He is also notable for being the inaugural holder of the prestigious Lucasian Professorship of Mathematics, a post later held by his student, Isaac Newton.

In 1624, Thomas married Ann, daughter of William Buggin of North Cray, Kent and their son Isaac was born in 1630.

From this marriage, he had at least one daughter, Elizabeth (born 1641), and a son, Thomas, who apprenticed to Edward Miller, skinner, and won his release in 1647, emigrating to Barbados in 1680.

[3] Isaac went to school first at Charterhouse (where he was so turbulent and pugnacious that his father was heard to pray that if it pleased God to take any of his children he could best spare Isaac), and subsequently to Felsted School, where he settled and learned under the brilliant puritan Headmaster Martin Holbeach who ten years previously had educated John Wallis.

[4] Having learnt Greek, Hebrew, Latin and logic at Felsted, in preparation for university studies,[5] he continued his education at Trinity College, Cambridge; he enrolled there because of an offer of support from an unspecified member of the Walpole family, "an offer that was perhaps prompted by the Walpoles' sympathy for Barrow's adherence to the Royalist cause.

He is described as "low in stature, lean, and of a pale complexion," slovenly in his dress, and having a committed and long-standing habit of tobacco use (an inveterate smoker).

He was an altogether impressive personage of the time, having lived a blameless life in which he exercised his conduct with due care and conscientiousness.

He was made a Doctor of Divinity by Royal mandate in 1670, and two years later Master of Trinity College (1672), where he founded the library, and held the post until his death.

In 1675 he published an edition with numerous comments of the first four books of the On Conic Sections of Apollonius of Perga, and of the extant works of Archimedes and Theodosius of Bithynia.

Barrow was the first to find the integral of the secant function in closed form, thereby proving a conjecture that was well-known at the time.

Barrow applied this method to the curves It will be sufficient here to take as an illustration the simpler case of the parabola y2 = px.