The Circle of Knowledge is an informative book that was designed in 1917, to be both inspiring and entertaining. The book represents the modern, progressive spirit which fits that time, in its forms of expression and its editorship. The purpose of this work is to answer the why, who, what, when, where, how of the wide majority of curious minds, both young and adult, and encourage them to raise further questions. Special measures were taken in creating this work to isolate essentials from non-essentials; to differentiate human interest subjects of universal significance from those of little concern; to deliver living truths instead of dead vocabulary; and finally, to bring the whole within the knowledge of the intermediate reader, without regard to age, in an acceptable and exciting form. The use of visual outlines and tables; maps, drawings, and diagrams; the illustrated works of great painters, sculptors, and architects all are used to give the reader the valuable and cultural knowledge of past and present.

This publication includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728–1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations are accompanied by a contextualised study of each of these works and provide an overview of Lambert’s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.