A Treatise on Isoperimetrical Problems and the Calculus of Variations by Robert Woodhouse
Book Contents :-
1. The Problem of the Curve of Quickest Descent proposed.
2. Erimetrical Problems Proposed by James Bernoulli
3. Euler’s first Memoir on Isoperimetrical Problems
4. Euler’s second Memoir- General Formule of Solution
5. Euler’s Tract, entitled “‘Methodus inveniendi LineasCurvas Proprietate Maximi Minimive gaudentes”
6. Lagrange’s Memoir
7. Lagrange’s general Method of treating Isoperimetrical Problems
8. Particular Formule deduced from the General one
About this book :-
"A Treatise on Isoperimetrical Problems and the Calculus of Variations" by Robert Woodhouse is a classic early 19th-century mathematical text exploring "isoperimetrical problems"—problems of finding shapes that maximize or minimize areas under given constraints. The book also serves as an introduction to the "calculus of variations", presenting methods to determine functions that optimize certain quantities. Written in 1810, it combines historical insight with mathematical exposition, making complex topics more accessible to English-speaking mathematicians of the time.
Woodhouse emphasizes both theory and historical development, tracing ideas from continental mathematicians and translating them into the British mathematical tradition. The treatise includes worked examples and problem-solving strategies, illustrating how variational principles can be applied to geometric and physical problems. While the methods and notation are dated by modern standards, the text remains valuable for understanding the foundational ideas behind optimization in mathematics.
Today, the book is especially useful for historians of mathematics and those studying the evolution of analytical methods. Its clear treatment of "variational principles" and optimal-shape problems makes it an enduring reference for the early development of applied mathematics. Woodhouse’s work bridges the gap between historical exposition and practical problem-solving, reflecting the depth and rigor of early 19th-century mathematical scholarship.
Book Detail :-
Title:
A Treatise on Isoperimetrical Problems and the Calculus of Variations by Robert Woodhouse
Publisher:
Cambridge, Eng.
Year:
1810
Pages:
181
Type:
PDF
Language:
English
ISBN-10 #:
1165265974
ISBN-13 #:
978-1165265978
License:
Public Domain Work
Amazon:
Amazon
About Author :-
The author
Robert Woodhouse
(1773–1827) was a British mathematician and astronomer known for modernizing "Cambridge mathematics" through his promotion of continental analytical methods. Educated at Gonville and Caius College, he became Senior Wrangler in 1795 and later served as Lucasian Professor of Mathematics and Plumian Professor of Astronomy at Cambridge. Woodhouse authored influential works, including "A Treatise on Isoperimetrical Problems and the Calculus of Variations", which advanced understanding of the "calculus of variations" and "analytical methods" in England. His efforts inspired later mathematicians like Charles Babbage and George Peacock, marking him as a pioneer in Britain’s shift toward modern mathematical analysis.
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