Appian of Alexandria (c.95-c.165): one of the most underestimated of all Greek historians, author of a Roman History in twenty-four books.
Seleucus had served under Alexander the Great and was vizier after his death. In 320, he was made satrap of Babylonia. Although he lost possession of his satrapy between 315 and 311, he grew out to be one of the most powerful monarchs after Alexander.
The Greek historian Appian of Alexandria describes Seleucus' career in several chapters of his History of the Syrian War, which are here quoted in the translation of M.M. Austin.
The career of Seleucus
 After the Persians, Alexander the Great was king of the Syrians, as well as of all the people whom he saw. When he died leaving one very young son and another as yet unborn.note[Alexander's official wife Roxane was pregnant; she became mother of a boy, Alexander IV. His mistress Barsine was mother of a son named Heracles.] the Macedonians, being deeply attached to the family of Philip, chose as their king Arridaeus, Alexander's half-brother, although he was believed to be dim-witted, and changed his name from Arridaeus to Philip.
While the children of Alexander were growing up (they even placed the pregnant mother under guard), his friends divided the peoples of the empire into satrapies, which Perdiccasnote[Perdiccas was regent from 323 to 320.]shared out among them in the name of king Philip Arridaeus.
Not long after, when the kings were put to death, the satraps became kings.note[Philip Arridaeus was executed in 316 by Olympias, the mother of Alexander the Great, who fought for the rights of her son's son Alexander IV (more). In the winter of 312/311, the satraps concluded a treaty and promised to give their powers to the boy king, when he was old enough. Instead, the boy was immediately killed. In 306, the first of the Diadochi, Antigonus Monophthalmus, accepted the royal title, soon followed by the other rulers.] The first satrap of the Syrians was Laomedon of Mytilene, appointed by Perdiccas, and then Antipater, who after Perdiccas was guardian of the kings. Ptolemy, the satrap of Egypt, sailed against Laomedon and sought to bribe him to hand over Syria, which protected Egypt's flank and was a good base to attack Cyprus. He failed and so arrested him, but Laomedon bribed his guards and escaped to Alcetas in Caria. For some time Ptolemy ruled Syria; he sailed back to Egypt after leaving garrisons in the cities.note[In 319-318.]
 Antigonus was satrap of Phrygia, Lycia and Pamphylia, and was appointed overseer of the whole of Asia by Antipaternote[Successor of Perdiccas as regent.] when he returned to Europe. He besieged Eumenes, satrap of Cappadocia, whom the Macedonians had voted an enemy, but Eumenes escaped and seized control of Media. Eventually Antigonus captured Eumenes and put him to death, and on his return was received in great pomp by Seleucus the satrap in Babylonia.note[In the spring of 315.]
One day Seleucus insulted an officer without consulting Antigonus, who was present, and Antigonus out of spite asked for accounts of his money and his possessions; Seleucus, being no match for Antigonus, withdrew to Ptolemy in Egypt. Immediately after his flight, Antigonus deposed Blitor, the governor of Mesopotamia, for letting Seleucus escape, and took over personal control of Babylonia, Mesopotamia and all the peoples from the Medes to the Hellespont (Antipater was dead by now).
With so much territory in his power he became at once an object of jealousy to the other satraps. And so an alliance was formed between Seleucus, the chief instigator of the coalition, Ptolemy, Lysimachus satrap of Thrace, and Cassander son of Antipater, who ruled the Macedonians in his father's name. They sent a joint embassy to Antigonus to demand that he share out between them and other Macedonians, who had been expelled from their satrapies, the territory he had acquired and his money. Antigonus treated them with scorn, and so they went to war jointly against him,note[The ultimatum was delivered in the winter of 315/314; the Third Diadoch War started in the spring.] while he made counter-preparations, expelling the remaining garrisons of Ptolemy in Syria and laying his hands on the parts of Phoenicia and Coele Syria, as it is called, that were still under Ptolemy.
 Crossing the Cilician Gate, he left his son Demetrius, then about 22 years old, at Gaza with his army to meet the attacks of Ptolemy from Egypt. Ptolemy won a brilliant victory over him at Gaza and the young man took refuge with his father. Ptolemy immediately sent Seleucus to Babylon to recover his rule, giving him for the purpose 11,000 infantry and 300 cavalry. With such a small force Seleucus recovered Babylon, where the inhabitants received him enthusiastically, and within a short time he greatly extended his empire.note[In the second half of May 311. As we will see in a moment, Seleucus immediately took Media from its pro-Antigonus satrap Nicanor, and added Elam in 310.]
Antigonus defeated an attack by Ptolemy, winning a brilliant victory over him at sea off Cyprus; his son Demetrius was in command.note[The naval battle off Salamis in 306.] This splendid achievement caused the army to proclaim both Antigonus and Demetrius kings; the other kings were dead by this time, Arridaeus the son of Philip, Olympias and the sons of Alexander.note[Philip Arridaeus was executed in 316 by Olympias, the mother of Alexander the Great, who fought for the rights of her son's son Alexander IV (more). In the winter of 312/311, the satraps concluded a treaty and promised to give their powers to the boy king, when he was old enough. Instead, the boy was immediately killed. In 306, the first of the Diadochi, Antigonus Monophthalmus, accepted the royal title, soon followed by the other rulers. Go here for the story of the new kings., who received their titles in 306-305.]. Ptolemy's own army also proclaimed him king, so that his defeat should not place him in a position of inferiority vis-à-vis the victors. And so for these men different circumstances led to similar results; the rest immediately followed their example and from satraps they all became kings.
 And so it was that Seleucus became king of Babylonia, and also of Media, after he had killed in battle with his own hand Nicanor who had been left by Antigonus as satrap of Media.note[In the winter of 311/310, five years before Seleucus accepted the royal title. Appian's chronology is a bit confused.] He waged many wars against Macedonians and barbarians; the two most important were against Macedonians, the latter war against Lysimachus king of Thrace, the former at Ipsus in Phrygia against Antigonus, who was commanding his army and fighting in person although over 80 years old.
After Antigonus had fallen in battle,note[At Ipsus, in 301.] the kings who had joined with Seleucus in destroying Antigonus, shared out his territory. Seleucus obtained then Syria from the Euphrates to the sea and inland Phrygia.note[Which was occupied by Lysimachus and became really Seleucus' land after he had defeated him in 281.] Always lying in wait for the neighboring peoples, with the power to coerce and the persuasion of diplomacy, he became ruler of Mesopotamia, Armenia, Seleucid Cappadocia (as it is called),note[The central part of Cappodocia was occupied by the Galatians; the northern part became an independent kingdom under the name Pontus.] the Persians, Parthians, Bactrians, Arians and Tapurians, Sogdia, Arachosia, Hyrcania, and all other neighboring peoples whom Alexander had conquered in war as far as the Indus. The boundaries of his rule in Asia extended further than those of any ruler apart from Alexander; the whole land from Phrygia eastwards to the river Indus was subject to Seleucus. He crossed the Indus and made war on Sandracottus,note[The Indian king Chandragupta Maurya of the Ganges valley. In 304, they concluded a peace treaty, in which Seleucus gave up all lands east of the Hindu Kush and received many war elephants.] king of the Indians about that river, and eventually arranged friendship and a marriage alliance with him. Some of these achievements belong to the period before the end of Antigonus, others to after his death.
[...]note[A section with omina is omited.]
 Immediately after the death of Alexander he became commander of the Companion cavalry,note[In fact, he was chiliarchos, "vizier".] which Hephaestion and after him Perdiccas had commanded during Alexander's lifetime, then after this satrap of Babylonia and eventually after satrap, king. His great successes in war earned him the surname of Nicator [the Victorious]; this explanation seems to me more likely than that it was due to the killing of Nicanor.
He was tall and powerfully built; one day when a wild bull was brought for sacrifice to Alexander and broke loose from his bonds, he resisted him alone and brought him under control with his bare hands. That is why his statues represent him with horns added.
He founded cities through the whole length of his empire; there were sixteen called Antioch after his father,note[Not all towns in this catalogue were really founded by Seleucus; his descendants also built cities, and several were in fact foundations of Alexander.] five Laodicea after his mother, nine named Seleucia after himself, four called after his wives, three Apamea and one Stratonicea. Of these the most famous up to the present are the two Seleucias, by the sea and on the river Tigris, Laodicea in Phoenicia, Antioch under Mount Lebanon and Apamea in Syria. The others he called after places in Greece or Macedonia, or after his own achievements, or in honor of Alexander the king. That is why there are in Syria and among the barbarians inland many Greek and many Macedonian place-names, Berroea, Edessa, Perinthus, Maronea, Callipolis, Achaea, Pella, Europus, Amphipolis, Arethusa, Astacus, Tegea, Chalcis, Larissa, Heraea, Apollonia, also in Parthia Soteira, Calliope, Charis, Hecatompylos, Achaea, among the Indians Alexandropolis, and among the Scythians an Alexandria Eschatê. Also, called after the victories of Seleucus himself there is Nicephorium in Mesopotamia and Nicopolis in Armenia very near to Cappadocia.
 They say that when he was undertaking the foundation of the two Seleucias, that of Seleucia by the sea was preceded by a portent of thunder, and that is why he consecrated thunder as their divinity, and the inhabitants continue to worship thunder and sing hymns in its honor up to the present day. They also say that for the foundation of Seleucia on the Tigris the Magians were ordered to select the day and the hour when the digging of the foundations was to begin, but they falsified the hour, as they did not wish to have such a stronghold threatening them. Seleucus was waiting for the given hour in his tent, while the army ready for work kept quiet until Seleucus would give the sign. Suddenly at the more favorable hour they thought someone was ordering them on to work and sprang up; not even the efforts of the heralds could hold them back. The work was completed, but Seleucus in despair questioned the Magians a second time about the city; they asked for a promise of impunity and then spoke: "Sire, what has been fated, for better or for worse, no man or city can change (for there is a fate of cities as well as of men). It pleased the gods that this city should last a long time, because it came into being at this hour. We feared it would be a stronghold against us and sought to divert the decrees of fate, but they proved stronger than the cunning of the Magians and the ignorance of a king.
Fortune has smiled on the beginnings of this city of yours; it shall be great and long-lasting. Fear of losing our own prosperity led us into error; we ask you to confirm your pardon to us."
 Seleucus had 72 satraps under him,note[This is greatly exaggerated. Twenty is a better estimate.] so vast was the territory he ruled. Most of it he handed over to his son,note[Antiochus Soter (281-261). Seleucus' descendants are called the Seleucids, his kingdom the Seleucid empire or - to use its real name - Asia.] and ruled himself only the land from the sea to the Euphrates. His last war he fought against Lysimachus for the control of Hellespontine Phrygia; he defeated Lysimachus who fell in the battle, and crossed himself the Hellespont.note[He defeated Lysimachus in the battle of Corupedium (281).] As he was marching up to Lysimacheanote[The capital of Lysimachus' kingdom, on the Hellespont.] he was murdered by Ptolemy nicknamed Keraunos who was accompanying him.note[In September 280. His surname means "thunderbolt".]
This Keraunos was the son of Ptolemy Soter and Eurydice the daughter of Antipater; he had fled from Egypt through fear, as Ptolemy had in mind to hand over his realm to his youngest son. Seleucus welcomed him as the unfortunate son of his friend, and supported and took everywhere his own future assassin. And so Seleucus met his fate at the age of 73, having been king for 42 years.