A History of Geometry

AN ILLUSTRATED & IDIOSYNCRATIC HISTORY
OF GEOMETRY

(viewed through tools of the trade)

The Myth of the Flat Earth - A 15th Century manuscript of 13th Century theologian Gautier de Metz's popular 'Image du Monde', with God creating a very round earth. Of course it is spherical, only dummies would consider it otherwise.

It is not even vaguely up for discussion. But now that is out of the way, I want to take a little journey through the craft and art of the geometer.

This is called an 'Architect's Table' or 'Drafting Table' and I am rather fond of these vintage models, with their wooden boards and tracking tools - kinda sexy/funky/romantic.

Mind you, to draw upon one of these is not so practical, as the wooden surface creates movement upon the surface of the paper, when drafting in pencil, or finishing in ink.

An undesirable wrinkling effect, that upsets most designers, who generally have a fair dose of OCD running through their veins - me included.

A military compass. This was invented either by Thomas Hood, a British mathematician, or by the Italian mathematician and astronomer Galileo Galilei, depending upon your historical sources.

I have a deep love for finely crafted tools, as you will see as you scroll down and through this page, it reflects my many years as an antiques dealer, where I developed a love of fine craftsmanship and beautiful design - oh, and that wonderful tactile sense of holding a beautifully balanced object.

The bummer being, then as now, that great inventions are so often co-opted by the military for destructive purposes, having being born from the mystic creative minds, and subsequently turned into weapons.

A fitted box of mathemtical instruments, made by Giacomo & Domenico Lusverg, of Rome, working 1688 - 1710. The materials here are brass, copper, glass and steel.

This is originally from the Medici Collection, and currently housed at the Museo Galileo - more of this heaven later.

If this has no appeal to you, I simply cannot understand you. I mean, tools as beautiful as jewellery, in a fitted box, from the Medici Family Collection are about as good as it gets. 

And to work with these... I wish.

Fitting the infinite into the finite - The squaring of the circle.

One might suggest that the masonic square represents the earth and the compass circle represents the celestial spiritual realm. 

Much has been written, and wildly extrapolated from this understanding of the infite aspect of Pi, though here, in this essay, I wish to describe the powerful use of the tools of geometry, in a historical and artistic context.

Another weakness of mine. A massed collection.

This particular collection include many Stevens calipers and dividers c.1886 and also other historical drafting tools, and when seen, en masse like this create a strident narrative that appeals to my inner collector.

Everything counts, in large amounts.

Another funky, funktional, sculptural drafting table, of a time long before CAD was a thing, and encourages me to be grateful for my love of hand-drawn architectural and technical drawings, that is the very substance of my own later career.

Hand made, hand designed, hand drawn - it's becoming a thing of the past, but in this time of the artisanal revival there is hope.

I don't use one of these, but I do use many vintage tools, and I might acquire one of these simply for the aesthetic and presence.

A kind of lineage and honouring of the past geometers.

The Ancient of Days by William Blake, originally published in his1794 work 'Europe a Prophecy'.

It draws its name from one of God's titles in the Book of Daniel and shows Urizen, using a huge pair of compasses to delineate the material world at the moment of creation.

This is a Gnostic interpretation of the creation story where a demiurge (a subordinate deity) creates, rather than a benevolent God as the Creator.

Blake sees this moment of creation as rational order being imposed upon chaos - a moment of sublime error - the reduction of the infinite to the finite, and the destruction of imagination.

Creation, as related to the geometer's tools, and craft. And a note - the implement used, is not a compass, it is called a pair of compasses.

More delights housed within the Museo Galileo - Institute and Museum of the History of Science, Florence.

I would love to visit this place, and I am entertaining the possiblity of a pilgrimage, and by the way, they have Galileo's middle finger on display. 

Yes, you read that right.

Yes, this is Galileo's middle finger. 

Euclid of Alexandria was a Greek mathematician, often referred to as the founder of geometry or the father of geometry.

He lived during the reign of Ptolemy I and almost nothing is known of his life, and no likeness or first hand description of his physical appearance has survived antiquity, and so depictions of him (with a long flowing beard and cloth cap) in works of art are necessarily the products of the artist's imagination.

He probably studied for a time at Plato's Academy in Athens but, by Euclid's time, Alexandria, under the patronage of the Ptolemies and with its prestigious and comprehensive Library, had already become a worthy rival to the great Academy.

Euclid wrote perhaps the most important and successful mathematical textbook of all time, the “Stoicheion” or “Elements”, which represents the culmination of the mathematical revolution which had taken place in Greece up to that time.

This divine piece of kit was created by Giacomo Lusverg, a master craftsman who lived and worked in Rome from 1672 until 1689, the year of his death.

He created mathematical tools, from drawing and topographic surveying, to sundials, compasses, and ellipses, for a largely aristocratic customer base.

For these implements I have shown here, would have been extremely expensive, a high luxury of their day, all housed within a snug fitted travelling case.

A travelling drawing set, Paris, circa 1690.

This is made from brass and steel, and housed within a shagreen case.

Shagreen (shark skin), was used to case luxury travelling goods, as it was durable, strong, beautiful and distinctively expensive.

The tools here, signed by the maker, protractor, folding ruler, square and compasses will all fit discretely within this carrying case.

Leapfrogging a few centuries here, this is something I have in my own collection, and that I use for my art, when drawing ellipses.

Called the Omicron Ellipsograph, this is the very rare large model, made in1954 by the Omicron Company of Glendale, CA. I also have the smaller model 17, for any geeks out there... and I guess if you are reading this, this means you.

It is a beautifully crafted design object, and a real pleasure to use, made of steel, aluminium and perspex, and an example is housed in the Smithsonian Museum.

Last one of these, I promise.

The whole vintage industrial taste has been trending for sometime now, as an element of interior design.

Archimedes (born c. 287 bce, Syracuse, Sicily, Italy - died 212/211 bce, Syracuse), the most famous mathematician and inventor in ancient Greece. 

He is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. 

He was an accomplished engineer but loved pure mathematics. Stories from Plutarch, Livy, and others describe machines invented by Archimedes for the defense of Syracuse, and again, to me, this is the abuse of knowledge, in service of destruction.

The hijacking of intelligence for war.

John Wood the Elder's set of drawing instruments, which were sold to the Bath Preservation Trust at Clevedon Auction Rooms for £21,000.

John Wood, the Elder, (1704 – 23 May 1754), was an English architect, working mainly in Bath.

In 1740 he surveyed Stonehenge and the Stanton Drew stone circles. He later wrote extensively about Bladud and Neo-Druidism.

So here, a physical link of many aspects of current and historical esotericism - and a lovely set of tools.

A complete set of mathematical drawing instruments circa late 1700s by G.Adams, in a fitted case of oak and mahogany.

Those parallel rulers, made of cut brass and polished steel would be a delight to use.

In my own collection I use an ebony and brass pair.

An attractive adjustable cast bronze and fruitwood T square. This rather extravagant 19th Century tool looks to have been made in the 1880's.

The head is marked with the initials E.A.A, and is designed for use with an architects drawing board.

An exquisite box of mathematical instruments, 18th century. Wood, brass, leather and gilt brass. Unknown maker. 

What I particularly like about this set, is the leather bound book form, whereby it might be concealed in plain sight, upon a library shelf, hiding it's valuable contents.

It houses several compasses and dividers, a plumb level, squares, a radio latino, rulers, a quadrant, a surveying compass, a trigonometer, and a cylindrical weight tapering to a point and fitted with a ring. 

Everything that I would like.

Please Santa.

Another beautifully leather boxed late16th Century astronomical compendium, late century. 

The tools are steel and brass, and housed within a fine Moroccan leather gilded and tooled case.

I bet it has a lovely smell too... geek alert.

God as Architect and Geometer, with the Genesis creation narrative (Genesis 11-26) illustrating a view of how the cosmos originated.

"In the beginning God created the heavens and the earth" - with her/his tools of course.

Remarkably, an anonymous collection, housed within the Museo Galileo, though when I visit the museum, I shall find out more I hope.

With the inclusion of several compasses I imagine that this might have been used for navigation and/or mapping.

And - that fine brass colouring... such subtle beauty.

I am getting close to the end of this smorgasbord of delights, and this set, with (what appears to be an) astrolabe, suggests an astronomical application.

Missing some components this shagreen cased set of mathematical instruments dates around the turn of the 17th and 18th Centuries.

This fine set of mathematical instruments was made by Bartholomew Newsum, circa 1570, and forms part of a collection of 16th Century artillery instruments.

I could put them to a far more productive, creative and positive use.

Make Love. Not War.

A lovely pair of fine and large wrought iron and brass dividers, showing that simple estate craftsmanship has an elegance and economy of design that is as beautiful as the luxury silver and brass tools further back on this essay.

These are possibly made by an estate blacksmith, of European origin.

Simple is good - a typical school set, dating from the middle of the 20th Century, much like my first set. Though mine was a Helix, not a Winsor and Newton.

Does exactly what it says on the lid.

Woman teaching the geometry of Euclid's Elements c 1310 AD 

Detail of a scene in the bowl of the illuminated letter 'P' with a woman holding a set square and using a compass to measure distances on a diagram.

In her left hand she holds a square, an implement for testing or drawing right angles. She is watched by a group of students.

In the Middle Ages, it is unusual to see women represented as teachers, in particular when the students appear to be monks.

She is most likely the personification of Geometry, based on Martianus Capella's famous book De Nuptiis Philologiae et Mercurii, 5th Century, a standard source for allegorical imagery of the seven liberal arts.

Illustration at the beginning of Euclid's Elementa, in the translation attributed to Adelard of Bath.

Illumination attributed to Meliacin Master died AD 1312.



Thank you for joining me on this journey, and may you find the tools you desire.