Carlos III and his court of enlightened ministers govern in Madrid. There, well related, Betancourt is formed, he is promoted and he will end up being conceded a grant to study in Paris in 1784.
In January 1779 he enrols at the Colegio de San Isidro in Madrid, managed by his maternal cousin, beginning classes of geometry, algebra and trigonometry, that he is going to do at the same time as night studies at the Real Academia de Bellas Artes de San Fernando, moved by his great love of drawing that he had since childhood.
In 1780, in his second course, he follows up with classes of mathematical analysis, differential and integral calculus, theory of curves and analytical mechanics. Just like the previous year he takes his public exams on these matters [See “Exercicio de Matemáticas que ha de tener en los Estudios Reales de esta Corte”]. He also sends some examples of his drawings from the Academia de San Fernando to his family, concretely a figure of full body and two heads [See the drawings] that opted for the prize of the academy. [See Letter from Betancourt to his father August 16th, 1780: Letter 1].
The following year Betancourt holds an exposition of his paintings and finishes his artistic studies at San Fernando; he practices his French [See Letter from Betancourt to his parents August 20th, 1781: Letter 2]; he studies physics at San Isidro and has the opportunity to attend the making of laboratory instruments. At the same time, his brother José and his sister María continue to present memoirs to the Real Sociedad de Amigos del País de Tenerife: María on textiles and dyes, and José on the implementation of a printing press. Precisely Agustín himself was entrusted, after being named representative of the society in Madrid, with the acquisition of printing characters for the Society of La Laguna as his brother José had proposed.
It seems that the good formation of Agustín, his direct and franc character, and his good personal relationships in Madrid made the Conde de Floridablanca, D. José Moñino, give him a mission of some importance, an informative visit to the Canal Imperial de Aragón, after the breakage of the Brocal reservoir, which he will make with Alonso de Nava y Grimón, marques de Villanueva del Prado (both will later write a memoir titled Noticias de la Acequia Imperial o Canal Real de Aragón). After finishing this job successfully, the first incursion into civil engineering of our author, Betancourt will be asked by Floridablanca to inspect the mines of Almadén that had been working since the times of the Roman Empire.
The inspection that Betancourt made at Almadén concluded in several proposals of improvement that were carried out successfully, which must have impressed the Secretary of State. This work was expressed in three memoirs. The First Memoir is dedicated to the water of the mines and its extraction. The Second Memoir studied the machinery used in the extraction of the mineral. And the Third Memoir was about the works of the smelting of the mineral and its packing. The three are dated in 1783. Some notes (incomplete) are conserved about the journey that Betancourt made on the way to Ciudad Real in which leaving from Aranjuez he passes through Toledo, Fernán Caballero and other towns. [See notes June 1783: Letter 4].
Another event worth mentioning of this time was the first launching of an aerostatic balloon in Spain, work of Agustín de Betancourt. It took place in presence of the Royal Court on November 29th 1783. José de Viera y Clavijo, another illustrious Canarian, launched his own balloon on December 15th of the same year. As known the first public exhibitions of aerostatic balloons had been carried out by the Montgolfier Brothers just a few months earlier in France
