[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 ):-
... 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 on the topic Optica Promota. In the preface he writes:-
Moved by a certain youthful ardour and emboldened by the invention of the elliptic inequality, I have girded myself with these optical speculations, chief among which is the demonstration of the telescope.
The reader may not understand Gregory's reference to "the elliptic inequality" which in fact refers to Kepler's discoveries. Gregory, in Optica Promota, describes the first practical reflecting telescope now called the Gregorian telescope.
The book begins with 5 postulates and 37 definitions. He then gives 59 theorems on reflection and refraction of light. There follows propositions on mathematical astronomy discussing parallax, transits and elliptical orbits. Next Gregory gives details of his invention of a reflecting telescope. A primary concave parabolic mirror converges the light to one focus of a concave ellipsoidal mirror. Reflection of light rays from its surface converge to the ellipsoid's second focus which is behind the main mirror. There is a central hole in the main mirror through which the light passes and is brought to a focus by an eyepiece lens. The tube of the Gregorian telescope is thus shorter than the sum of the focal lengths of the two mirrors. His novel idea was to use both mirrors and lenses in his telescope. He showed that the combination would work more effectively than a telescope which used only mirrors or used only lenses.
The book was only a theoretical description of the telescope for at this stage one had not been constructed. Gregory remarks in the book :-
... on his lack of skill in the technique of lens and mirror making ...
In 1663 Gregory went to London. There he met Collins and a lifelong friendship began. One of Gregory's aims was to have Optica Promota published and he achieved this. His other aim was to find someone who could construct a telescope to the design set out in his book. Collins advised him to seek the help of a leading optician...