a name given to certain lines used for the transformation of figures, so called from Roberval the inventor of them.

These lines are the boundaries of lines infinitely ex- tended in length, yet equal to other spaces which are terminated on all sides.

It is observed by the abbot Gallois, that the method of transforming figures which is explained at the end of Roberval's treatise of Indivisibles, was the same with that afterwards published by James Gregory, in his Geometria Universalis, and also by Dr Barrow in his Lectiones Geometricae; and that it appears from Torri- celli's letter, that Roberval was the inventor of this me- thod of transforming figures, by means of certain lines, called by Torricelli, for that reason, Robervallian lines.

The same author adds, that J. Gregory probably first learned this method at Padua in the year 1668; for the method was known in Italy in 1646, although the book was not published till 1692.

David Gregory endeavoured to refute this account, in vindication of his uncle James, whose answer appeared in the Phil. Trans. for 1694, and the abbot rejoined in the Memoirs of the French Academy for 1703; so that it remains in a state of uncertainty to which of the two we are to ascribe the invention.