[John Gregory] was a man of courage and foresight but was not conspicuous for outstanding intellectual gifts ...
James seems to have inherited his genius through his mother's side of the family. Janet Anderson's brother, Alexander Anderson, was a pupil of Vi¨¨te. He acted as an editor for Vi¨¨te and fully incorporated Vi¨¨te's ideas into his own teaching in Paris. James was the youngest of his parents three children. He had two older brothers Alexander (the eldest) and David, and there was an age gap of ten years between James and David.
James learnt mathematics first from his mother who taught him geometry. His father John Gregory died in 1651 when James was thirteen and at this stage James's education was taken over by his brother David who was about 23 at the time. James was given Euclid's Elements to study and he found this quite an easy task. He attended Grammar School and then proceeded to university, studying at Marischal College in Aberdeen.
Gregory's health was poor in his youth. He suffered for about eighteen months from the quartan fever which is a fever which recurs at approximately 72-hour intervals. Once he had shaken off this problem his health was good, however, and he wrote some years later that the quartan fever (see for example [20]):-
... is a disease I am happily acquainted with, for since that time I never had the least indisposition; nevertheless that I was of a tender and sickly constitution formerly.
Gregory began to study optics and the construction of telescopes. Encouraged by his brother David, he wrote a book