a name given to certain lines used for the transformation of figures; thus called from their inventor Roberval, an eminent French mathematician, who died in 1675, aged 76 years. These lines bound spaces that are infinitely extended in length, which are nevertheless equal to other spaces that are terminated on all sides.

The Abbot Gallois, in the Memoirs of the Royal Academy, anno 1693, observes, that the method of transforming figures, explained at the latter end of Roberval's Treatise of Indivisibles, was the same with that afterwards published by James Gregory, in his Geometria Universalis, and also by Barrow in his Lectiones Geometricae; and that, by a letter of Torricelli, it appears, that Roberval was the inventor of this manner of transforming figures, by means of certain lines, which Torricelli therefore called Robervallian lines. He adds, that it is highly probable that J. Gregory first learned the method in the journey he made to Padua in 1668, the method itself having been known in Italy from the year 1646, though the book was not published till the year 1692.

This account has been, we think, completely refuted by David Gregory in his vindication of his uncle, published in the Philosophical Transactions of 1694. The Abbot, however, rejoined in the Memoirs of the French Academy of 1703; and it is but fair to observe, that Dr Hutton, speaking of the controversy, expresses himself as if he thought it undecided.