An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and…

(8 User reviews)   2518
By Charlotte Girard Posted on Nov 15, 2025
In Category - Adventure
Byerly, William Elwood, 1849-1935 Byerly, William Elwood, 1849-1935
English
Ever wonder how we can describe heat flow, sound waves, or even the shape of a drum mathematically? This book holds the key. Forget thinking it's just a dry old textbook. It's more like the instruction manual for a superpower—the ability to break down any repeating pattern, no matter how wild, into simple, predictable waves. The 'mystery' here is how something as abstract as a mathematical series can perfectly describe the real, physical world around us. If you've ever been curious about the hidden math in music or how engineers design everything from bridges to cell phones, this book shows you the elegant foundation. It's not light reading, but the payoff is seeing the world in a whole new way.
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Late Rector of Bucknell, Oxon; Editor of the Fourth Edition of Dr. Scrivener’s “Plain Introduction to the Textual Criticism of the New Testament”; and Author of “A Guide to the Textual Criticism of the New Testament” Πᾶσι Τοῖς Ἁγίοις ἐν Χριστῷ Ἰησοῦ PHIL. i. 1 London George Bell And Sons Cambridge: Deighton, Bell and Co. 1896 CONTENTS Preface. Introduction. Chapter I. Preliminary Grounds. Chapter II. Principles. Chapter III. The Seven Notes Of Truth. Chapter IV. The Vatican And Sinaitic Manuscripts. Chapter V. The Antiquity of the Traditional Text. I. Witness of the Early Fathers. Chapter VI. The Antiquity Of The Traditional Text. II. Witness of the Early Syriac Versions. Chapter VII. The Antiquity Of The Traditional Text. III. Witness of the Western or Syrio-Low-Latin Text. Chapter VIII. Alexandria and Caesarea. Chapter IX. The Old Uncials. The Influence Of Origen. Chapter X. The Old Uncials. Codex D. Chapter XI. The Later Uncials And The Cursives. Chapter XII. Conclusion. Appendix I. Honeycomb—ἀπὸ μελισσίου κηρίου. Appendix II. Ὄξος—Vinegar. Appendix III. The Rich Young Man. Appendix IV. St. Mark i. 1. Appendix V. The Sceptical Character Of B And א. Appendix VI. The Peshitto And Curetonian. Appendix VII. The Last Twelve Verses Of St. Mark’s Gospel. Appendix VIII. New Editions Of The Peshitto-Syriac And The Harkleian-Syriac Versions. General Index. Index II. Passages Of The New Testament Commented On. Footnotes “Tenet ecclesia nostra, tenuitque semper firmam illam et immotam Tertulliani regulam ‘Id verius quod prius, id prius quod ab initio.’ Quo propius ad veritatis fontem accedimus, eo purior decurrit Catholicae doctrinae rivus.”—CAVE’S _Proleg._ p. xliv. “Interrogate de semitis antiquis quae sit via bona, et ambulate in eâ.”—Jerem. vi. 16. “In summa, si constat id verius quod prius, id prius quod ab initio, id ab initio quod ab Apostolis; pariter utique constabit, id esse ab Apostolis traditum, quod apud Ecclesias Apostolorum fuerit sacrosanctum.”—TERTULL. _adv. Marc._ l. iv. c. 5. PREFACE. The death of Dean Burgon in 1888, lamented by a large number of people on the other side of the Atlantic as well as on this, cut him off in the early part of a task for which he had made preparations during more than thirty years. He laid the foundations of his system with much care and caution, discussing it with his friends, such as the late Earl of Selborne to whom he inscribed The Last Twelve Verses, and the present Earl of Cranbrook to whom he dedicated The Revision Revised, for the purpose of sounding the depths of the subject, and of being sure that he was resting upon firm rock. In order to enlarge the general basis of Sacred Textual Criticism, and to treat of the principles of it scientifically and comprehensively, he examined manuscripts widely, making many discoveries at home and in foreign libraries; collated some himself and got many collated by other scholars; encouraged new and critical editions of some of the chief Versions; and above all, he devised and superintended a collection of quotations from the New Testament to be found in the works of the Fathers and in other ecclesiastical writings, going far beyond ordinary indexes, which may be found in sixteen thick volumes amongst the treasures of the British Museum. Various events led him during his life-time to dip into and publish some of his stores, such as in his Last Twelve Verses of St. Mark, his famous Letters to Dr. Scrivener in the _Guardian_ Newspaper, and in The Revision Revised. But he sedulously amassed materials for the greater treatise up to the time of his death. He was then deeply impressed with the incomplete state of his...

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Okay, let's clear something up right away. This isn't a novel with characters and a plot twist. The 'story' here is the incredible journey of an idea. The book explains Fourier's big insight: that you can take any messy, complicated, repeating shape or signal—like a heartbeat, a sound wave, or the temperature change over a day—and rebuild it perfectly using only simple, smooth sine and cosine waves. It then shows how to apply this powerful tool to solve real problems in three dimensions: on spheres (like modeling climate), in cylinders (like analyzing pipes), and in more general shapes.

Why You Should Read It

I know, it sounds technical. But the magic is in the 'why.' This book connects the dots between pure math and the physical universe in a way that feels almost like detective work. You start to see the hidden mathematical skeleton in everything. The writing is from another era, so it demands your focus, but there's a beautiful clarity to it. It's like getting a masterclass from a brilliant, patient teacher who assumes you're genuinely interested in understanding, not just memorizing formulas.

Final Verdict

This is not for the casual reader looking for a bedtime story. It's a book for the curious mind. If you're a student in physics or engineering hungry for the historical roots of your field, a programmer working with signals or graphics, or just an avid learner who gets a thrill from understanding fundamental ideas that shape our technology, this is a classic worth tackling. Think of it as a challenging but deeply rewarding hike for your brain.



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Matthew Wright
1 year ago

Beautifully written.

John Anderson
1 year ago

Helped me clear up some confusion on the topic.

Emma Rodriguez
1 year ago

Wow.

Thomas Torres
6 days ago

A must-have for anyone studying this subject.

Melissa Thomas
2 months ago

The layout is very easy on the eyes.

4.5
4.5 out of 5 (8 User reviews )

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