A Reading Day

 

Today I was booked in to read from the Dee library at the Royal College of Physicians.  I did have opportunity to do this once before; I got one day in back in 2020 before all the libraries closed due to COVID and I had to head home far too early.  It was so good to be back and to be working with Katie again, who is the special collections librarian.  She not only helped me  by "fetching" the books I needed but also with her huge amount of knowledge in this area - and even with interacting with me about the writing I want to do.  I accessed again some of the books I had accessed before (the Alexander, the Cardano, and the Archimedes) but also others that my studies of Dee have led me to in the meantime (Copernicus/Rheticus, Frisius, Llull, Plotinus/Ficino, and Postel).  I'll post just a couple of imagines from my RCP reading to give an idea.

The above is from the Mathemalogium of Andreas Alexander (1503).  Dee was reading this when he was imprisoned by Queen Mary I ("Bloody" Mary).  The writing he did in the margins of this book is very neat, and I always imagine that is because he had time on his hands!  On this page he makes a correction to the printed text.  Here is a square with sides of length 4 (given in Roman Numerals as iiij) and a diagonal given as having length 32 (written xxxij), but rather than 32, it should be the square root of 32.  The symbol in front of xxxij is handwritten by Dee, an old form of the square root symbol.

The book above connects two of "my" mathematicians.  It was written by Cardano but owned by Dee, and used by Dee as a textbook of astrology (which was an expected area of learning for a scholar at that time - at least one working with math and astronomy - and often for physicians as well, since astrology tied into diagnoses).  Cardano and Dee eventually met (1552), but Dee most likely had this book prior to that and was using it to learn from during his time in the Low Countries.  You can see Dee's writing on the left-hand page (neater on some days than others).  I included this picture because it involves both Dee and Cardano, but my name is here too -- on the slip of paper sticking out of the top of the book.  Am I ever in august company!!

I walked from the RCP to the British Library - about a 20-minute walk.  Along the way I found this business area with some little restaurants, and I definitely needed a lunch break!  Tucked way in the back corner was a little Italian Café and also some rather fun seating.  I think this is "Regent's Place."

As I resumed my journey to the British Library, I saw what is in the following two pictures.  Can you tell what they are before scrolling further?

A quick peek, and then onward to the British Library.  I had spent more time at the RCP than planned because I found out the British Library was open until 8pm.  Yea!

Pencils only in the reading room.  Everything else goes in the locker.  (Cameras are OK for many items.)  I took a picture to make sure I'd remember which locker my stuff was in! 

I'd been particularly excited to access the Jacopo Silvestri book from Dee's library.  It is the second book on cryptography ever printed (1526) and was bought in Venice by Dee in 1563.  The shelf mark is 556.b.20. When I first opened the book I thought they'd given me the wrong thing.  It turns out there are two books bound together - despite having nothing to do with each other - the book I wanted was at the back.  The book at the front was a 1620 book on sign language, which was interesting too!

I also consulted a Cardano book here at the British Library - one that I had requested in 2020 and was booked in to see, but the library closed due to COVID before I got a chance to do so.

I love this book!  I ended up reading almost the entire thing.  I'm interested in it, of course, because it is written by Cardano, but it also has pretty "famous" connections.  It seems that Shakespeare must have been very familiar with it, as much of his "To Be Or Not To Be" soliloquy are almost word-for-word from this book.  I took so many pictures of it that I'm having a hard time finding exactly the ones I want to illustrate this, but notice the end of the second page here: "Seeing then men die with such ease, what can Death be better compared to than a Dream."  And in Hamlet's soliloquy we have, " 'tis a consummation devoutly to be wish'd.  To die, to sleep; to sleep, perchance to dream - "  I realize this is a pretty common sentiment, but there are many more connections here, closer connections.  Also, it is thought that just before that scene, when Polonius comes upon Hamlet in the library and asks Hamlet what he is reading, and Hamlet says, "Words, words, words" that the book Hamlet is holding in his hand is this book of Cardano.  Personally, I found the book quite compelling and helpful, as it says on the title page, "Of great use in these times," well, in great use in this time too, I think.

Precious treasures:

Fun fact - there's actually a little mystery here.  The date (bottom of spine) on the Silvestri book is 1616, but I know it to have been published in 1526.  Additionally, the inscription on the inside that is written in John Dee's hand indicates that he purchased it in 1563 in Venice.  Well, that is impossible if it was published in 1616 (which is 7 years after his death!).  When I was back at the RCP the next day, I mentioned it to Katie, and she thought about the dates and realized almost immediately that in Roman numerals there is only one symbol difference between 1526 and 1616, so an easier mistake in that system than in ours, using MDCXVI instead of the correct MDXXVI.  The only difference is an X vs. a C.

Short Post and Break Announcement

 

Today, Monday, was filled with archival reading, first at the Royal College of Physicians and then at the British Library.  I have no words to describe the awesomeness of the precious treasures I was handling today.  However, I realized this morning that I've been spending so much time filling my entire days with activity and my entire nights with recording activities (2 blogs, facebook, and a written journal - in order to preserve every memory in every way possible) that I wasn't really prepared for the readings I was undertaking today.  I also ended up so tired in the British Library that I couldn't physically keep my eyes open to read, so I am going to have to take a break from posting for a few days.  Once I get to Winchester and Oxford (later this week) things will slow down a lot.  I don't have nearly as much planned there.  Speaking of Oxford, I haven't taken time to research and request the items I wish to consult at the Bodleian, and that's really what I'm here for is research, so I really need to get my head on straight and make time for that.  I was doing so well - blogging the "day of" and then one day late, and now it's May 9, but the events I last blogged about happened on May 6.  It's definitely time to get my time and activity level under control.  

I think I can't end without posting a few more pictures, but I also kind of want to hold off until I can discuss them fully - but because I can't hold back, here are a small handful:

Above is a book written by "my" mathematician Girolamo Cardano and owned and annotated by "my" mathematician John Dee.  My name is on the reader's card sticking out of the top.  You cannot imagine my joy connecting Dee and Cardano (who did meet in 1552) and also my own name by doing this reading.  (The book is Cardano's Libelli quinque and is in the collection of the Royal College of Physicians.)

Above is the title page of one of my favorite books of all time, the Mathemalogium of Andreas Alexander (1503).  This is also in the RCP collection.  I've written about it before in this blog (2 years ago) but found new things to write about, which will be coming up!

Today is the first time I consulted the book above, Girolamo Cardano's Three Books of Consolation.  Even though I was so tired I wanted to put my head down right there and take a nap, I read almost every word of this book.  It's AMAZING!  It is now tied for favorite with the book above.  More about it when I do a full post about today. (This is in the British Library, and the shelf-mark is 8405.a.9)

Girolamo Cardano in London

Frontispiece of Girolamo Cardano in the copy of Libelli Quinque owned by John Dee

Over the two years that I have been planning this math history sabbatical, I have been reading widely and deeply of Girolamo Cardano.  However, because I had to give up my planned time in Italy due to the COVID-19 pandemic, I can really only write this one post about Cardano rather than the 5 to 10 I had been planning on.  His life is SO INTERESTING that I find myself having to hold back very strongly right now from sharing all that I could about him because I yet hope to get to Italy some day and to be able to share about him bit-by-bit accompanied by pictures of locations relating to his life.

Though unable to travel in Italy, I was still able to study Cardano "on location" at least to some degree, as he did spend some time in England and does have a connection with John Dee whose life and work I was able to research to a greater extent during this abbreviated sabbatical.

And so, on to Cardano  .  .  .

Girolamo Cardano was famous throughout Europe as a physician and, in 1552, he was prevailed upon by the ailing Archbishop of St. Andrews, John Hamilton, to make the uncharacteristic move of traveling all the way to Scotland from his beloved Milan.  On his way home from Edinburgh Cardano spent time in London. Cardano was in London as a guest of the court of King Edward VI and was staying with Sir John Cheke in the area of Southwark.  

Southwark Cathedral, London

Southwark Cathedral, London

Courtiers wished Cardano's opinion on the king's health, but even more so wanted to know what Cardano saw in the stars with regard to the king's future, so Cardano was asked to draw up a horoscope of the king (which, as we have seen, can be a dangerous proposition). 

Southwark Cathedral, London

When Cardano was introduced to the king he was told what title to use, but, out of respect for the Pope, Cardano would not address the king as being defender of the faith and head of the church of England.  Because of these scruples Cardano received for his services only 100 pounds rather than the 500 to 1000 pounds he otherwise would have been paid.  Despite this, Cardano's audience with the king went well, both of them being impressed with the other.  The king asked about Cardano's writings and ideas, and Cardano wrote of Edward that he "was a wonderful boy who, I was told, had already learned seven languages.  He was as fluent in French and Latin as in his native tongue.  He was trained in logic and was extremely intelligent.  He was in his fifteenth year when I met him.  He asked me, speaking in Latin as beautifully and fluently as myself, `What new ideas does your book De Rerum Varietate contain?'"  Cardano, in his later writing in a commentary on Ptolemy, also expressed that Edward "was very open and most amiable" and that he was "so cheerful; he brought youth back to his teachers; he played the lute; he was interested in public affairs; and he was a free spirit  .  .  ."

The mid-sixteenth century was quite a time in England.  Edward's father, Henry VIII, had broken with Rome and gone through multiple wives in order to get a son to maintain the Tudor line.  Edward had two older sisters in the wings who could ascend the throne after him -- one Catholic and one Protestant.  Edward was young, only nine years old when he ascended to the throne.  According to his father's will, there was supposed to have been a Regency Council appointed for him, but somehow his uncle, Edward Seymour, became sole Lord Protector of the Realm, while his other uncle Thomas Seymour, who had married the last of Henry VIII's six wives, plotted and schemed in the background.  By the time of Cardano's visit both of these uncles had been beheaded, and the 1st Duke of Northumberland, John Dudley, whose father had been killed by the king's father, was leading the government.

If I were Cardano, I don't think I would have wanted to cast a horoscope of King Edward -- or anyone else at court for that matter!  As requested, however, Cardano did cast a horoscope for the king, and for whatever reason, through error or through expediency, he predicted a virtuous and wise reign along with a reasonably long life for Edward.  Sadly, by the next summer this brilliant and engaging young king was dead.

Dee's copy of Cardano's Libelli Quinque (with thanks to RCP London for permission to post)

But let's back up a bit and talk about other elements of Cardano's London sojourn.  While there Girolamo Cardano met John Dee, a man 26 years his junior.  Despite the age difference this visit isn't surprising given that Cardano was staying with Dee's former tutor, John Cheke, and that Cheke was closely connected with the court. Cheke had been a tutor of Prince Edward and had since been appointed Gentleman of the Privy Chamber and had served for some time as a Member of Parliament and was also, briefly, Secretary of State.  The meeting is also not surprising given Dee's familiarity with and appreciation of Cardano's work.

The pictures above and below are images from Dee's copy of Cardano's work Libelli Quinque.  From all of the marginalia and working and reworking of horoscopes it seems that Dee was using this book to teach himself how to cast horoscopes.  (I would like to have thought that Cardano may have given this book to Dee during their time together in London, but given all the work in it, it seems that Dee had this book four or five years earlier when he was studying in Louvain.)  In the picture above, you see Dee correcting or reworking Cardano's work seemingly in order to train himself, and in the picture below you see Dee doing his own work in the margin and then scratching it out and starting over.

Dee's copy of Cardano's Libelli Quinque (with thanks to RCP London for permission to post)

In the picture below you see a lot less crossing out than is the case two pictures above.  It may be that Dee was correcting a printing error here.  As you can imagine, printers of the time would have had a particularly hard time setting the type for this sort of work.  The placement of the information in each section of the square was important, so it may be that Dee was simply copying over the information to the correct position here.

Dee's copy of Cardano's Libelli Quinque (with thanks to RCP London for permission to post)

Cardano and Dee discussed many things in their time together -- among other topics, they discussed the magical properties of a gem that they were inspecting, and they also talked together of a perpetual motion machine.  Certainly they must have discussed astrology -- perhaps also mathematics.  If there were ever conversations in this world that I would like to have overheard, the conversations between these two men would certainly be near the top of my list!

Historical Plaque at Southwark Cathedral, London

In 1552, when Cardano was in London, the structure that is now Southwark Cathedral was present and had the role of a parish church at that time.  Though certainly there has been tremendous change to all of London in the last 468 years, including renovations or additions to this church, its location and at least some of its features would have been familiar to Cardano and Dee.  It is, after all, the oldest gothic church building in London.  Shakespeare, who was a parishioner here, was a close contemporary of theirs (and Shakespeare may have modeled the magician Prospero in his play The Tempest after John Dee).

Southward Cathedral, London

The pictures above and below were taken from the same spot, just looking in different directions.  Southwark Cathedral, above, is very close to the Thames, below.

Facing away from the cathedral and towards the Thames

The focus of this post is Cardano, but as I fear it will be at least a year before I can continue my travels, I want to point out that the waterfront below contains a quotation from Sir Walter Raleigh, "There are two things scarce matched in the universe, the sun in its heaven and the Thames upon the earth."  Dee was an adviser to the explorers, including Raleigh, under Queen Elizabeth I in the quest for empire, but that is another story for another day (or another year).

The Thames waterfront, with Raleigh quote, as seen from Southwark Cathedral

Just to put it all in context I've taken a short video showing the area in the pictures above.  Thank you for following me in my math travels -- this was as far as I was able to journey, due to the COVID-19 pandemic, but I sure hope to be back with more content in a year!
 

Travel

A major tarmac delay in from a previous trip

POST SCRIPT: I had drafted this post to go up on March 11, the day I was to fly out to Rome.  Most of my time in Italy is (was?) to have been spent in northern Italy, but as I watch the coronavirus warnings on the news it looks like if I were to head to the areas of Venice, Padua, Pavia, and especially Milan, that I may not be allowed out and into the UK to continue my travels.  That's just a prediction, but I fly out in 2 weeks and will spend (would have spent?) 5 weeks in Italy.  Who knows what that virus is going to do over that period of time. So at this point everything is up in the air (no pun intended), and I'm scrambling to change over the course of a few days the plan that had been carefully crafted over the course of a year and a half (two years, really).  Originally my concerns about travel were the discomfort of long flights and the details of setting up phone service in Europe-- am getting a little change of perspective on that.

*****

This trip that I am beginning is an AMAZING opportunity!  However,  to say I'm looking forward to countless hours sitting on a plane would be a lie.   And to say I'm not nervous about this trip would also be a lie. I am a shy, introverted person who appreciates above all else the comforts of home; I also tend a bit towards anxiety.  (And some of you reading this are chuckling right now because you know that to say I tend a "bit" towards anxiety is like saying the ocean is a "bit" wet!)  BUT, I am so passionate about the history of mathematics and about the particular mathematicians that I am studying that there is no way I would not have jumped at the chance to do what I am doing!

As I've been reading about my mathematicians, something that has caught my eye has been their travel experiences.  I mentioned in my introductory post that Cardano and Dee had met in London (1552).  That meeting actually happened as Cardano was on his way back home to Pavia from Scotland - an even further destination.  As the second most renowned physician of his day (behind Vesalius), Cardano was asked by Archbishop of St. Andrews, John Hamilton, to come and treat him.  Cardano left Italy on February 23, 1552 and arrived in Scotland on June 29, 1552 - a journey of just over 4 months!  He did have a bit of a "layover" in Paris  .  .  . but still, in comparison to the somewhat less than 24 hours it will take me to cover the 6250 miles from home to Rome, the FOUR MONTHS it took Cardano to cover the 1500 miles from home to Edinburgh is quite the journey and kind of puts mine in perspective.

On the other hand, I won't have servants along attending me  .  .  .  hmm  .  .  .

John Napier left his Edinburgh home in 1563 to travel to the European Continent in order to continue his education. He was just 13 years old at the time!  He would have had a servant with him, but no amount of help could come near to alleviating the rigors of travel.  Depending on weather (and pirates!) it could take up to 10 days to go by ship the short distance from Scotland to the Netherlands.  Traveling by land was actually harder.  Among other things it was best to present one's-self as being impoverished so as to avoid the notice of the robbers who roamed the roads.  Even at an inn it wasn't a good idea to pay for a bed or a good meal because that would show you had money, so sleep might have to be on a bench or table or in a stable.  As uncomfortable as this sounds, it might not have been so bad in comparison to a bed, however, as a bed might have to be shared by multiple travelers (strangers) and could be filthy and flea-infested.

It isn't known where Napier studied on the Continent.  It may have been as nearby as the Low Countries, or further on to Paris or Geneva (most likely), or perhaps even as far away as Italy.  But one thing is certain, his travels would have been neither brief nor comfortable!

And then there's John Dee who left his most dearly beloved home in Mortlake, England to travel to central Poland.  He set out on September 21, 1583.  Once he had made his way along the Thames and out into the North Sea, a storm drove his ship back towards shore where they would have to wait a week for a new anchor to arrive. Getting back from ship to dinghy to shore was an ordeal that left Dee falling into the sea and becoming "foul arrayed in the water and ooze."  Once across the sea, they made their way across the Netherlands towards Denmark, a trip not made easier since Dee had packed at least 800 of his very favorite books!  Onward they went through Germany and then, with "slow, perilous progress," over into Poland.  Between two of the cities in their travels they had to hire two-dozen men to clear a two-mile stretch of road to enable their coaches to pass, after which they found themselves marooned outside the city, which was surrounded by floods.  On February 3, 1584, he finally arrived in Lask.  This journey, as had Cardano's, took just over four months.

So, no matter what the next 24 hours have in store, I'll be spanning the distance of about a fourth of our globe in that relatively short time - and mostly sitting in a chair!  One car, three planes, and a train later, I will arrive at my hotel, which is located directly behind the Pantheon in Rome - and that will be a glorious sight to behold!!  POST POST SCRIPT - Well, that was the original plan - not at all sure what the alternative plan will turn out to be - a much more "interesting" journey than anticipated!!  I sure hope it doesn't get as "interesting" as any of the three examples above!

Introduction to Second Sabbatical -- "Sorcerer Mathematicians of the Renaissance"

My first sabbatical was such an amazingly life-changing experience and has so positively impacted my students and my teaching, that it has been my dream to do something similar again.  During fall semester 2018 I worked hard to put together a worthy proposal, and approval was granted!

Cardano, Dee, and Napier

My previous sabbatical was focused on the history of mathematics from the Renaissance to the present in northern Europe, which was quite a wide sweep of history to try to take in.  This time my focus will be on three 16th-century mathematicians whom I refer to as "The Sorcerer Mathematicians of the Renaissance."  They are Girolamo Cardano (1501-1576), John Dee (1527-1609), and John Napier (1550-1617).

John Dee Exhibit, Royal College of Physicians, London 2016

John Dee's crystal ball

Prior to my first sabbatical I had not heard of John Dee -- embarrassing to admit, but there it is.  Thankfully, while I was in London the Royal College of Physicians was hosting a John Dee exhibit along with a variety of other Dee events. I found myself captivated.  A book on display there linked John Dee with one of my favorite Italian mathematicians, Girolamo Cardano. I later learned that they had met, despite a quarter-century difference in their ages and despite living at such a distance from each other at a time when long-distance travel was onerous to say the least!  This link was the seed of the idea for this second sabbatical.

Dee's copy, with his marginal notes, of Scaliger's "critique" of Cardano

Additionally during those first travels I learned more of John Napier -- also a Renaissance-era mathematician with a reputation for dabbling in the dark arts.  How could I resist opportunity to study these three more deeply and in conjunction with each other?  (And if any mathematicians are going to capture the imaginations of my students, wouldn't it be these three?!  Crystal balls, castles, the Spanish Inquisition, codes, feuds, spy-craft, the occult, lost treasure, etc., etc., etc.)

John Napier's Tower House/Castle, Edinburgh, Scotland 2019

Beginning March 12, 2020, I will be "walking in the footsteps" of these mathematicians as closely as possible.  I will be visiting places where they lived, studied, worked, worshiped, and died.  I will read in library and museum archives, focusing especially on original documents such as diaries and letters.  I will attend any and all talks, tours and events that I can find relating to these mathematicians.

Mathematically I will be studying their work on their terms, as they wrote it and understood it.  The Renaissance Era was as much a rebirth and flowering of mathematics as it was of art, music and literature.  These three mathematicians were deeply involved in this flowering that gave rise to the mathematics (and thus the technology) that we have today.  For example, in 1545 Girolamo Cardano published Ars Magna, or The Great Art, an extremely influential mathematics text that is a basis of our modern algebra.  John Napier created logarithms, an invention that so shortened the time needed for calculations that he is said to have “doubled the life of the astronomer.”  John Dee worked with mathematics relating to navigation and calendar reform and is the first person to have used the term “British Empire,” a phrase he coined in his role as adviser to Queen Elizabeth I.

Though their mathematical contributions are profound, there is much more than mathematics that attracted me to these three.  John Dee may have been a spy for Queen Elizabeth I and is thought to have inspired Ian Fleming’s James Bond character as well as Shakespeare’s Prospero and Marlowe’s Dr. Faustus.  What kind of life must he have lived to have inspired such a diversity of fictional characters?!  Girolamo Cardano was the second most renowned physician of his day and was also a gambler and an astrologer who was imprisoned by the Inquisition for, ostensibly, casting a horoscope of Jesus Christ.  John Napier was an elder in his church, but he was also considered a sorcerer by his neighbors, an opinion he seems to have encouraged!  That was a very fine line to walk, particularly in the 16^th century when people were burned at the stake for witchcraft. Because of his reputation as a sorcerer, he was contracted to use his skills to search for treasure in Scotland’s Fast Castle.  

There is a great deal more to what I am doing and exploring, but hopefully that gives a sense of the journey -- enough to tempt you to follow along!

Speaking of the journey, I had these maps up on the wall of my office all last semester in order to encourage and inspire myself.  Not having traveled prior to 2016, I learned in my first sabbatical that I'm a pretty "manic" traveler, don't know how to rest and take down time -- but that's in large part because this is my chance to access so much!  I'll be staying in 11 different cities over the course of 8 weeks and will be taking side-trips to other cities as well.

In Italy my focus is mainly Cardano (though while I'm there I'll also do a bit of looking into Bruno, Fibonacci, Pacioli, Somerville, etc.).  I will be visiting the cities of

Rome

Naples

Florence

Vinci

Pisa

Bologna

Urbino

Venice

Padua

Milan

Sirmione

Pavia

In England I'll focus mainly on Dee, and in Scotland I'll focus mainly on Napier.  The cities I'll be visiting in the United Kingdom are

London

Oxford

Eyemouth

Edinburgh

Gartness

St. Andrews

I have been researching this with varying levels of intensity since my last sabbatical, and this research has now shifted into very high gear.  I need to go in with a lot of knowledge in order to get as much out of this as I possibly can.  I plan to begin regular blog posts a few days after landing in Rome on March 12, so watch this space in order to learn about those "Sorcerer Mathematicians of the Renaissance!"


PS  This blog is a continuation from my previous sabbatical, so all the posts from those travels can be found below.  

PPS As of February 25, 2020, there may need to be significant changes to the above due to the spread of the coronavirus epidemic, which has now breaking out in northern Italy.

Mathematicians of Edinburgh

When first planning these mathematical travels I had only planned a couple of days for Edinburgh.  My interest was in John Napier, a very interesting character who also invented logarithms and is responsible for popularizing the use of the decimal point.  After seeing Merchiston Tower, which is all that remains of his castle in Edinburgh and is now part of Edinburgh Napier University, and after touring Lauriston Castle, home of his brother, I was going to be on my way to my myriad of mathematical stops in England.

However, as I began to look into Edinburgh I became aware of more and more mathematicians and mathematical physicists of note who were associated in some way with Edinburgh.  Along with Napier, these are:

Girolamo Cardano
Colin MacLaurin
John Playfair
Mary Somerville
William Thompson, Lord Kelvin
James Clerk Maxwell
Peter Guthrie Tait

and, currently, Sir Michael Atiyah, geometer and Fields Medal winner.

Clearly my Edinburgh sojourn needed to be extended, and I ended up reserving six days in Edinburgh rather than the two I had initially planned.  Even at that I need to focus on two or three and just touch on the others.  In this post I am sharing landmarks that all of these mathematicians would have been familiar with - that's not to say that some changes may not have been made to certain places such as Edinburgh Castle and Holyrood Palace between the time of Napier (b. 1550) and Atiyah (b. 1929).

EDINBURGH CASTLE

HOLYROOD PALACE

HOLYROOD PARK AND ARTHUR'S SEAT

St. Anthony's Chapel ruins in Holyrood Park - partway up to Arthur's Seat

Overlooking the city from near the top of Arthur's Seat

ST. GILES' CATHEDRAL

EDINBURGH UNIVERSITY

Main Campus

"New College" Campus - now a divinity school

"New College" Campus

"New College" Campus (with John Knox)

THE FIRTH OF FORTH

I haven't gotten close yet, but here it is from a bit below Arthur's Seat

CALTON HILL (with or without observatory and various monuments)

Observatory and Playfair Monument

Edinburgh - the Athens of the North

Viewing across Old Calton Burial Ground

Top left - looking over Holyrood Palace

Post Script - this idea of common landscapes was confirmed today (March 31, 2016) when I visited the National Portrait Gallery and saw the piece below from 1820 showing Calton Hill and Arthur's Seat behind it.