LHopital's Analyse des infiniments petits: An Annotated Translation

In this review of LHopital's Analyse des infiniments petits, the reviewer finds a scholarly edition that will appeal to historians of mathematics and serious students of calculus. This annotated translation presents both Johann Bernoulli's long-hidden Latin lecture notes and the first faithful English rendering of lHopital's 1696 textbook, making it the single best reason to buy: access to primary source material with careful commentary that clarifies authorship, context, and originality. Readers seeking a readable modern textbook will find it demanding, but those studying the history and development of differential calculus will value its depth.

Key Features

• Dual source translation: Includes the first English translation of Bernoulli's lecture notes alongside lHopital's original text to enable direct comparison and scholarly study.
• Annotations and commentary: Detailed notes explain historical context and mathematical choices, making obscure 17th century terminology accessible to modern readers.
• Textual fidelity: The edition aims for a faithful translation of lHopital's French text, preserving the structure and intent of the original work for accurate scholarship.
• Discovery context included: Explains the 1920s discovery of Bernoulli's notes in Basel and how that affected attribution and interpretation of the textbook.
• Scholarly utility: Serves as a primary source resource for research in the history of calculus and the interplay between Bernoulli and lHopital.

Who It's For

This volume is best for historians of science, graduate students in mathematics or history, and professional researchers who need a reliable English translation of foundational calculus texts. The combination of Bernoulli's Latin notes and lHopital's French original, with annotations, makes it particularly useful for comparative study and citation in academic work.

Those looking for a step-by-step modern calculus textbook or an introductory teaching manual should look elsewhere; the book prioritizes historical fidelity and commentary over pedagogical simplicity, and so assumes familiarity with historical mathematical language and notation.

Pros & Cons

Pros

• Provides the first English translation of Bernoulli's lecture notes, opening access to important primary material.
• Careful annotations illuminate historical context and clarify difficult passages for researchers.
• Faithful rendering of lHopital's 1696 text preserves original arguments and innovations for scholarly analysis.

Cons

• The edition is scholarly and dense, so it is not ideal for casual readers or beginners in calculus.

Specifications

Title	LHopital's Analyse des infiniments petits: An Annotated Translation
Contents	Bernoulli's Latin lecture notes and lHopital's French text with annotations
Type	Scholarly annotated translation / historical monograph
Editors/Authors	Robert E E. Bradley, Salvatore J. Petrilli, C. Edward Sandifer
Series	Science Networks. Historical Studies, 50
Subject	History of mathematics; differential calculus

Our Verdict

This annotated translation is a strong purchase for historians and advanced students who need direct access to early calculus sources; its faithful translations and scholarly commentary make it good value for research and citation, though it is not intended as an introductory teaching text.

Frequently Asked Questions

Does this edition include Bernoulli's lecture notes?
Yes, it contains the first English translation of Johann Bernoulli's Latin lecture notes alongside lHopital's text.

Is this a modern textbook for learning calculus?
No, the volume is a historical and scholarly edition focused on primary sources and commentary rather than step-by-step instruction.

Who edited this translation?
The annotated translation and commentary are by Robert E E. Bradley, Salvatore J. Petrilli, and C. Edward Sandifer.