Since Atlantis is located at the Equator, the only information needed to establish its coordinates is the meridian line that intersects it. I believe Tommaso Campanella knows this meridian line and gave this information to Cardinal Richelieu and King Louis XIII. 
Subsequently, Richelieu and Louis XIII declared this meridian line, called the Ferro's Meridian as the new Prime Meridian on maps in 1634. So back then, the coordinates of Atlantis was exactly 0° N and 0° E. However, since the adoption of the Greenwich Meridian as the current Prime Meridian, the Ferro’s Meridian is now located at 18° 8' 7" W.
The Ferro’s Meridian passes through the Tip of Orchilla or Cape Orchilla, which is the westernmost point of the island of El Hierro, nicknamed Isla Del Meridiano (the Meridian Island). Until 1492 the Tip of Orchilla was believed to be the end of the world that was beyond the Ocean Dark inhabited by fierce monsters.
A journey was made from that coutry in 1724 to establish its exact location. In many maps of the sixteenth and seventeenth century, the Orchilla meridian appears as meridian 0. A lighthouse, called the Faro de Punta Orchilla, was built above the line representing this meridian.
The Ferro’s Meridian passes through the Atlantic Ocean, where according to Athanasius Kircher’s map, the lost city of Atlantis is to be found. 
Going back to the topic of alchemy, which you may have noticed by now is the common thread of this website, there is a popular legend about Cardinal Richelieu and his involvement with alchemy and Nicolas Flamel.
Nicolas Flamel was a successful scrivener and manuscript-seller who developed a posthumous reputation as an alchemist due to his reputed work on the philosopher's stone.
An alchemical book published in Paris in 1612 as Livre des figures hiéroglypiques and in London in 1624 as Exposition of the Hieroglyphicall Figures was attributed to Flamel. In the publisher's introduction Flamel's search for the philosopher's stone was described. According to that introduction, Flamel had made it his life's work to understand the text of a mysterious 21-page book he had purchased. The introduction claims that, around 1378, he traveled to Spain for assistance with translation. On the way back, he reported that he met a sage, who identified Flamel's book as being a copy of the original Book of Abraham the Mage. With this knowledge, over the next few years Flamel and his wife allegedly decoded enough of the book to successfully replicate its recipe for the Philosopher's Stone, producing first silver in 1382, and then gold.
What had happened to the book of Abraham the Mage? Nicolas Flamel had bequeathed his papers and library to a nephew named Perrier, who was interested in alchemy and of whom he was very fond. For two centuries the precious heritage was handed down from father to son, without anything being heard of it.
Traces of it are found again in the reign of Louis XIII. A descendant of Flamel, named Dubois, who must still have possessed a supply of the projection powder made from the Philosopher’s Stone, threw off the wise reserve of his ancestor and used the powder to dazzle his contemporaries. In the presence of the King, he changed leaden balls with it into gold. As a result of this experiment, it is known he had many interviews with Cardinal de Richelieu, who wished to extract his secret. Dubois, who possessed the powder but was unable to understand either Flamel's manuscripts or the book of Abraham the Jew, could tell him nothing and was soon imprisoned at Vincennes.
It was found that he had committed certain offences in the past, and this enabled Richelieu to get him condemned to death and confiscate his property for his own benefit. At the same time the proctor of the Chitelet, no doubt by order of Richelieu, seized the houses that Flamel had owned and had them searched from top to bottom. About this time, at the church of Saint-Jacques la Boucherie, robbers made their way in during the night, lifted Flamel's tombstone and broke open his coffin. It was after this incident that the rumor spread that the coffin had been found empty, and that it had never contained the body of Flamel, who was supposed to be still alive.
Through whatever means, it is believed Richelieu took possession of the book of Abraham the Mage. He built a laboratory at the Chateau of Rueil, which he often visited to read through the master's manuscripts and to try to interpret the sacred hieroglyphs. But that which a sage like Flamel had been able to understand only after twenty-one years of meditation was not likely to be at once accessible to a politician like Richelieu. Knowledge of the mutations of matter, of life and death, is more complex than the art of planning strategies or administering a kingdom. Richelieu's search gave no good results.
Sources:
http://www.flamelcollege.org/flamel.htm |