Background
Albert Girard was born in 1595 in Saint-Mihiel, France.
Netherlands
Albert Girard
Rapenburg 70, 2311 EZ Leiden, Netherlands
Albert studied under Willebrord Snell at the University of Leiden.
Rapenburg 70, 2311 EZ Leiden, Netherlands
Albert studied under Willebrord Snell at the University of Leiden.
https://www.amazon.co.uk/Tangentes-Trigonometrie-Triangles-Plusieurs-Operations/dp/0274079860/?tag=prabook0b-20
1626
https://www.amazon.co.uk/Invention-Nouvelle-lAlgebre-Classic-Reprint/dp/025913578X/?tag=prabook0b-20
1629
Albert Girard was born in 1595 in Saint-Mihiel, France.
Albert studied under Willebrord Snell at the University of Leiden.
After graduating, Girard went to work for Prince Frederick Henry of Nassau. Yet just as the French did not consider him fully one of their own because of his religion, he was not Dutch either, and he never succeeded in securing the patronage so necessary to the career of a mathematician in the seventeenth century. On the other hand, he was able to supplement his income in an unusual way, as a professional lute-player.
Also a widely published translator, Girard was responsible for translating a number of works from French into Flemish, the language of Holland, and from Flemish into French. Some of these include Henry Hondius’ treatise on fortifications, mathematical works of Samuel Marolois, the Arithmetic of Simon Stevin, and Stevin’s works. He also prepared sine tables and a succinct treatise on trigonometry and published theoretical work, Invention nouvelle en l’algèbre in 1629. Although in the preface to the trigonometric tables he promised that he would very soon present studies inspired by Pappus of Alexandria, no such work on these matters appeared. Likewise, his restoration of Euclid’s porisms, which he stated he “hopes to present, having reinvented them,” never appeared.
Contributions to the mathematical sciences are scattered throughout Girard’s writings. It should be said at the outset that, always pressed for time and generally lacking space, he was very stingy with words and still more so with demonstrations. Thus, he very often suggested more than he demonstrated. Girard was the first to state publicly that the area of a spherical triangle is proportional to its spherical excess. This theorem, stemming from the optical tradition of Witelo, was probably known by Regiomontanus and definitely known by Thomas Harriot, who, however, did not divulge it. Girard gave a proof of it that did not fully satisfy him and that he termed “a probable conclusion.” It was Bonaventura Cavalieri who furnished, independently, a better-founded demonstration.
In his writings on geometry, Girard identified multiple types of quadrilaterals and pentagons, defined 69 of 70 types of hexagons, and became the first mathematician to state that the area of a spherical triangle is proportional to its spherical excess. He improved on the work of Rafaello Bombelli for extracting the cube roots of binomials. In addition, Girard developed a simplified means for demarking the cube root still in use today.
In the theory of numbers Girard translated books V and VI of Diophantus from Latin into French. For this work he knew and utilized not only Guilielmus Xylander’s edition, as Stevin had for the first four books, but also that of Claude Gaspar Bachet de Méziriac, which he cited several times. Girard stated the whole numbers that are sums of two squares and declared that certain numbers, such as seven, fifteen, and thirty-nine, are not decomposable into three squares; but he affirmed, as did Bachet, that all of them are decomposable into four squares. The first demonstration of this theorem was provided by Joseph Lagrange.
Albert Girard was a prominent mathematician. He is noted for giving the inductive definition for the Fibonacci numbers. He was the first to use the abbreviations 'sin', 'cos' and 'tan' for the trigonometric functions in a treatise. Girard also showed how the area of a spherical triangle depends on its interior angles. The result is called Girard's theorem.
Girard was a member of the Reformed church. In a polemic against Honorat du Meynier he accused the latter of injuring “those of the Reformed religion by calling them heretics.” This explains why he settled in the Netherlands, the situation of Protestants being very precarious in France.
In algebra, as in the theory of numbers, Girard showed himself to be a brilliant disciple of Viéte, whose “specious logistic” he often employed but called “literal algebra.” In his study of incommensurables Girard generally followed Stevin and the tradition of Euclid. Unlike Harriot and Descartes, Girard never wrote an equation in which the second member was zero. He particularly favored the “alternating order,” in which the monomials, in order of decreasing degree, are alternately in the first member and the second member. That permitted him to express, without any difficulty with signs, the relations between the coefficients and the roots. For him, the introduction of imaginary roots was essentially for the generality and elegance of the formulas. In addition, Girard gave the expression for the sums of squares, cubes, and fourth powers of roots as a function of the coefficients.
It was said that Girard was quiet-natured and, unlike most mathematicians, did not keep a journal for his personal life.
