Ptolemy in the context of "Heloros"

Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals (e.g., establishing a reliable calendar or determining how to cure a variety of illnesses) as well as more abstract investigations belonging to natural philosophy. Classical antiquity is traditionally defined as the period between the 8th century BC (beginning of Archaic Greece) and the 6th century AD (after which there was medieval science). It is typically limited geographically to the Greco-Roman West, Mediterranean basin, and Ancient Near East, thus excluding traditions of science in the ancient world in regions such as China and the Indian subcontinent.

Ideas regarding nature that were theorized during classical antiquity were not limited to science but included myths as well as religion. Those who are now considered as the first scientists may have thought of themselves as natural philosophers, as practitioners of a skilled profession (e.g., physicians), or as followers of a religious tradition (e.g., temple healers). Some of the more widely known figures active in this period include Hippocrates, Aristotle, Euclid, Archimedes, Hipparchus, Galen, and Ptolemy. Their contributions and commentaries spread throughout the Eastern, Islamic, and Latin worlds and contributed to the birth of modern science. Their works covered many different categories including mathematics, cosmology, medicine, and physics.

Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.

The early history of Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subject is Euclid's Elements, written during the Hellenistic period. The works of renown mathematicians Archimedes and Apollonius, as well as of the astronomer Hipparchus, also belong to this period. In the Imperial Roman era, Ptolemy used trigonometry to determine the positions of stars in the sky, while Nicomachus and other ancient philosophers revived ancient number theory and harmonics. During late antiquity, Pappus of Alexandria wrote his Collection, summarizing the work of his predecessors, while Diophantus' Arithmetica dealt with the solution of arithmetic problems by way of pre-modern algebra. Later authors such as Theon of Alexandria, his daughter Hypatia, and Eutocius of Ascalon wrote commentaries on the authors making up the ancient Greek mathematical corpus.

Geocentrism is a superseded astronomical model description of the Universe with Earth at the center. It is also known as the geocentric model, often exemplified specifically by the Ptolemaic system. Under most geocentric models, the Sun, the Moon, stars, and planets all orbit Earth. The geocentric model was the predominant description of the cosmos in many European ancient civilizations, such as those of Aristotle in Classical Greece and Ptolemy in Roman Egypt, as well as during the Islamic Golden Age.

Two observations supported the idea that Earth was the center of the Universe. First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. The stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographical poles of Earth. Second, Earth seems to be unmoving from the perspective of an earthbound observer; it feels solid, stable, and stationary.

Theon of Alexandria (/ˌθiːən, -ɒn/; Ancient Greek: Θέων ὁ Ἀλεξανδρεύς; c. AD 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.

Hypatia (born c. 350–370 – March 415 AD) was a Neoplatonist philosopher, astronomer, and mathematician who lived in Alexandria, at that time in the province of Egypt and a major city of the Eastern Roman Empire. In Alexandria, Hypatia was a prominent thinker who taught subjects including philosophy and astronomy, and in her lifetime was renowned as a great teacher and a wise counselor. Not the only fourth century Alexandrian female mathematician, Hypatia was preceded by Pandrosion. However, Hypatia is the first female mathematician whose life is reasonably well recorded. She wrote a commentary on Diophantus's thirteen-volume Arithmetica, which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's Almagest, based on the title of her father Theon's commentary on Book III of the Almagest.

Hypatia constructed astrolabes and hydrometers, but did not invent either of these, which were both in use long before she was born. She was tolerant toward Christians and taught many Christian students, including Synesius, the future bishop of Ptolemais. Ancient sources record that Hypatia was widely beloved by pagans and Christians alike and that she established great influence with the political elite in Alexandria. Toward the end of her life, Hypatia advised Orestes, the Roman prefect of Alexandria, who was in the midst of a political feud with Cyril, the bishop of Alexandria. Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March 415 AD, she was murdered by a mob of Christians led by a lector named Peter.

The Ptolemy world map is a map of the world known to Greco-Roman societies in the 2nd century. It is based on the description contained in Ptolemy's book Geography, written c. 150. Based on an inscription in several of the earliest surviving manuscripts, it is traditionally credited to Agathodaemon of Alexandria.

Notable features of Ptolemy's map is the first use of longitudinal and latitudinal lines as well as specifying terrestrial locations by celestial observations. The Geography was translated from Greek into Arabic in the 9th century and played a role in the work of al-Khwārizmī before lapsing into obscurity. The idea of a global coordinate system revolutionized European geographical thought, however, and inspired more mathematical treatment of cartography.

Terra incognita or terra ignota (Latin "unknown land"; incognita is stressed on its second syllable in Latin, but with variation in pronunciation in English) is a term used in cartography for regions that have not been mapped or documented. The expression is believed to be first seen in Ptolemy's Geography c. 150. The term was reintroduced in the 15th century from the rediscovery of Ptolemy's work during the Age of Discovery. The equivalent on French maps would be terres inconnues (plural form), and some English maps may show Parts Unknown. Similarly, uncharted or unknown seas would be labeled mare incognitum, Latin for "unknown sea".

The geography of North Africa has been reasonably well known among Europeans since classical antiquity in Greco-Roman geography. Northwest Africa (the Maghreb) was known as either Libya or Africa, while Egypt was considered part of Asia.

European exploration of sub-Saharan Africa begins with the Age of Discovery in the 15th century, pioneered by the Kingdom of Portugal under Henry the Navigator. The Cape of Good Hope was first reached by Bartolomeu Dias on 12 March 1488, opening the important sea route to India and the Far East, but European exploration of Africa itself remained very limited during the 16th and 17th centuries. The European powers were content to establish trading posts along the coast while they were actively exploring and colonizing the New World. Exploration of the interior of Africa was thus mostly left to the Muslim slave traders, who in tandem with the Muslim conquest of Sudan established far-reaching networks and supported the economy of a number of Sahelian kingdoms during the 15th to 18th centuries.

The Fertile Crescent (Arabic: الهلال الخصيب al-hilāl al-ḵaṣīb) is a crescent-shaped region in the Middle East, spanning modern-day Iraq, Israel, Jordan, Lebanon, Palestine, and Syria, together with northern Kuwait, south-eastern Turkey, and western Iran. Some authors also include Cyprus and northern Egypt.

The Fertile Crescent is believed to be the first region where settled farming emerged as people started the process of clearance and modification of natural vegetation to grow newly domesticated plants as crops. Early human civilizations such as Sumer in Mesopotamia flourished as a result. Technological advances in the region include the development of agriculture and the use of irrigation, of writing, the wheel, and glass, most emerging first in Mesopotamia.