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ALEXANDER THE GREAT (356-323 B.C.)

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Although the ancient Hindu mathematician Apastambha had achieveda good approximation for √2, and the ancient Babyloniansan ever better √2, neither of these ancientcultures achieved a approximation as good as Egypt's,or better than π ≈ 25/8, until the Alexandrian era.

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Resistance to Alexander. On a superficial view, Alexander’s conquest of the Achaemenid empire was made possible by his victories at the Granicos, Issos, and Gaugamela, but overemphasizing their importance has led to underestimating the strength and tenacity of the resistance organized or inspired by the Achaemenid authorities. Military defeat was not followed by an immediate collapse of the empire and a rapid, painless Macedonian takeover. After the battle of the Granicos, Alexander encountered many obstacles, such as the long resistance of the defenders of Halicarnassos in Caria. His advance from Issos to Egypt was far from easy; Tyre defied him for seven months, and Gaza under the eunuch Batis for several weeks. Nor was the problem solved by the victory of Gaugamela and the occupation of the empire’s three great centers. Darius was still alive and ready to fight at the head of a new army. His assassination in July, 330, by east Iranian conspirators (Bessos, Nabarzanes, Barsaentes, Satibarzanes, Oxyarthes) marked the end of the Achaemenid dynasty but not the end of the Iranian resistance. At first this was led by Bessos, the satrap of Bactria. After Alexander’s invasion of Bactria and capture of Bessos, the struggle in Bactria and Sogdiana was kept up by Spitamenes and broadened into a general revolt. This was particularly dangerous because the Bactrian and Sogdian nobles were determined to maintain at all costs the privileged socio-political status that they had enjoyed under the Achaemenid regime, and were well provided with military, financial, and manpower resources (Briant, in Klio, 1978, pp. 70-77; idem, Index 8, 1978-79, pp. 70-72). Furthermore both Bessos and Spitamenes could, for the time at least, count on long-standing alliances with the chiefs of the Sacae beyond the Syr Darya (Briant, Etat et pasteurs au Moyen-Orient ancien, Paris and Cambridge, 1982). The virtual parity of the opposing forces explains why Darius’s death in Hyrcania was followed by three years of heavy fighting before Alexander could leave Bactria by the Kabul valley route for India. To overcome the resistance, he had to modify his tactics and logistic arrangements, nor did he shrink from indiscriminate terror to coerce the nobles into early transfer of allegiance. The strength and duration of the resistance also account for certain steps which Alexander took before his departure to India. He settled thousands of Greco-Macedonian military colonists in dozens of garrisons, citadels, and new towns under the direct authority of the provincial administration, thereby putting an end to the socio-political dominance of the Sogdo-Bactrian nobility (Briant, in Klio, 1978, pp. 70-78). According to Diodorus Siculus, there were 23,000 colonists in Bactria and Sogdia in 324-23. In order to safeguard his rear Alexander ordered a levy from all the provinces of 30,000 youths who were to serve him both as soldiers and as hostages (Quintus Curtius 8.5.1).

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Of this Heaviside said,"Should I refuse a good dinner simply because I do notunderstand the process of digestion?"

Sofia Kovalevskaya (aka Sonya Kowalevski;née Korvin-Krukovskaya)was initially self-taught, sought out Weierstrass as her teacher,and was later considered the greatest female mathematician ever(before Emmy Noether).

The main Macedonian army disembarked in Asia Minor in 334. A Macedonian force sent in 336 was still holding the town of Abydos on the Hellespont in 334, while Darius had not yet fully mobilized the royal army against a danger which the Achaemenid authorities must have somewhat underrated. The foolish tactics of the Persian satraps on the Granicos river in May, 334, gave Alexander a quick victory in his first pitched battle and a clear road to the Anatolian coast. Now he declared his intention to conquer Asia completely and permanently (Diodorus Siculus, Library of History 18.17.2). From 334 onward Alexander had in view the whole extent of the empire as it had been in Darius I’s time, a fact that is confirmed by his correspondence with Darius in the years 333-31 (P. Briant, Alexandre, pp. 136-43). In Anatolia Alexander was able to count on the good will of Greek communities eager to be rid of their Persian-appointed tyrants; within a few months the Anatolian satrapies were “macedonized” while continuing to be administered on Achaemenid lines, which meant that many regions such as Bithynia and Paphlagonia were not in fact subjected to Macedonian rule.

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ALEXANDER THE GREAT (356-323 B.C.). Ascending the throne on the assassination of his father Philip II in 336, Alexander quickly took up Philip’s grand scheme to land an army in Asia and “liberate the Greek cities from the Achaemenid yoke;” but from the first his territorial ambitions appear to have reached beyond the Mediterranean horizon (cf. his questioning of Darius’ ambassadors, Plutarch, Alexander 5.1-3). Alexander lacked neither information nor informants; fugitive satraps had found asylum at the Macedonian court, and Macedonian troops had been engaged in Asia Minor since 336. He could also draw on the writings of the Greek historians and travelers, such as Xenophon, Ctesias, and above all Herodotus, in whose work Philip’s court historians had evidently taken great interest (G. Murray, Classical Quarterly 22/2, 1972, pp. 200-13).

It is the life of Alexander the king … that I am writing in this book, and the multitude of the deeds to be treated is so great that I shall make no other preface than to entreat my readers, in case I do not tell of all his famous actions, nor even speak exhaustively at all in each particular case, but in example for the most part, not to complain.
For it is not Histories that I am writing, but Lives; and in the most illustrious deeds there is not always a manifestation of virtue or vice, nay, a slight thing like a phrase or a jest often makes a greater revelation of character than battles where thousands fall, or the greatest armaments, or sieges of cities.
Accordingly, just as painters get the likenesses in their portraits from the face and the expression of the eyes, wherein the character shows itself, but make very little account of the other parts of the body, so I must be permitted to devote myself rather to the signs of the soul in men, and by means of these to portray the life of each, leaving to others the description of their great contests.

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