Coloquio del IMUNAM - C.U.

My talk will focus on one aspect of the dynamics that led to the consideration of ratios of geometric quantities as numerical quantities through the evolution of the notion of angles in theoretical astronomical works.

First, I will show how Ptolemy (2nd century), while trying to determine the distance between the Earth and the Moon, is forced to manipulate the ratios of geometric quantities in order to quantify angles. This difficulty inherent to the quantification of angles leads him, while trying to calculate the diameters of the planets, to renounce to a direct method and to use a method requiring numerous manipulations of ratios.

In the second episode, I will show how Al-Battani (IX-Xth century), certainly for practical reasons linked to observation, came to elaborate a numerical representation of the angles in order to compare the apparent diameters of the stars between them.

Finally, I will conclude by showing a proposal, in my opinion a fully mathematical one, by al-Biruni (11th century) which consists in taking up the direct method abandoned by Ptolemy and applying it algebraically, i.e. without taking into account the geometrical or numerical nature of what he manipulates. A quick analysis of the paragraphs surrounding this proposition will suffice to convince us that this is indeed a proposition that the author knows to be audacious and modern.