Kirby’s Method of Perspective was called Dr. Brook Taylor’s Method of Perspective Made Easy. So who was Brook Taylor, and why did his method of perspective need to be made easy? In this post I will answer the first question.
Taylor’s name is known to generations of calculus students through Taylor series. A Taylor series represents a function as an infinite series with coefficients calculated from the derivatives of the function at a particular point. If the series converges nicely, it allows you to approximate the value of a function by a simple finite sum. Back in the early 18th century (Taylor’s theorem is from 1715), using infinite series as a way to deal with intractable functions was a popular topic, although the properties of infinite series were not completely understood. However, Brook Taylor (1685—1731) did a lot more than prove that one theorem. He wrote his first paper while still an undergraduate at Cambridge, and belonged to a circle of mathematicians who corresponded, and sometimes challenged each other with problems, but did not see a need always to publish their results, and certainly not in a timely manner.
Taylor was elected to the Royal Society in 1712, and became its secretary in 1714. He then published a stream of papers, mostly in the Philosophical Transactions of the Royal Society, on a wide variety of subjects, not all of which would be considered mathematics today. In 1715 he published two books, his major works. The first was Methodus Incrementorum Directa et Inversa, the first book on the calculus of finite differences, which included Taylor’s Theorem (actually, he proved two versions of this result). The other was Linear Perspective, about which we shall have more to say later.
Taylor’s personal life was marred with tragedy and ill-health. In 1721, he married a Miss Brydges. His father did not approve of the match and broke off relations with his son. The unfortunate Mrs. Taylor died in 1723 in childbirth with their first-born, who also did not survive. Her death led to a rapprochement with his father, and in 1725 he married again, to Sabetta Sawbridge, with his father’s approval. In 1729, he inherited an estate from his father, but in 1730 his wife died, again in childbirth. This time, the baby, Elizabeth, survived, but Taylor’s own fragile health gave out and he died at Somerset House in 1731. His poor orphan grew up and married Sir William Young, Bart. Kirby dedicated a plate to her.