Archimedes gave geometrical demonstrations to find the volume of a sphere and the ellipsoids of revolution in totally different ways, although both lead to the same integral,∫[2a,0]x (2a — x)dx. Nicolas Bourbaki -a group of French mathematicians-state their views on why Archimedes had no concept of integral calculus as follows: "Might it not be that Archimedes regarded such a standpoint as extreme 'abstraction,'and dared to concentrate on studying characteristic properties of each figure he was working on ?" Certainly there is something in what Nicolas Bourbaki say. However, their views do not answer fully the question To the solution of this difficult problem, in my opinion, an important clue can be found by considering Archimedes' scholastic career in chronological order. It was not until Archimedes wrote On Spirals in his late forties or early fifties that he could work out the summing of the series 1²+2²+…n². In his later work On Conoids and Spheroids Archimedes could obtain for the first time the sum of a series ∑Xk(2a—Xk), necessary to give geometrical proofs about the volume of the ellipsoids of revolution However,it was difficult for Archimedes,in writing On the Sphere and Cylinder I, to obtain the sum. Therefore, he proved the theorem about the volume of a sphere in a way not making use of such summation When the same integral appeared, Archimedes could not notice the internal connection unifying them. This may be because, for one thing, he excluded from geometry, due to their mechanical nature, the discussions using indivisibles found in The Method which could have been a clue toward noticing the internal connection. Secondly, obtaining the sum of a series was not a simple matter to Archimedes who lacked the necessary algebraic symbols.

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There have been several influential controversies in classical studies since the beginning of the twentieth century, and assuredly one of them is the problem of the origin of Greek drama. The purpose of this paper is to reconsider the problem of the origin of Roman drama as contrasted with that of Greek drama.

It is a well-known fact that Jane Ellen Harrison's Prolegomena to the Study of Greek Religion published in 1903 caused much controversy. She maintained that the origin of Greek drama consisted in the Dionysiac ritual, and Gilbert Murray and F. M. Conrnford supported her theory. The theory of these scholars called the Cambridge Ritualists was refuted thoroughly by Sir Arthur Pichard-Cambridge and has been considered untrustworthy in classical studies, whereas it is still exercising a great influence on theater research.

In contrast, the origin of Roman drama has rarely been discussed. The materials which tell the origin are restricted. The most important one is found in Livy's History, in which several primitive dramatic performances are described, but none of these performances seems to have underlain the Roman drama. Roman drama did not evolve undergoing various stages, but it just began in 240 B. C. when the Greek dramas were translated into Latin and performed.

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Diodorus' accounts of the Sicilian Slave Wars have been a source ofcontroversies This paper deals with two particular problems among them the blaming of C Gracchus' equestrian jury in the aetiology of the First War, a notorious anachronism that has vexed scholarship since Mommsen, and the accusation against 'Italian' landowners as having encouraged the highway robbery by their slaves, but whose presence in any large number on Sicilian soil at this period is not much attested by other evidence Some scholars maintain that these passages go back to Posidonius, whose contribution, to whatever extent, as a source to the Diodoran narrative of the First War is beyond doubt I shall below present some likeliest routes for the transmission of the information that has caused these problems 1) Roman Sources The ubiquitous criticisms of Roman magistrates in the narrative smack of narrow partisan hostility within the ruling oligarchy, and it has been suggested that our difficulties result from Posidonius' use of a Roman source coloured by conservative pique against the knights Among Posidonius' Panaetian connexions the most important was P Rutilius Rufus, whose semi-autobiographical history in Greek was certainly one of Posidonius' sources, and whose sorry experience at the repetundae trial in 92 might well suggest a Rutilian origin of the troublesome passages Yet evidence reveals Rutilius' attentiveness to the niceties of law, and his work, like other Republican memoirs, was written primarily for his own political apologia Thus I doubt that this Roman Stoic dared jeopardise the whole credibility of his apologia by a trifling distortion of the history of the extortion court Furthermore, if we allow for an interpreter, Posidonius' potential Roman sources need not be restricted to works written in Greek The annals of Fannius, if the historian is to be identified with C Fannius M f, yet another disciple of Panaetius and the anti-Gracchan consul in 122, are a strong possibility Another candidate would be Sempronius Asellio, who, like Rutilius and Posidonius, belonged to the same Polybian school of history and whose kinsman Diodorus alone in ancient traditions praises for his governorship of Sicily immediately after the Second War 2) Posidonius' Narrative Pattern Many scholars have perceived a structural and thematic parallelism between the accounts of the two wars One school of thought further stretches this deductive tendency of Posidonius the Philosopher-Historian into a strictly formulated 'narrative pattern', claiming that the philosopher, for want of information, retrojected the conditions in Sicily around the time of the Second War, or those in Southern Italy at the time of the Spartacus War, to the island of the 130s, and that in this process he 'reduplicated' an equestrian/Italian involvement in the First War Yet in my view the whole idea of a narrative pattern stands on far too many unattested premises, and hence to attribute our particular problems to this nebulous paradigm risks circularity In fact the similarities between the two Diodoran accounts are no more striking than the obvious differences This fact suggests that the author had fairly detailed knowledge of each war, thus rendering it unlikely that he, simply out of horror vacui, made up part of the account of one war on the analogy of another 3) Local Sources These details include 'folkloric' anecdotes, which all concern Sicehot Greeks, and without doubt go back to the same community But how did they find their way into the current text? Posidonius' famous trip to the West may have included an investigative sojourn in Sicily, but Diodorus himself was a Sicilian, born in a town only a few tens of miles away from the epicentres of both wars within thirty years after the Second War Thus he would have been as well placed as Posidonius to draw

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The aim of this article is to put forward a new historical interpretation of the Second Macedonian War, by focusing on Roman diplomatic efforts toward the Hellenistic States before the outbreak of the War in the late fall of 200 B.C.E.. As a consequence of the First Macedonian War, Rome had become diplomatically isolated, and Macedonia had secured dominance over the Hellenistic States as a result of the Phoenice Treaty of 205 B.C.E.. However, immediately after the conclusion of the Second Punic War of 201 B.C.E., Rome decided to embark upon a new campaign against Macedonia. In the context of the lengthy Second Punic War severely exhausting Rome and dampening the will for war among the Roman people to an unprecedented low, the deployment of troops in the autumn of 200 B.C.E., even against the backdrop of various diplomatic events, stands out as peculiar. In trying to explain this march to war, researchers to date have cited a heightened sense of crisis in Rome brought on by rumors of an alleged secret pact between Macedonia and Syria to divide Egypt. In response to these interpretations, the author of this article examines the circumstances and preparations made in Rome leading up to the deployment of troops, Rome's actions towards the Hellenistic States up until that time, and the state of affairs prior to the war with Greece and Asia Minor, including Roman allies, Rhodes and Pergamum. Through this analysis, the author concludes that ultimately, the Second Macedonian War was neither a preemptive strike meant to counter any secret pact, nor a war of defense. Rather, in its deployment of troops against Macedonia, Rome was responding to the changing situation in Greece and saw a unique opportunity to seek revenge.

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