This work was originally published anonymously.

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton (...) himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia. (shrink)

Pascal has long been regarded as one of the most brilliant and versatile of the world's thinkers. This chronological and carefully annotated survey explores the full range of his intellectual achievements. It also includes a chapter on his life. Renowned as mathematician, physicist, scourge of Jesuit moral theology, and staunch, though perceptive, champion of Christianity, Pascal devoted himself in full measure to science and religion. His work on conic sections, the probability calculus, number theory, cycloid curves and hydrostatics is considered (...) in detail. So, too, is his notorious prize competition on the cycloid and its aftermath. The author's analysis of the Provincial Letters and the unfinished Thoughts emphasises their many distinctive features, both thematic and technical. He discusses Pascal's lesser known works, all of them pertaining to theology or the philosophy of religion. Blaise Pascal contains a chapter on the famous wager argument and a wide-ranging bibliography. (shrink)

In 1813, J.-V. Poncelet discovered that if there exists a polygon of n-sides, which is inscribed in a given conic and circumscribed about another conic, then infinitely many such polygons exist. This theorem became known as Poncelet’s porism, and the related polygons were called Poncelet’s polygons. In this article, we trace the history of the research about the existence of such polygons, from the “prehistorical” work of W. Chapple, of the middle of the eighteenth century, to the modern approach of (...) P. Griffiths in the late 1970s, and beyond. For reasons of space, the article has been divided into two parts, the second of which will appear in the next issue of this journal. (shrink)

This is an attempt to explain Kepler’s invention of the first “non-cone-based” system of conics, and to put it into a historical perspective.

In his Brouillon Project on conic sections, Girard Desargues studies the notion of traversale, which generalizes that of diameter introduced by Apollonius. One often reads that it is equivalent to the notion of polar, a concept that emerged in the beginning of 19th century. In this article we shall study in great detail the developments around that notion in the middle part of the Brouillon project. We shall in particular show, using the notes added by Desargues after the first draft (...) was written, how here arises a new theory, that of the polarity associated to a conic section. We shall show that besides a natural correspondance between points and lines, Desargues has understood that a conic induces on every line in its plane an involution, and how he progressively handles the considerable conceptual difficulties he has to deal with when trying to explain clearly his novative ideas. (shrink)