Bradley on L’Hospitial, Another CSHPM Online Colloquium, Fri. Jan. 28

First posted Monday, January 24, 2022 / Yom sheni, 22 Shevat, 5782

By David Orenstein

This coming Friday, January 28, the Canadian Society for History and Philosophy of Mathematics / La Société Canadienne d’Histoire et de Philosophie des Mathématiques (CSHPM/SCHPM) will host another of its monthly online Colloquia, which got started in the Fall of 2020 in response to the pandemic. A fellow University of Toronto Alumnus, Robert Bradley, of Adelphi University’s Mathematics Department, will speak to us on L’Hospital:

***CSHPM Online Colloquium: Robert Bradley (Jan 28th)***

The Canadian Society for History and Philosophy of Mathematics ( invites members as well as the broader scholarly community to the next talk in our online colloquium series via Zoom. Participants are encouraged to become members (for as little as $10-$30/year, depending on your employment status), but it is not required. Non-members can get regular updates on our activities by liking us on Facebook ( The talk will last 30 minutes, followed by a Q&A.

ROBERT BRADLEY, Mathematics, Adelphi University, will deliver the 18th talk of the CSHPM Online Colloquium series.

DATE: January 28th
TIME: Vancouver 11:00; Montreal/Toronto 14:00

TITLE: The Marquis’ Beak

ABSTRACT: The Marquis de l’Hôpital wrote the first calculus textbook, “Analyse des infiniment petits” (1696).  In his preface, he made it clear that most of the results in his book were not his own, due rather to Leibniz and the Bernoulli brothers, particularly Johann I Bernoulli.  Over the centuries, it has become clear that the Marquis deserves priority for almost nothing in his textbook, and certainly not for the famous Rule that bears his name.

One of de l’Hôpital’s original contributions was in the area of evolutes and inflection points: a geometric construction that led him to the discovery of a cusp of the second kind, also called a ramphoid cusp, for its similarity in shape to a bird’s beak.  In the context of the “Analyse,” this cusp is simply an elegant curiosity.  However, the Marquis’ Beak became a matter of renewed interest in the 1740s, attracting the attention of Gua de Malves, Euler, and d’Alembert.  Their contributions to this topic illuminate the 18th century conceptual shift in the calculus from geometric to algebraic.

Please distribute this information to all who might be interested. The information to join the session via Zoom is as follows:

Topic: CSHPM Online Colloquium: Robert Bradley
Time: Jan 28, 2022 11:00 AM Pacific Time (US and Canada)

Join Zoom Meeting

Meeting ID: 611 1497 4252
Password: 052883


As I stated earlier, Michael Barany and I got to debate the “Success of the 1924 Toronto International Mathematical Congress” as the October 23, 2020, CSHPM Online Colloquium.

In this year of online events, it’s also good to know the times in other Standard Time Zones / pour d’autres Heures normales.    (Thank you, Sandford Fleming! / Merci à vous, Sandford Fleming!)

Thus, for Canadians / Ainsi, pour nous les canadien(ne)s :

11:00 am PST/HNP (UBC, SFU, UVic, UNBC, etc.)

= 12:00 noon MST/HNM (U of A, UCalgary, ULethbridge, etc.)

= 1:00 pm CST/HNC (USask, URegina, UBrandon, U of M, U Winnipeg, etc.)

= 2:00 pm EST/HNE (Western, McMaster, U of T, York U, Queen’s, Carleton, U d’Ottawa, U de M, UQÀM, McGill, Laval, USherbrooke, etc.)

= 3:00 pm AST/HNA (UNB, U de Moncton, Dalhousie, Acadia, UPEI, etc.)

= 3:30 pm NST/HNT-N (Memorial, Grenfell C, etc.)


Or for our European friends / ou pour nos ami(e)s européen(ne)s:

= 7:00 pm GMT/HMG (Trinity C Dublin, UBelfast, UAberystwyth, St. Andrews, ULondon, Cambridge U, Coimbra, etc)

= 8:00 pm CEST/HNEC (Sorbonne, UBruxelles, Humboldt, Leyden, UGénève, etc.)

Adelphi University has two Campuses: Garden City, Nassau County (Long Island), New York, and Manhattan, New York, New York. Much like York University with its Keele and Glendon campuses.

Rob Bradley has given many talks at our CSPHM/SCHPM Annual Meetings (usually in conjunction with the CFHSS/FCHSS annual Congresses (The Learneds of old):

(2010, Concordia) “Cauchy’s Algebraic Analysis”

(2008, UBC) “Cauchy’s Analysis: A Break with the Past?”

(2007, Concordia) “Euler’s Resolution of Cramer’s Paradox”

(2005, Waterloo) “The Geonese Lottery and the Partition Function”

(2004, Cambridge, UK) “Three Bodies? Why not Four? The Motion of the Lunar Apdsides”

(2003, Dalhousie) “The Curious Case of the Bird’s Beak” [Sound familiar?]

(2002, U of T) “…Disputes in the Euler-DAlembert Correspondence”

And that’s just the first decade of the 21st Century!

You might remember Guillaume François Antoine, Marquis de L’Hospital for L’Hospital’s Rule from Differential Calculus:

The limit for the quotient of functions, at a given value of the independent variable, equals the limit of the quotient of their derivatives at the same value.

This Theorem is stated, proved, and applied in six examples, on pp. 621-626 in Gorge B. Thomas, Jr.’s (MIT) Calculus and Analytic Geometry from 1951.

1951! That’s when I was born! Making it even better, my copy’s front endpaper is inscribed: “Seymour Steinhor”. He was my mother’s younger brother, who did so much to aim me towards an abiding passion for mathematics and the natural sciences. But that’s another story!

Selon mon Petit Larousse 2000, page 1469b:

« L’HOSPITAL (Guillaume de), marquis de Sainte-

Mesme, Paris 1661 – id. 1704, mathématicien

français. Il fut initié au calcul infinitésimal par

J. Bernoulli [lequel: Jean ou Jaques / Johann ou Jakob?]

et en publia le premier manuel. »

Si j’ai raison, le premier manuel du calcul infinitésimal au Canada est de Jean Langevin en 1848 (Baillargeon, 1994, p. 329):

Traité élémentaire de calcul différentiel at de calcul intégral.

Mais ça, c’est aussi une autre histoire!



  1. Noël Baillargeon (1994), Le Séminaire de Québec de 1800 à 1850. Les Presses de l‘Université Laval, Saint-Foy, Québec, (vi) + 410 pp. (et une carte pliée hors texte), incl. Biblio. 18 pp., Index 15 pp., maintes notes en bas du page.
  2. Michel Legrain et Yves Garnier, réds. (1999), Le Petit Larousse 2000. Larousse, Paris, 1784 pp. et en coverture 3 pp. drapeaux mondiaux et à la fin 11 pp. cartes de la francophonie (y compris le Canada) et mondiales.
  3. Gorge B. Thomas, Jr.’s (1951) Calculus and Analytic Geometry, in Addison-Wesley Mathematics Series of eight books by 1951. Addison-Wesley, Cambridge Mass., (viii) + 685 + (49) [Answers to Problems] pp., incl. 5 pp. Index.

 Links / Liens:

1. CSTHA Post inviting you to Oct. 23, 2020, CSHPM Debate on 1924 Toronto IMC.

2. Invitation to Oct. 28, 2022, CSHPM Online Colloquium, Posted (Facebook) Jan. 21.

3. Adelphi University’s webpage.

4. Robert Bradley’s webpage.

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