公元前3世紀末，正是羅馬共和國與迦太基，為了爭奪西西里島的霸權而開戰的時期。地處西西里島的敘拉古一直都是投靠羅馬，但是公元前216年迦太基大敗羅馬軍隊，敘拉古的新國王希罗尼姆斯（英语：Hieronymus of Syracuse）（希倫二世的孫子），立即見風轉舵與迦太基結盟，羅馬共和國於是派馬克盧斯將軍領軍從海路和陸路同時進攻敘拉古。國難當前，保家衛國的責任感促使阿基米德奮起抗敵，於是他絞盡腦汁，日以繼夜的發明各種禦敵武器。
西塞羅在他的对话录《国家论》中曾大致提到过阿基米德，这部对话录描述了一段发生在公元前129年的虚构的谈话。公元前212年，据说在占领敘拉古之后，馬庫斯·克勞狄斯·馬塞勒斯将军将两部用于天文学的机械装置带回了罗马，这两部装置显示了太阳，月亮和五个行星的运动。西塞羅还提到了由泰勒斯和欧多克索斯设计的类似装置。对话录表明，马塞勒斯将其中一部机器据为已有，另外一部则捐赠给了罗马的功德庙。马塞勒斯持有的那一部后来被公开展示，据西塞罗说，加勒斯向斐勒斯（英语：Lucius Furius Philus）演示的过程被后者记录如下
a.^ In the preface toOn Spirals addressed to Dositheus of Pelusium, Archimedes says that "many years have elapsed since Conon's death."Conon of Samos livedc. 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 byTheon of Alexandria;Principles, addressed to Zeuxippus and explaining the number system used inThe 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 BenjaminA History of Mathematics (1991)ISBN0-471-54397-7 "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), wheres is the semiperimeter — was known to Archimedes several centuries before Heron lived. Arabic scholars also attribute to Archimedes the 'theorem on the brokenchord' ... 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 askiff with wax, a reference to pitch (tar) or wax.[17]
^Knorr, Wilbur R. Archimedes and the spirals: The heuristic background.Historia Mathematica（英语：Historia Mathematica） (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)
^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.
^Archimedes of Syracuse. The MacTutor History of Mathematics archive. 1999年1月 [2008-06-09]. （原始内容存档于2013-06-20）.
Clagett, Marshall. Archimedes in the Middle Ages5 vols. Madison, WI: University of Wisconsin Press. 1964–1984.
爱德华·扬·戴克斯特豪斯. Archimedes. Princeton University Press, Princeton. 1987.ISBN 0-691-08421-1. Republished translation of the 1938 study of Archimedes and his works by an historian of science.
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