**Girard Desargues** was a French mathematician who was a founder of projective geometry. His work centred on the theory of conic sections and perspective.

- They moved to Lyon but certainly retained the property in Condrieu since Girard (Junior) spent time there towards the end of his life.
- Prior to Taton's research it was wrongly believed that Desargues was born in 1593 because in Adrien Baillet's 1691 biography of Descartes states that Desargues was three years older than Descartes.
- Taton discovered a horoscope of Desargues giving his birth at 6:30 on 21 February 1591.
- There is no information about Desargues' education and about his early life.
- Desargues seems to have made several extended visits to Paris in connection with a lawsuit for the recovery of a huge debt.
- It is thus clear that Desargues had every opportunity of acquiring a good education, could afford to buy what books he chose, and had leisure to indulge in whatever pursuits he might enjoy.
- In his later years, these seem to have included designing an elaborate spiral staircase, and an ingenious new form of pump, but the most important of Desargues' interests was Geometry.
- The Parisian leaders would have to agree a sum in payment, with the required assurances, provide a site for Villette and Desargues' machine to be installed, and then they would build it, or have it built, and wait a month for their payment, only to be made when it is judged satisfactory.
- And therefore we agree that Villette and Desargues begin to execute them at their own expense, with the charge that they will not be able in any way to plant their machines in the river nor in any place on the edges and shores of it before permission is given in our presence by the masters of works of the city and masters of the bridges of it, so that they cannot harm or prejudice the navigation path, the approach and the unloading of goods.
- No further correspondence survives and it is assumed that Villette and Desargues chose not to go ahead under the conditions imposed on them.
- We suggest that the address from which Desargues sent his letter and the fact that he offers no Paris recommendations, indicates that he had newly arrived in Paris.
- We mentioned above Adrien Baillet's 1691 biography of Descartes where Desargues' incorrect year of birth is given.
- Baillet states that Desargues was an engineer involved in the siege of La Rochelle in 1628 and it was there that he first met Descartes.
- There is no additional evidence to substantiate this claim, although given Desargues' skills, it certainly appears plausible.
- That Desargues would be involved in such an undertaking would certainly seem possible.
- There is, however, a statement in C Adam and P Tannery (eds.), Oeuvres de Descartes Ⓣ(Works of Descartes) (1897) that Descartes first met Desargues in 1637.
- When in Paris, Desargues became part of the mathematical circle surrounding Marin Mersenne (1588-1648).
- It was probably essentially for this limited readership of friends that Desargues prepared his mathematical works, and had them printed.
- Bosse states that Desargues was given a royal licence to publish several of his writings in 1630.
- This adds a little weight to Desargues assisting Cardinal Richelieu in the siege and, probably, being involved in other work by the Royal side.
- Mersenne writes in one of his letters that Desargues met Pierre Gassendi in Paris before 1632.
- Mersenne states in 1635 that Desargues was a regular attender of his meetings and his comment makes it look as though he had been doing so for some time.
- In 1635-36 Mersenne published La Harmonie Universelle Ⓣ(Universal harmony) which contains a short paper by Desargues entitled Une méthode aisée pour apprendre et enseigner à lire et escrire la musique Ⓣ(An easy method for learning and teaching to read and write music).
- Here perhaps we have an indication that Desargues had been under the influence of Mersenne during the period in which his ideas on geometry were taking their definitive form.
- Desargues wrote on 'practical' subjects such as perspective in Exemple de l'une des manières universelles du S.G.D.L. touchant la pratique de la perspective sans emploier aucun tiers point, de distance ny d'autre nature, qui soit hors du champ de l'ouvrage Ⓣ(Example of one of the universal ways of Desargues affecting the practice of perspective without using any third point, a distance point or any other kind, which lies outside the picture field) (1636), the cutting of stones for use in building in Brouillon project d'exemple d'une manière universelle du S.G.D.L. touchant la pratique du trait a preuves pour la coupe des pierres en l'architecture Ⓣ(Draft project of an example of a universal way by Desargues on the practice of the line has evidence for the cutting of stones in architecture) (1640) and sundials in Manière universelle de poser le style aux rayons du soleil en quelconque endroit possible, avec la règle, le compas, l'esquerre et le plomb Ⓣ(Universal way of placing the style in the rays of the sun in any possible place, with the ruler, the compass, the square and the plummet) (1640).
- One immediately wonders who or what "S.G.D.L." is, but this is simply "Desargues" from the initials of "Sieur Girard Desargues Lyonnais".
- This work on perspective must have led Desargues to develop a new approach to geometry.
- The description of Desargues' stone cutting method, in a form that those working on stone would understand, was produced by Desargues' disciple Abraham Bosse (1604-1676) in 1643.
- Bosse also describes Desargues' work on sundials and, as Desargues's original publication has not survived, this is our only information about this text.
- Pascal must be referring here to Desargues' most important work, the one in which he invented his new form of geometry, which has the title Brouillon project d'une atteinte aux evenemens des rencontres du Cone avec un Plan Ⓣ(Rough draft for an essay on the results of taking plane sections of a cone)).
- Only one is now known to survive, and until this was rediscovered, in 1951, Desargues' work was known only through a manuscript copy made by Philippe de la Hire (1640-1718).
- It begins with pencils of lines and ranges of points on a line, considers involutions of six points (Desargues does not use or define a cross ratio), gives a rigorous treatment of cases involving 'infinite' distances, and then moves on to conics, showing that they can be discussed in terms of properties that are invariant under projection.
- Desargues' famous 'perspective theorem' - that when two triangles are in perspective the meets of corresponding sides are collinear - was first published in 1648, in a work on perspective by Abraham Bosse.
- It is clear that, despite his determination to explain matters in the vernacular, and without direct reference to the theorems or the vocabulary of Ancient mathematicians, Desargues is well aware of the work of ancient geometers, for instance Apollonius and Pappus.
- It seems highly likely that it was in fact from his work on perspective and related matters that Desargues' new ideas arose.
- Desargues' work on perspective led to a very unpleasant argument.
- The preface to the book credited Desargues but he was very upset to see his ideas presented with many errors and his reaction was to place placards around Paris.
- This looks like a massive overreaction by Desargues and it prompted an equally vicious response by Du Breuil who counterattacked with a pamphlet claiming that Desargues' 1636 paper on perspective presented ideas that had been published earlier by Jean-Louis de Vauzelard in Perspective cilindrique et conique Ⓣ(Cylindrical and conical perspective) (1630) and by Jacques Aleaume in Introduction a la perspective, ensemble a l'usage de compas optique et perspective Ⓣ(Introduction to perspective, together with the use of the optical compass and perspective) (1628).
- He also infuriated Desargues by claiming that, for all practical purposes, his work was without value.
- Desargues kept up the argument by publishing Six erreurs des pages 87, 118, 124, 128, 132 et 134.
- The publishers Melchior Tavernier and Francois l'Anglois then attacked Desargues by publishing a collection of articles criticising his work in Advis charitables sur les diverses oeuvres et feuilles volantes du Sieur Girard Desargues, Lyonnois Ⓣ(Helpful advice on the various works and manuscripts of M.
- Desargues of Lyon) (1642).
- This work included a letter written by Jean Beaugrand in August 1640, shortly before his death, in which he criticised Desargues' projective study of conics.
- At this point Desargues seems to have turned to Abraham Bosse to publish clarifications of his work and to defend it against these attacks.
- As we noted above, Bosse published two treatises in 1643 presenting in a simpler way Desargues' work on stone cutting and on sundials.
- A new attack came in 1644 from Jacques Curabelle with the 81-page book Examen des oeuvres de Sieur Desargues, Lyonnois Ⓣ(Examination of the works of M.
- Curabelle claimed that Desargues' lack of practical experience makes his work useless.
- A vicious argument between Curabelle and Desargues followed with various pamphlets attacking each other and with Desargues threatening to sue Curabelle if he did not retract.
- Desargues appears to have grown tired of the continuous battles he was involved in and, from 1645, turned to architecture.
- Let us end this biography with two quotes regarding Desargues' mathematical contributions.
- In a work published in 1639 Desargues set forth the foundation of the theory of four harmonic points, not as done today but based on the fact that the product of the distances of two conjugate points from the centre is constant.

Born 21 February 1591, Lyon, France. Died October 1661, Lyon, France.

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Geometry

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive