Posts Tagged ‘Archimedes’

A Treasury of Ancient Mathematical Texts

February 4, 2017

Henrietta Midonick, The Treasure of Mathematics: 1 (Harmondsworth: Penguin 1968)


I realise that the history of mathematics is an arcane subject, that few people will have much interest in, having struggled enough with the subject at school. But with Black History Month, there is immense interest amongst scholars of Black and Asian history about restoring Black and Asian scientists and mathematicians to their rightful place in history.

I picked up this book in one of the secondhand bookshops in Cheltenham about a year or so ago. It’s a collection of ancient and medieval mathematical texts from Ancient Egypt, Babylon, China, India, Islam, the Jews and, of course, the ancient Greeks. The blurb for it runs

Mathematics is the only true international language. men can communicate more directly, precisely and logically in pure mathematics than in any other tongue. Moreover we have much to learn from the achievements of past civilizations in this field: even modern computers have not fathomed all the intricacies of Stonehenge. In this fascinating collection of original sources (many of them published in a popular edition for the first time) Henrietta Midonick shows individual mathematicians grappling with varied problems – some practical, such as architecture, money valuation, mechanics, astronomy and calendar calculation; others verging on philosophy, such as the existence of zero and the concept of infinity. Her arrangement also demonstrates the growth of key ideas in geometry, arithmetic, logic and calculus.

Volume 1 documents the growth of mathematical science in the civilizations of Babylon, Ancient Egypt, the Mayas, India and China, and assesses the revolutionary discoveries of Plato, Archimedes and Euclid in classical antiquity.

Among the various extracts are pieces on Babylonian mathematics; four geometrical problems from the Moscow Papyrus, which dates from Ancient Egypt, c. 1850 BC; the Rhind Mathematical Papyrus, again from Egypt, c. 1650 BC; the Bakhshali Manuscript, from 4th century AD India; the Mayas – discussing their system of numbers, the calendar, arithmetic and chronology, and the Quipu, the method of keeping statistical records using knots, used by the ancient Incas in South America.

Chinese mathematicians include Wan Wang, from the 12th century BC, Chou Kung, c. 1100 BC; Chang Tsang, died 152; Liu Hui, 3rd century AD; Sun-Tsu, from the same century; Hsia-Hou Yang, 6th century AD; Wang Hs’iao-T’ung, 7th century AD, Li Yeh, c. AD 1178-1265; Ch’in Chiu-Shao, c. AD 1250; Yang Hui, c. AD 1275; Chu Chi-Chieh, c. AD 1300.

The Indian scholars collected include Aryabhata the Elder, c. AD. 476; Brahmagupta, AD 598; and Bhascara Acharya, AD 1114-c. 1185.

It also includes the Algebra of Mohammed ben Musa al-Khowarismi, who founded much of modern algebra, including giving it its modern name.

The two Jewish mathematicians collected include the Mishnat ha-Middot of Rabbi Nehemiah, from c. AD 150; and the Method of Division of Immanuel Ben Jacob Bonfils, c. AD 1350.

The ancient Greeks include Hippocrates of Chios, 5th century BC; an extract from Plato’s Dialogues; the Elements of Euclid of Alexandria, c. 300 BC; Apollonius of Perga’s Conic Sections, from the same period; Archimedes’ On Spirals, Mechanical Problems, and Quadrature of the Parabola, Pappus, c. AD 300, and Proclus, AD 410-485.


Ancient Babylonian Multiplication Table for X 10.

For the non-mathematician like myself these texts aren’t easy reading. There are diagrams to help, but many of them, as the pioneering works of their time, are trying to express difficult mathematical ideas without the modern language of Maths, and so it can be difficult understanding what they are trying to describe. Nevertheless, this is an important collection of some of the classic texts of ancient mathematics on which the structure of modern maths has been built.

Ecotricity and Solar Power in the 19th Century

April 7, 2015

Pifre Steam Press

Abel Pifre’s Solar-Powered Printing Press

Yesterday I reblogged a fascinating piece from Tom Pride’s site. Tom had posted up a little video of an interview with the chief of Ecotricity, explaining why he had donated money to and was backing Labour. The CEO stated that while he had his reservations about Labour, he thought they were the best party to promote green energy. He felt that a second term of the Tories would be disastrous for this country.

He mentioned the great benefits of renewable power, It’s decentralised nature meant that a potential failure in one of the stations would certainly be as catastrophic as the failure of a nuclear power station. Furthermore, people were able to generate green energy at home. You can see this in practice today with the number of ordinary houses with solar panels on the roof.

The potential of sunlight as a source of power has been known since the ancient world, when Archimedes in the 3rd Century BC sank an invading Roman fleet off Sicily by getting the Greek soldiers to concentrate the sunlight reflected from their bronze shields on the approaching ships.

Over 2000 years later, in 1882 the French engineer, Abel Pifre, demonstrated the ability of solar power to drive modern industrial machinery in an experiment at the Tuileries Gardens in Paris. He set up a concave mirror, 3 1/2 metres in diameter. In the centre of the mirror was a boiler with a valve. This operated a small motor, running at 3/5 horsepower. This drove a Marinoni press, which printed off a copy of a newspaper, which Pifre had written himself, the Sun-Newspaper.

The device operated from one O’clock to half past five, printing off the newspapers as the rate of 500 copies an hour.

The solar press was ingenious, and demonstrated the immense potential of the technology. It doesn’t seem to have been taken up because it was uneconomical compared to coal and later the petrochemical industries. Despite this, such machines clearly have massive potential and may at last come into their own as the world tries to move away from fossil fuels because of the harm they do to the environment.

And fans of Steampunk literature can always have fun imagining what might have happened, if the Victorians not only built Charles Babbage’s Difference Engine, but also had the eminent good sense to power it and their cities with solar power.