Book of Lemmas

The Book of Lemmas is a book attributed to Archimedes by Thābit ibn Qurra, though the authorship of the book is questionable. It consists of fifteen propositions (lemmas) on circles.

The Book of Lemmas was first introduced in Arabic by Thābit ibn Qurra; he attributed the work to Archimedes. In 1661, the Arabic manuscript was translated into Latin by Abraham Ecchellensis and edited by Giovanni A. Borelli. The Latin version was published under the name Liber Assumptorum.T. L. Heath translated Heiburg's Latin work into English in his The Works of Archimedes.

The original authorship of the Book of Lemmas has been in question because in proposition four, the book refers to Archimedes in third person; however, it has been suggested that it may have been added by the translator. Another possibility is that the Book of Lemmas may be a collection of propositions by Archimedes later collected by a Greek writer.

The Book of Lemmas introduces several new geometrical figures.

Archimedes' first introduced the arbelos in proposition four of his book:

The figure is used in propositions four through eight. In propositions five, Archimedes introduces the Archimedes' twin circles, and in proposition eight, he makes use what would be the Pappus chain, formally introduced by Pappus of Alexandria.

Archimedes' first introduced the salinon in proposition fourteen of his book:

Archimedes proved that the salinon and the circle are equal in area.

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