# Pascal

Blasie Pascal (1623-1662) was born in Clermont, France. His mother passed away when he was just three years old leaving him with his three sisters and father who decided to teach his son himself. From a very young age (12) Pascal had an interest in mathematics. His first discovery was that the sum of three angles in a triangle equals two right-angled triangles (O’Connor and Robertson, 1996). Once he formed an interest in mathematics his father introduced him to Marin Mersenne (1588-1648), and it was at the Académie Parisiensis where he first presented his one-page proofs on projective geometry theorems. Pascal had his first piece of work published in 1640 which was in relation to conic sections. He then went on to create a calculator which would help his father with his work collecting taxes (Biography.com).

Blaise Pascal, Traitez de l’Equilibre des Liqueurs et de la Pesanteur de la Masse de l’Air… (Paris, 1664), Diagram 2.

In 1647 Pascal proved that a vacuum (a space void of matter) does, in fact, exist above the atmosphere. An approximation to such a space is a region with a gaseous pressure much less than atmospheric pressure (Chambers, 2004). Evangelista Torricelli’s mercury barometer of 1643 and Pascal’s experiments both demonstrated a partial vacuum. Pascal worked on mathematics and physics writing a treatise on the Equilibrium of Liquids (1653) in which he explains Pascal’s law of pressure. The image above alludes to the property that liquids weigh in proportion to their height.

Blaise Pascal, Traitez de l’Equilibre des Liqueurs et de la Pesanteur de la Masse de l’Air… (Paris, 1664), p. 157.

Pascal’s book Traitez de l’Equilibre des Liqueurs et de la Pesanteur de la Masse de l’Air contains eight chapters on the equilibrium of liquids as well as nine chapters on the weight of the mass of the air. The main contents are fragments of other works by Pascal, experiments on the equilibrium of fluids, appendices: Fourth book of statics, by Simon Stevin, fifth book of statics, by Simon Stevin (1548-1620), Galileo’s remarks on nature’s abhorrence of a vacuum and Torricelli’s letters on the pressure of the atmosphere ((Spiers and Spiers, 1937).

Blaise Pascal, Traitez de l’Equilibre des Liqueurs et de la Pesanteur de la Masse de l’Air… (Paris, 1664), Diagram 1.

Euclid was the first person to influence Pascal towards mathematics. This was due to his book Elements which was the first maths book Pascal had ever read (O’Connor and Robertson, 1996). In fact, when Pascal was just fifteen years old he had come to admire the work of Girard Desargues (1591-1661) who used to meet at Mersenne’s also. Desargues wrote on practical subjects such as perspective and the cutting of stones for use in building and sundials. Desargues’ most important work, the one in which he invented his new form of geometry, has the title Rough draft for an essay on the results of taking plane sections of a cone (O’Connor and Robertson, 1995). As well as Euclid and Desargues, Pascal was influenced by Descartes, Cardano, Montaigne, Epictetus and Cornelius Jansen (Simpson).

Sources

Blaise Pascal Biography, biography.com (A&E Television Networks, 2016).

Chambers, Austin, Modern Vacuum Physics (Taylor and Francis, 2004), p 1.

O’Connor, J.J. and E.F. Robertson, Blaise Pascal, MacTutor History of Mathematics, (University of St Andrews, December 1996)

O’Connor, J.J. and E.F. Robertson, Girard Desargues, MacTutor History of Mathematics, (University of St Andrews, August 1995)

Pascal, Blaise; Barry, Frederick; Spiers, I. H. B. and A. G. H. Spiers (trs./translators), The physical treatises of Pascal: the equilibrium of liquids and the weight of the mass of the air (Columbia University Press, 1937).

Simpson, D., Pascal Biography, Internet Encyclopedia of Philosophy.

Text: Aoife Mathews and Fionnán Howard