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A rich nation, constantly embroiled in warfare and more often than not being invaded, has built, about a couple decades ago, a grand city over the old capital.

It houses a very large population of 300 thousand, and it's very well strategically placed, about 50 kilometers from the city lies the coast, with another, albeit much smaller, similarly built city acting as port, this is great because the ocean in which the coast is set brings very rich trade, which made both cities major trade hubs in the continent.

The city is built on top of fertile plains and has a particularly thick river running through town. The technology available to the civilization is similar to that of the late 16th century and early 17th, along with the architectural / engineering knowledge of the Romans (not sure if the Romans would be able to rival that of the 16th century Europeans in this aspect, but the Rome was the first city to achieve a population of one million in Europe [133 B.C.], a feat only seen in Europe again after nearly two millennia [London 1810 A.C.], and they had a pretty awesome sewage system, which I intend to mimic in the city).

As already mentioned, the nation is constantly warring, so the city has huge, thick walls, with many bastions around it, similar to the walls of star fortress, made to deflect cannon fire, allowing the city to hold besiegers at bay if their only hope of conquest is through an invasion on the city.
The city is also built to withstand a long siege, it has huge underground storehouses that store food and supplies, and I thought of having large farms and estates inside the city, but I think that it would take up too much valuable space and would not be cost-effective or efficient. I also thought of some sort of vertical farming mumbo jumbo but I'm not sure of how that would work.

The city is also a knowledge hub, it has three universities, four military schools, an observatory, many schools and it houses the central government, the royal palace and the court, and contributing more to the scholarship of the city, the community is, as already mentioned, an economic center, attracting merchants from all over the world, and many markets and banks have been built on the city, attracting even more traders.

Last but not least, I'm aware that the city would be VERY expensive to built, but that won't be a problem, for the kingdom has since long been wanting to build a grandiose capital, and has hoarded money / goods / resources for centuries to build such city, and even then that nearly wasn't enough, the government almost got in debt and lost a lot of influence because of the construction, but eventually, it paid off, so finances won't be much of a problem here fellows.

So, with this information in mind, how large would be this city? Keep in mind that it was also built with a small "extra space" to allow growth.

P.S. - I'm an architecture illiterate, so please explain your ideas to me, and point out my mistakes. P.S. 2 - If anyone has a cool sounding name for the city, I'm all ears.

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    $\begingroup$ Paris in 1550 had an estimated population of 275,000, Their defensive strategy was to use fortified outlying cities instead of the capital to tie down invaders. If the capital is besieged, where will the relieving army come from? Hoarding money may be the wrong idea - city earthwork defenses were often built over generations by the local labor, not contracted out...and many had to be rebuilt several times as technology changed. Standing armies and garrisons tend to be very, very expensive. $\endgroup$ – user535733 Dec 29 '17 at 6:18
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    $\begingroup$ What kind of food preservation will these vast storehouses use, and how will you keep pests from consuming all the stores? $\endgroup$ – user535733 Dec 29 '17 at 6:21
  • $\begingroup$ @user535733 About the outlying fortifications, the idea for the city here would be that around it, there would be many fortresses and castles, garrisoning relief armies, instead of cities. And about the hoarding money, sorry, I phrased myself bad, I meant also supplies and products, such as gold, in order to pay for the city's construction. About the contracted out, as I already mentioned, the city was made to be grand, it had to be built professionally to reflect the nation's will. And about the technology, I planned this world to be sort of "in amber" on military terms $\endgroup$ – Jedboo Dec 29 '17 at 6:35
  • $\begingroup$ @user535733 By that I mean, military technology is progressing very slowly, and since long have cannons be used, so these defensive wall surely won't be outdated, and they're being orderly maintained too. About the standing armies, as I said, this country is constantly embroiled in war, and has developed a professional citizen army, much like the Romans, it's not terribly large, but it's very well-trained and capable, and the government dedicates much of their finances to the military, for the survival of the nation depends on it. $\endgroup$ – Jedboo Dec 29 '17 at 6:38
  • $\begingroup$ @Jedboo Because transportation is still very elementary back in the 1700s, you can't really have an outlying fortress or castle without a city to support it. Also, if cannons are in play, don't waste your time with city walls. You'd be much better off putting those resources into mangling the terrain and fortifying the roads in and out. $\endgroup$ – corsiKa Dec 29 '17 at 6:41
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Large cities of ~1500

Wikipedia conveniently has a list, and it is well sourced from Chandler, Modelski, Morris and others in the field. Lets run down some of the largest cities from 1500-1600. I rank all cities above 200,000 by their median estimate in the time range. I skipped pre-Columbian estimates for New World cities.

Beijing 700,000

Beijing's city walls were completed in 1553, right in the middle of this time period. It had two sets of walls, the 'Inner Wall' and 'Outer Wall.' Interestingly, the Inner Wall was not inside the Outer Wall, but directly north of it. The inner city wall was 24 km long, and the outer wall was 28 km long. Together, I estimate they enclosed about 50 km$^2$. This makes the total density within the walls about 14,000 per km$^2$.

Istanbul 600,000

The Theodosian walls still stood as the boundary of the city in the 1500s. There was some suburban development outside the walls, and a lot of development across the Golden Horn in Galata or Pera. The modern area inside the walls is the Fatih district; combined with Beyoglu to the north to represent the suburban areas, that gives an area of 22 km$^2$ for a density of about 27,000 per km$^2$.

Vijayanagar 500,000

The modern Hampi archaeological site is 41 km$^2$. The inner city walls were somewhat smaller than this, but since there were more wells outside the walls than inside, this larger number is likely more accurate. This gives a density of about 12,000 per km$^2$. Medieval travelers claimed that there was a second outer wall that enclosed a large area of farmland, around 500-750 km$^2$. So an alternate lower density could be calculated for this city.

Cairo 300,000

Old Cairo has largely been buried under the new, so there isn't a lot of good information on how big the old city was. According to (unsourced) Wikipedia, by the end of the 15th century, Cairo was composed of Old Cairo, Downtown Cairo, Bulaq, and Azbakeya. Measuring these areas on Google Maps, I get a total area of around 20 km$^2$; for a density of 15,000 per km$^2$.

Kyoto 300,000

Wikipedia has a 1696 map of Kyoto (a little after our time period), where it covers what is the modern day Kamigyo, Nakagyo and Simogyo wards. These wards have a total area of 21 km$^2$. Since we measured the city in 1700, we ought to use the 1700 population of 350,000, giving us a density of 16,000 per km$^2$.

Paris 250,000

Paris' city walls for this time period were finished in 1383 (the Wall of Charles V) and covered 4.4 km$^2$. Maps made in this period (like this one from 1572) show some development outside the walls. If we estimate the actual city size as the 1st through 6th arrondissements of modern Paris, we get an area of 10 km$^2$ for a density of 25,000 per km$^2$.

Hangzhou 250,000

Several sources list Hangzhou as being this big, but it had been much larger in the past, up to a million people and probably the largest city in the world for most of the 1200s. It was sacked by the Mongols in 1276 and declined, though it was still bigger than Beijing when Marco Polo and Ibn Battuta visited in roughly 1290 and 1345, respectively. The problem is, smaller 1500s Hangzhou with only a quarter of the population certainly didn't fill out its old size, and it is difficult to estimate the occupied area of the city was at this point. There must have been substantial ruins surrounding the occupied parts of the city center.

Tabriz 250,000

I can't find any useful information on Medieval or Early Modern Tabriz.

Naples 200,000

I couldn't find much information on the old walls of the city, but based on the location of the gates, I estimate that the old city occupied what is now San Ferdinando (which was explicitly developed by the Spanish in the 16th century) and the 2nd municipality (which includes the old port town along with Avvocata, another area developed by the Spanish). Summed together, these areas are about 6 km$^2$, for a density of 33,000 per km$^2$.

Agra 200,000

This is another one that is tough to adjudicate. Agra was only founded in 1504. Agra fort, a 0.4 km$^2$ walled city was built on the location at that time, and served as the capital of Sikandar Lodi's empire until the death of his son in battle in 1526. Then there were years of chaos and the fortress was ruined until Akbar re-united Northern India and made it his capital again, completing a rebuild of the fort in 1573. But then Akbar moved his palace to Fatehpur Sikri, about 35 km to the southwest, in 1571 and stayed at that site until the local water supply ran out in 1585. After that, the emperors finally moved back to Agra. The conclusion is, the population was probably in a lot of flux over time, and there were never proper city walls, just a small fort.

Conclusion: 10-30 km$^2$

Our density estimates for the largest cities of the 16th century range from 12,000 to 33,000 per km$^2$. Thus, if you want a city of 300,000 people, it should have a geographical area anywhere from 10 to 30 km$^2$, based on real world precedents.

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