In Padua his work took a more purely mathematical turn, and resulted in a book ‘pursuing a hint suggested by his own thoughts,’ of which he had only a few copies printed. It was entitled _Vera Circuli et Hyperboles Quadratura_, and Montucla in writing of it says that the title is misleading, and that the author does not claim, except approximately, through his infinite converging series to find the square of a circle or hyperbola. Collins, to whom a copy was sent, read part of it before the Royal Society. Lord Brouncker and Dr Wallis were enthusiastic in its praise, and under such encouragement Gregorie published it along with some fresh matter under the title of _Geometriae Pars Universalis inservieus Quantitatum Curvarum Transmutationi et Mensurae_. The book came out in Padua with the permission of the State of Venice, and was a great success. Before its publication the Royal Society showed their appreciation of it by making Gregorie a Fellow. This was in January 1668; in March he was still in Padua, but in all the confusion of departure, and not long after he returned to Scotland, and back to his much loved Aberdeenshire, where happiness was awaiting him on all sides. There was Kinairdy to visit with its many charms, and there was Aberdeen, and at Elrick there was a cousin who was after all, it is easy to guess, the end of his journey. This was Mary Burnet, the widow of John Burnet, who to his great joy consented to become his wife, and was married to him in 1669. The astronomer found love-making dreadfully time-consuming, and vaguely regretted it. You see, it was apt to interrupt his correspondence with Huygens and Halley, with Newton and Collins, with Dr Wallis and Lord Brouncker. Here is a pathetic letter from him written in the early part of the year to one of his mathematical correspondents—‘I have several things in my head as yet only committed to memory, neither can I dispose of myself to write them in order and method till I have my mind free from other cares.’ His wife was only twenty-three, although this was her second marriage, and even when after Mr Gregorie’s death she married Mr Ædis, she was still young and very beautiful. A rare piece of her work remains in the tapestries which adorn the Magistrates’ Gallery in St Nicholas Church in Aberdeen. Susannah and Jephtha’s daughter were her subjects, and there they are still, looking out of their panels, from the midst of their beautiful blue and green landscapes, with the rigid uncertainty of tapestry portraits. Bailie Burnet would have been proud if he could have foreseen what a combination of ecclesiastical and civic honour was to fall to his wife’s needlework.