Über die Picard'schen Gruppen aus dem Zahlkörper der dritten und der vierten…

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Bohler, Otto Bohler, Otto
German
Okay, hear me out. I just finished this incredibly niche but weirdly fascinating book about abstract algebra from 1905. It's called something like 'On the Picard Groups from the Number Fields of the Third and Fourth...' by Otto Bohler. Think of it as a historical detective story, but the clues are complex mathematical objects called 'Picard groups' in specific types of number fields. The central mystery is figuring out the structure and properties of these groups, which are like hidden blueprints within the number system itself. Bohler is basically trying to map uncharted territory in pure math. It's not a casual read, but if you love the history of ideas or seeing how foundational math problems were tackled over a century ago, it's a remarkable little time capsule. It feels like peeking over the shoulder of a mathematician from another era.
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Chapter I. THE CASE OF THE LAST TWELVE VERSES OF S. MARK’S GOSPEL, STATED. Chapter II. THE HOSTILE VERDICT OF BIBLICAL CRITICS SHEWN TO BE QUITE OF RECENT DATE. Chapter III. THE EARLY FATHERS APPEALED TO, AND OBSERVED TO BEAR FAVOURABLE WITNESS. Chapter IV. THE EARLY VERSIONS EXAMINED, AND FOUND TO YIELD UNFALTERING TESTIMONY TO THE GENUINENESS OF THESE VERSES. Chapter V. THE ALLEGED HOSTILE WITNESS OF CERTAIN OF THE EARLY FATHERS PROVED TO BE AN IMAGINATION OF THE CRITICS. Chapter VI. MANUSCRIPT TESTIMONY SHEWN TO BE OVERWHELMINGLY IN FAVOUR OF THESE VERSES.—PART I. Chapter VII. MANUSCRIPT TESTIMONY SHEWN TO BE OVERWHELMINGLY IN FAVOUR OF THESE VERSES.—PART II. Chapter VIII. THE PURPORT OF ANCIENT SCHOLIA, AND NOTES IN MSS. ON THE SUBJECT OF THESE VERSES, SHEWN TO BE THE REVERSE OF WHAT IS COMMONLY SUPPOSED. Chapter IX. INTERNAL EVIDENCE DEMONSTRATED TO BE THE VERY REVERSE OF UNFAVOURABLE TO THESE VERSES. Chapter X. THE TESTIMONY OF THE LECTIONARIES SHEWN TO BE ABSOLUTELY DECISIVE AS TO THE GENUINENESS OF THESE VERSES. Chapter XI. THE OMISSION OF THESE TWELVE VERSES IN CERTAIN ANCIENT COPIES OF THE GOSPELS, EXPLAINED AND ACCOUNTED FOR. Chapter XII. GENERAL REVIEW OF THE QUESTION: SUMMARY OF THE EVIDENCE; AND CONCLUSION OF THE WHOLE SUBJECT. APPENDIX (A). APPENDIX (B). APPENDIX (C). APPENDIX (D). APPENDIX (E). APPENDIX (F). APPENDIX (G). APPENDIX (H). POSTSCRIPT. L’ENVOY GENERAL INDEX. Footnotes THE CODEX [Transcriber’s Note: This e-book contains much Greek text which is central to the point of the book. In the ASCII versions of the e-book, the Greek is transliterated into Roman letters, which do not perfectly represent the Greek original; especially, accent and breathing marks do not transliterate. The HTML and PDF versions contain the true Greek text of the original book.] On the next page is exhibited an _exact Fac-simile_, obtained by Photography, of fol. 28 _b_ of the CODEX SINAITICUS at S. Petersburg, (Tischendorf’s א): shewing the abrupt termination of S. Mark’s Gospel at the words ΕΦΟΒΟΥΝΤΟ ΓΑΡ (chap. xvi. 8), as explained at p. 70, and pp. 86-8. The original Photograph, which is here reproduced on a diminished scale, measures in height full fourteen inches and one-eighth; in breadth, full thirteen inches. It was procured for me through the friendly and zealous offices of the English Chaplain at S. Petersburg, the Rev. A. S. Thompson, B.D.; by favour of the Keeper of the Imperial Library, who has my hearty thanks for his liberality and consideration. It will be perceived that the text begins at S. Mark xvi. 2, and ends with the first words of S. Luke i. 18. Up to this hour, every endeavour to obtain a Photograph of the corresponding page of the CODEX VATICANUS, B, (No. 1209, in the Vatican,) has proved unavailing. If the present Vindication of the genuineness of Twelve Verses of the everlasting Gospel should have the good fortune to approve itself to his Holiness, POPE PIUS IX., let me be permitted in this unadorned and unusual manner,—(to which I would fain add some circumstance of respectful ceremony if I knew how,)—very humbly to entreat his Holiness to allow me to possess a Photograph, corresponding in size with the original, of the page of CODEX B (it is numbered fol. 1303,) which exhibits the abrupt termination of the Gospel according to S. Mark. J. W. B. ORIEL COLLEGE, OXFORD, _June 14, 1871_. [[Illustration: Codex Sinaiticus facsimile page.]] [[Illustration: Codex Sinaiticus facsimile page.]] "MY WORD WILL NOT PASS AWAY" ἀμὴν γὰρ λέγω ὑμῖν, ἕως ἂν παρέλθῃ ὁ οὐρανὸς καὶ ἡ γῆ, ἰῶτα ἓν ἢ μία κεραία οὐ μὴ παρέλθῃ ἀπὸ τοῦ νόμου, ἕως ἂν πάντα...

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Let's be clear from the start: this isn't a novel. Otto Bohler's 1905 work is a specialized mathematics paper-turned-book, written in German, focused on a deep area of algebraic number theory. There are no characters or plot twists in the traditional sense.

The Story

The 'story' here is an intellectual pursuit. Bohler sets out to investigate the structure of what are called Picard groups (or ideal class groups) within certain algebraic number fields—specifically those related to cube roots and fourth roots. Imagine numbers not just as points on a line, but as part of a rich, multi-dimensional landscape. The Picard group is a key that helps mathematicians understand the unique factorization properties within that landscape. Bohler's work involves calculating, proving, and classifying these groups, trying to pin down their size and behavior. It's a foundational piece of the puzzle in understanding the architecture of numbers.

Why You Should Read It

You read this for the historical atmosphere, not for light entertainment. There's a quiet thrill in seeing raw, early 20th-century mathematical reasoning on the page. You witness the building blocks of a theory that would become much more polished later. It’s like looking at the original sketches for a now-famous masterpiece. The dedication to pure, abstract problem-solving is its own kind of narrative—one of curiosity and precision.

Final Verdict

This is a book for a very specific reader. It's perfect for historians of mathematics, graduate students in number theory who want to see the origins of their field, or anyone with a strong math background who enjoys reading primary sources. It's not for the casual reader or someone looking for a popular science book. Think of it as an artifact: a direct line to the mind of a mathematician working on the frontiers of knowledge over a hundred years ago.



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