How to solve Second Degree Algebraic Equations using Geometry

One of the most complicated problems faced by mathematicians was to calculate the solutions of the algebraic equations of each degree. First examples of first-degree equation solutions are reported in an Egyptian papyrus dating back to 1650 BC. In some Babylonian tablets, we find methods of resolution of some second-degree equations by geometric construction. Euclid, around 300 BC, de-scribed a geometric method for solving equations. The concept of equation, as we know it, was born and developed in the Arab world, above all thanks to Al-Khuwarizmi, which distinguishes six types of first and second-degree equations and resolves them using squared completion. Omar Khayyam, in his book Treatise on the proof of algebra problems, published in 1070, deals with the transformation of geometric problems into algebraic prob-lems and vice versa, and set in a general way how to bring them back to equa-tions at the maximum of third degree for which geometric solutions are proposed. (MARACCHIA, 2005) In 1748, Maria Gaetana Agnesi, a Milanese mathematician, published her main book Analytical Institutions for the use of Italian Youth. (AGNESI,1748) The first volume deals with the analysis of finite quantities and the second of the infinitesimal analysis. Maria Gaetana dedicates her work to the Empress Maria Theresa of Austria, an enlightened woman. In chapter II of the first book, Maria Gaetana deals with the study of first and second-degree equations by providing a method of solving second-degree equations by geometric means. Furthermore, she proposes some problems and exercises that can be solved with equations.