For the most part the teachers teaching it never studied the technique of discovery. The ancient Egyptians understood how to measure a sphere. They did so with a plumb line across great distances only to acknowledge that space is curved. The Ptolemy's (Macedonians in Egypt like Cleopoatra) were masters of geometry, they were the first one's to hypothesize about the size of the Earth and that it was a sphere. Of course they referenced Aristotle's acknowledgment of discovering Elephants in both Africa and India. This was Aristotle's first empirical observation that the Earth was in fact round! Aristotle travelled with Alexander The Great in his ambition to forever thwart Persia, he died somewhere in the borderlands between modern day Pakistan and India.
Nevertheless, France organized a scientific mission in 1735 to arrive at the Equator and measure the Earth.
The key to the shape of the planet was discovering the width of one degree latitude measured at the equator.
In 1735 a mission was organized by the French Academy of Sciences to fit explorers arriving in South America to accomplish this adventure. France was so eager to accomplish this exploration that it spent millions of dollars to obtain this very number.
The practical implication of this number is incalculable: it would help maintain accuracy in cartography, therefore assist in accurate navigation of the seas. It was instrumental in forging France into an Empire, unrivaled.
Newton's recently published theory of mechanics (physics) stipulated that the spinning earth would resemble more of an apple than a sphere, wider at the equator and flatter at the poles. For if the earth were a perfect sphere, then a degree latitude would be everywhere perfect.
To establish the width of one degree latitude at the equator would require thousands of measurements from positions not easily accessible.
Base camp was Quito, Ecuador.
The 200 mile arch that the scientists choose to survey traveled across a line of volcanoes in the Andes, each of which they had to climb. They camped at altitudes of 15,000 feet for months at a time, battling subzero temperatures and coping with altitude sickness while waiting for skies to clear. Good weather was essential for measurements required the use of known astronomy. There were 40 members assigned to this trip with over 200 slaves.
Many resident colonials, not understanding the mission or even what science was, took the French foreigners for smugglers. In South America of that time, all smugglers were believed to be Jews, practicing Judaism was punishable by death, the local head of the Inquisition took great interest in the travelers.
After nine long years of measuring the ground and the stars, the team of scientists finally triumphed in 1743. They now possessed the magic number of 68.70 miles for one degree latitude on the equator, as compared with 69.07 miles in Paris.
With the arrival of the War of Austrian Succession, England and Spain had drawn themselves into war against France, each member of the team had to make his own way home.
The first scientist to arrive in Paris was Pierre Bouguer, second was Charles Marie de La Condamine, who actually rode down the Amazon before crossing the Atlantic, he would later return and publish his findings in 1751.
The teams doctor, named Joseph de Jussieu didn't have the heart to leave behind the many people he came into contact with, especially those working in a silver mine that used mercury in separating ore, required his medical attention. He finally returned home to France after 36 years from the arrival of Pierre Bouguer.
The last to arrive was Jean Baptise Godin des Odonais who arrived in France 36 years after departing. He married a local women named Isabel yet were barred by Portuguese authorities from reentering Brazil to bring her home to France. They waited for one another 21 years in the Amazon, when he arrived dozens of miles upstream to discover her and bring her home to France. The year was 1773!
The Geodesic Mission of 1735 is chronicled by Larrie Ferreiro in "Measure of the Earth" Basic Books 2010.