it, nor is the people itself still a people if it is unjust, because it is no longer a multitude associated with one another by agreement on law and community of interest, as the people had been defined.
MARCUS: Then I'll continue to follow that divine man; I may praise him more often than I need to because of the admiration for him which moves me.
ATTICUS: You mean Plato, I suppose.
MARCUS: He's the one, Atticus.
ATTICUS: You could never praise him too much or too often. Even my own people, who never want anyone except their own founder to be praised, permit me to esteem him at my own discretion.
MARCUS: A good decision on their part. What could be more worthy of your own refinement? Your life and language appear to me to have achieved a combination of seriousness and humaneness, something that's extremely difficult.
ATTICUS: I'm very glad to have interrupted you, since you've given me such a grand statement of your opinion. But go on.
MARCUS: Then shall we start by praising the law in accordance with the true praise appropriate to its kind?
ATTICUS: Yes, just as you did with the religious law.
MARCUS: You see, then, that this is the power of the magistrate, that he be in charge and ordain behavior that is right and useful and in accordance with the laws. Just as the laws are in charge of the magistrates, so the magistrates are in charge of the people; it can truly be said that a magistrate is a law that speaks, and a law is a silent magistrate. There is nothing so consonant with the justice and structure of nature – and when I say that, I want you to understand that I'm speaking of the law – as the power of command, without which no home or state or nation or the whole race of mankind can survive, nor can nature as a whole or the world itself. The world obeys god, and land and sea obey the world, and human life follows the commands of the supreme law. And to come to things closer and more familiar to us: all early peoples once obeyed kings. This type of power was first offered to the most just and wise men (as was particularly true of our own commonwealth, so long as monarchic power was in charge), and then it was handed on in turn to their descendants, a custom which remains in effect among contemporary monarchies.