A History of Greek Mathematics is a book by English historian of mathematics Thomas Heath about history of Greek mathematics. It was published in Oxford in 1921, in two volumes titled Volume I, From Thales to Euclid and Volume II, From Aristarchus to Diophantus. It got positive reviews and is still used today. Ten years later, in 1931, Heath published A Manual of Greek Mathematics, a concise version of the two-volume History.
Thomas Heath was a British civil servant, whose hobby was Greek mathematics (he called it a "hobby" himself). He published a number of translations of major works of Euclid, Archimedes, Apollonius of Perga and others; most are still used today. [1]
Heath wrote in the preface to the book: [2]
The work was begun in 1913, but the bulk of it was written, as a distraction, during the first three years of the war, the hideous course of which seemed day by day to enforce the profound truth conveyed in the answer of Plato to the Delians. When they consulted him on the problem set them by the Oracle, namely, that of duplicating the cube, he replied, 'It must be supposed, not that the god specially wished this problem solved, but that he would have the Greeks desist from war and wickedness and cultivate the Muses, so that, their passion being assuaged by philosophy and mathematics, they might live in innocent and mutually helpful intercourse with one another.'
Ten years later, in 1931, Heath published A Manual of Greek Mathematics, a concise version of the two-volume History. In a preface Heath wrote that the Manual is for "the general reader who has not lost interest in the studies of his youth", while History was written for scholars. [3] The Manual contains some discoveries made in ten years after the publication of History, for example the new edition of Rhind Papyrus (published in 1923), some parts of then unpublished Moscow Papyrus, [3] [4] [5] and decipherment of Babylonian tablets and "the newest studies" of Babylonian astronomy. [5]
The book got positive reviews. Mathematician David Eugene Smith praised the book, writing in 1923 that "no man now living is more capable than he of interpreting the Greek mathematical mind to the scholar of today; indeed, there is no one who ranks even in the same class with Sir Thomas Heath in this particular". He also noted that Heath wrote in length about "five of the greatest names in the field of ancient mathematical research" (Euclid, Archimedes, Apollonius, Pappus, and Diophantus), given "each approximately a hundred pages". He called the book "destined to be the standard work". [6]
Philosopher John Alexander Smith wrote in 1923 that the book "has the eminent merit of being readable", and that "for most scholars the work is full and detailed enough to form almost a library of reference". [7]
Another reviewer from 1923 wrote that "covering as it does so much ground, it is not surprising that the book shows signs of ruthless compression". [8] The author was praised for the book, with one reviewer writing "In Sir Thomas Heath we have, as Erasmus said of Tunstall, a scholar who is dictus ad unguem". [2]
Historian of science George Sarton also praised the book in his 1922 review, writing that "it seems hardly necessary to speak at great length of a book of which most scholars knew long before it appeared, for few books have been awaited with greater impatience". He also noted careful explanation of solutions written in modern language, and "perfect clearness of the exposition, its excellent order, its thoroughness". [9]
The Manual, concise version of History, also received positive reviews. It was called a "fascinating little book", "a mine of information, a delight to read". [10] Sarton criticized the book because of the absence of chapters devoted to Egyptian and Mesopotamian mathematics. [5] Herbert Turnbull praised the book, especially its treatment of new discoveries of Egyptian and Babylonian mathematics. [11]
Mathematician Howard Eves praised the book in his 1984 review, writing that "the English-speaking population is particularly fortunate in having available the extraordinary treatise ... one finds one of the most scholarly, most complete, and most charmingly written treatments of the subject, a treatment certain to kindle a deep appreciation of that early period of mathematical development and a genuine admiration of those who played leading roles in it." [12]
Fernando Q. Gouvêa, writing in 2006, criticizes Heath's books as outdated and old-fashioned. [4] [13]
Benjamin Wardhaugh, writing in 2016, finds that Heath's approach to Greek mathematics is to "made them look like works of classic literature", and that "what Heath constructed might be characterized today as a history of the contents of Greek theoretical mathematics." [1] Reviel Netz in his 2022 book calls Heath's History "a reliable guide to many generations of scholars and curious readers". He writes that "Historiographies went in and out of fashion, but Heath still stands, providing a clear and readable survey of the contents of most of the works of pure mathematics attested from Greek antiquity." He has also noted that there was no other book on the subject written in a hundred years. [14]
Democritus was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. None of his work has survived.
Euclid was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
Aristarchus of Samos was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the known universe, with the Earth revolving around the Sun once a year and rotating about its axis once a day.
Euclid's Elements is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
Sir Thomas Little Heath was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English.
Apollonius of Perga was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. Gottfried Wilhelm Leibniz stated “He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.”
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes and different dimensions. The term can mean
Pappus of Alexandria was one of the last great Greek mathematicians of antiquity; he is known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.
Hippasus of Metapontum was a Greek philosopher and early follower of Pythagoras. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this. However, the few ancient sources which describe this story either do not mention Hippasus by name or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer.
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly attested from the late 7th century BC to the 6th century AD, around the shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire region, 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 proofs is an important difference between Greek mathematics and those of preceding civilizations.
On the Sizes and Distances (of the Sun and Moon) (Ancient Greek: Περὶ μεγεθῶν καὶ ἀποστημάτων [ἡλίου καὶ σελήνης], romanized: Perì megethôn kaì apostēmátōn [hēlíou kaì selḗnēs]) is widely accepted as the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa 310–230 BCE. This work calculates the sizes of the Sun and Moon, as well as their distances from the Earth in terms of Earth's radius.
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.
Hypsicles was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and the Book XIV of Euclid's Elements. Hypsicles lived in Alexandria.
This is a timeline of mathematicians in ancient Greece.
Metrodorus was a Greek grammarian and mathematician, who collected mathematical epigrams which appear in the Greek Anthology.
Diodorus of Alexandria or Diodorus Alexandrinus was a gnomonicist, astronomer and a pupil of Posidonius.
Paul-Louis ver Eecke was a Belgian mining engineer and historian of Greek mathematics. He produced influential French translations of the mathematical works of ancient Greece, including those of Archimedes, Pappus, and Theodosius.
