# 阿基米德

《沉思的阿基米德》（1620年費地英語Domenico Fetti畫作）

## 傳記

「阿基米德傳」的標準版本，在他死後許久才由古羅馬歷史學家寫就。敘拉古攻城由波利比烏斯在記於其《通史》（英文：「Universal History」）中，大約在阿基米德死後70年寫就，此後被普魯塔克和蒂托·李維引用。此文主要着墨與其為保衛城市所建的「戰爭機器」，未有詳述阿基米德為人。[14]

## 著作

• 《》
• 《》：此書討論物體的浮力，研究了旋轉拋物體在流體中的穩定性
• 《》：此書從幾個定義和公理出發，推出關於球與圓柱面積和體積等50多個命題
• 《》：此書從幾個基本假設出發，通過嚴格的幾何方法論證力學原理，並求出若干平面圖形的重心
• 數沙者英語The Sand Reckoner》：此書主要講述設計一種可以表示任何大數目的方法
• 槓桿論
• 劈錐曲面體與球體論
• 《》
• 螺線論英語On Spirals

## 註釋

a. ^ In the preface to On Spirals addressed to Dositheus of Pelusium, Archimedes says that "many years have elapsed since Conon's death." Conon of Samos lived c. 280–220 BC, suggesting that Archimedes may have been an older man when writing some of his works.

b. ^ The treatises by Archimedes known to exist only through references in the works of other authors are: On Sphere-Making and a work on polyhedra mentioned by Pappus of Alexandria; Catoptrica, a work on optics mentioned by Theon of Alexandria; Principles, addressed to Zeuxippus and explaining the number system used in The Sand Reckoner; On Balances and Levers; On Centers of Gravity; On the Calendar. Of the surviving works by Archimedes, T. L. Heath offers the following suggestion as to the order in which they were written: On the Equilibrium of Planes I, The Quadrature of the Parabola, On the Equilibrium of Planes II, On the Sphere and the Cylinder I, II, On Spirals, On Conoids and Spheroids, On Floating Bodies I, II, On the Measurement of a Circle, The Sand Reckoner.

c. ^ Boyer, Carl Benjamin A History of Mathematics (1991) ISBN 0-471-54397-7 "Arabic scholars inform us that the familiar area formula for a triangle in terms of its three sides, usually known as Heron's formula — k = s(s − a)(s − b)(s − c), where s is the semiperimeter — was known to Archimedes several centuries before Heron lived. Arabic scholars also attribute to Archimedes the 'theorem on the broken chord' ... Archimedes is reported by the Arabs to have given several proofs of the theorem."

d. ^ "It was usual to smear the seams or even the whole hull with pitch or with pitch and wax". In Νεκρικοὶ Διάλογοι (Dialogues of the Dead), Lucian refers to coating the seams of a skiff with wax, a reference to pitch (tar) or wax.[17]

## 參考文獻

1. ^ Knorr, Wilbur R. Archimedes and the spirals: The heuristic background. (愛思唯爾). 1978, 5 (1): 43–75. "To be sure, Pappus does twice mention the theorem on the tangent to the spiral [IV, 36, 54]. But in both instances the issue is Archimedes' inappropriate use of a "solid neusis," that is, of a construction involving the sections of solids, in the solution of a plane problem. Yet Pappus' own resolution of the difficulty [IV, 54] is by his own classification a "solid" method, as it makes use of conic sections." (page 48)
2. ^ Archimedes (c.287 - c.212 BC). BBC History. [2012-06-07]. （原始內容存檔於2018-10-04）.
3. ^ Calinger, Ronald. A Contextual History of Mathematics. Prentice-Hall. 1999: 150. ISBN 0-02-318285-7. Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287 212 BC), the most original and profound mathematician of antiquity.
4. ^ Archimedes of Syracuse. The MacTutor History of Mathematics archive. 1999年1月 [2008-06-09]. （原始內容存檔於2013-06-20）.
5. ^ Bell, Eric Temple. Men of mathematics 1st Touchstone. Simon & Schuster. 1986-10-15. ISBN 9780671628185.
6. ^ , Works of Archimedes, 1897
7. ^ 普魯塔克. Parallel Lives Complete e-text from Gutenberg.org. 古騰堡計劃. [2007-07-23]. （原始內容存檔於2007-07-11）.
8. ^ O'Connor, J.J.; Robertson, E.F. Archimedes of Syracuse. University of St Andrews. [2007-01-02]. （原始內容存檔於2007-02-06）.
9. ^ The Death of Archimedes: Illustrations. math.nyu.edu. New York University. [2018-11-17]. （原始內容存檔於2015-09-29）.
10. Rorres, Chris. Death of Archimedes: Sources. Courant Institute of Mathematical Sciences. [2007-01-02]. （原始內容存檔於2006-12-10）.
11. ^ Mary Jaeger. Archimedes and the Roman Imagination, p. 113.
12. ^ Rorres, Chris. Tomb of Archimedes: Sources. Courant Institute of Mathematical Sciences. [2007-01-02]. （原始內容存檔於2006-12-09）.
13. ^ Rorres, Chris. Tomb of Archimedes – Illustrations. Courant Institute of Mathematical Sciences. [2011-03-15]. （原始內容存檔於2019-05-02）.
14. ^ Rorres, Chris. Siege of Syracuse. Courant Institute of Mathematical Sciences. [2007-07-23]. （原始內容存檔於9 June 2007）.
15. ^ 希思, T.L. 《阿基米德全集（修订版）》. 陝西科學技術出版社. 2010年12月. ISBN 978-7-5369-2342-3.
16. ^ 阿基米德原著 《量圓》 《中國數學史大系》 副卷第一 第二章 第三編 希臘 197-203頁
17. ^ Casson, Lionel. Ships and seamanship in the ancient world. Baltimore: The Johns Hopkins University Press. 1995: 211–212 [2018-11-17]. ISBN 978-0-8018-5130-8. （原始內容存檔於2021-04-17）.

## 延伸閱讀

http://www.wilbourhall.org頁面存檔備份，存於互聯網檔案館） 《阿基米德著作》Heiberg版的PDF掃描件，現屬公共領域]