Tag Archives: Method of Perspective

Rev. Henry Putman

The Rev. Henry Putman (1725—1797) is an astonishingly obscure person, especially for someone who was minister of the Dutch Reformed Church at Austin Friars for 48 years and a Fellow of the Royal Society for thirty. He doesn’t rate a mention in the history of Austin Friars by J. Lindeboom, except in the list of ministers in the Appendix. He is presumably covered by this quote, “The persons and the activity of the ministers during the centuries following the turbulent early years, do not really call for comment. Though certainly faithful shepherds and teachers they are not remarkable for their outstanding learning or ecclesiastical achievements” (Lindeboom, 162).

His obituary in the Gentleman’s Magazine was somewhat kinder, declaring that, “His learning and piety were eminently conspicuous” and “He enjoyed the friendship of the most respectable of the established Clergy”. “Few men”, it continues, “have passed through this malevolent world better beloved and less censured than he.”

He appears not to have published any works either in or out of the Royal Society and the only note of him is in signing in support of some new members, most notably that of Andreas Joseph Planta, where he signed next to Joshua Kirby.

After his death, his library was sold off in a large sale by John White. However, it was mixed in with other books, “Rare, Splendid, and Valuable books… including the entire libraries of the Rev. Harvey Spragg…also of the Rev. Henry Putman”.

The catalogue does not identify which books came from which collection, but the sale did include a 3-volume collection of Kirby’s Method of Perspective, Perspective of Architecture, and his Architectonic Sector, listed as from 1768, the year after Putman and Kirby were both elected to the Royal Society, so it is quite possible that Kirby and Putman were friends.

Moens (1888) recorded Putman’s memorial inscription in the church he had the care of for so long:

Hier legt begraven het lyk van den Wel-Eerwaarden HENRIK PUTMAN lid der Koninglyke Maatschappye van Wetenschappen te London en oudste Predikant deezer Gemeente, Gebooren te Amsterdam den 8sten April 1725, Overleeden te London den lsten Maart, 1797, na dat hy aldaar ruim 46 Jaaren het Leeraars ambt had waargenomen.

Presumably this memorial also no longer exists, as the church was bombed during the Blitz.

In the night of the 15th to the 16th October, 1940, during one of the heavy air bombardments of London, a landmine attached to a parachute, sucked into the space enclosed by the higher office buildings surrounding the church, fell on Austin Friars. The explosion completely destroyed the church. A few pages from the Bible which was in the pulpit, some fragments of the walls and of the monuments, were all that remained of the edifice, which was reduced to a mountainous heap of rubble and dust. (Lindeboom, 191)

If I find out more, I will let you know.

Lindeboom, J. (1950). Austin Friars: History of the Dutch Reformed Church in London 1550—1950. The Hague: Martinus Nijhoff.

Moens, W.J.C. (1884). The Marriage, Baptismal, and Burial Registers, 1571 to 1874, and Monumental Inscriptions, of the Dutch Reformed Church, Austin Friars, London: With a Short Account of the Strangers and Their Churches. London: King and Sons.

Kirby Live Again!

I am giving a talk at MathFest in Hartford on August 1.  Intended for a wide audience, this talk will show how Kirby’s networks of subscribers evolved over the publication of his series of books between 1748 and 1754 to trace the patronage circles that ended with Kirby’s appointment as tutor in perspective to the then Prince of Wales.

Here’s the abstract:

How Brook Taylor Got Joshua Kirby a Position

In 1748, Joshua Kirby was a provincial coach-painter in Ipswich, Suffolk. By 1755 he was tutor in perspective to the Prince of Wales (the future George III). In between, he published Dr. Brook Taylor’s Method of Perspective Made Easy, a book that aimed to explain Brook Taylor’s notoriously difficult Linear Perspective. Using the subscription lists of the three works he published during this period, we trace how Kirby’s expanding social networks brought him to the notice of those in power.

Justly esteemed eminent masters

An anonymous essay published in the Universal Magazine in November 1748 on The Art of Painting contained, besides technical advice, a brief list “of those painters of our nation, now living … [who] are justly esteemed eminent masters”. The list is interesting for providing a snapshot at an early period. Both Gainsborough and Reynolds, then young and largely unknown, make the cut. The list is as follows:

Austin, Browne, Barrat, Blakey, Crank, Dandridge, Eccard, Ellys, Fry, Gainsborough, Goupy, Goodwin, Green, Grilsieir, de Groit, Hayman, Hogarth, Hoar, Hone, Hymore, Hudson, Jenkins, Knapton, Lambert, Lens, Mathias, Monamie, Murry, Penny, Pine, Pond, Ramsey, Reynolds, Scot, Shackleton, Seymour, Soldy, Somers, Spencer, Smith, Toms. The two Vanhakens, Van Blake, Van Diest, Vanderbank, Vandergucht, Verelst. Wills, Wotton, Worsdale, Williams, Wood, Wilks, Wilson, Wollaston. Zink.

It would be fair to say that their reputations have diverged in the intervening centuries.

Seven years later, not all of these artists were alive, or living in England, but of those that were, some nineteen subscribed to Kirby’s Method of Perspective.

Brook Taylor’s Linear Perspective

Joshua Kirby claimed in his Method of Perspective that he was making Brook Taylor’s work easier to understand for gentlemen and practitioners. Brook Taylor’s Linear Perspective was published in 1715, with a revised edition in 1719. His work is austere, rigorous and mathematically challenging. Perhaps as a result, it went largely unread, and, even after it was popularized by Kirby, Highmore, and others, it seems to have been more appreciated than read. In recent scholarship, Kirsti Andersen has studied Taylor’s work most deeply.

When Brook Taylor wrote Linear Perspective, few in Britain had gone before him, and certainly not attempting a coherent theoretical approach; in this respect Britain was far behind the Continent. The inadequacy of his predecessors caused Taylor to sweep away the old vocabulary and replace it with his own set of terms and concepts, including linear perspective. As he wrote in his Preface,

In this Treatise I have endeavour’d to render the Art of Perspective more general, and more easy, than has yet been done. In order to do this, I find it necessary to lay aside the common Terms of Art, which have hitherto been used, such as Horizontal Line, Points of Distance, &c. and to use new ones of my own; such as seem to be more significant of the Things they express, and more agreeable to the general Notion I have formed to my self of this Subject.

He succeeded in his aim of rendering the theory of perspective `more general’, but perhaps not `more easy’ to mere mortals. Like many mathematicians, his definition of `easy’ did not match that of the general populace. His constructions are simple, they use few ideas and few construction lines, but they require a great deal of mathematical maturity and do not lend themselves easily to actual practice.

The first clue to his generality lies in his getting rid of the horizon line. Taylor inhabited a Euclidean geometrical world, not a Cartesian one. To him,

Perspective is the Art of drawing on a Plane the Appearances of any Figures, by the Rules of Geometry.

Definition I. The Center of the Picture is that Point where a Line from the Spectator’s Eye cuts it …at Right Angles.

Taylor has three ingredients: a spectator, a picture plane, and the original plane of the objects to be represented. He sees no reason why the picture plane should be perpendicular to the ground plane, and hence, he has no need of horizons and horizontals. Here’s his illustration, showing the ‘leaning plane’.

I just love his approach, but then I don’t have to use it to paint. He introduces the terms vanishing point and vanishing line, and treats the one and two-dimensional cases as on equal footing in a manner which is wonderful to behold. Many of Taylor’s propositions take various pieces as given (in the Euclidean sense) and require finding the remaining points. The proofs unfold in a Euclidean manner, and there are practically no examples. He also, as you would expect, leans heavily on ratio theory. Here is Theorem 2:

Any Line in the Representation of a Figure parallel to the Picture, is to its Original Line, as the Principal Distance is to the Distance between the Spectator’s Eye, and the Plane of the Original Figure.

And here is Proposition 10:

Having given the Center and Distance of the Picture, and the Vanishing Line of a Plane, and the Vanishing Point of the Intersection of that Plane, with another Plane perpendicular to it; to find the Vanishing Line of that other Plane.

He covers the whole theory of perspective in 40 pages.

Related Posts

Who was Brook Taylor?

Method of Perspective

Related Works

Andersen, K., 1992, Brook Taylor’s Work on Linear Perspective: A Study of Taylor’s Role in the History of Perspective Geometry. Including Facsimiles of Taylor’s Two Books on Perspective. New York: Springer.

Andersen, K., 2006. The Geometry of an Art. The History of the Mathematical Theory of Perspective from Alberti to Monge. New York: Springer.

Who was Brook Taylor?

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.

Related Posts

Brook Taylor’s Linear Perspective

Method of Perspective