He is sentenced to first degree murder charges and put in the care of Dr. Loomis at the Smith Grove Warren County Sanitarium.
Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers, Diophantus being always satisfied with a rational, even if fractional, result and not requiring a solution in integers.
In the Letter to Magister Theodore indeterminate problems are chiefly worked, and Leonardo hints at his being able to solve by a general method any problem of this kind not exceeding the first degree.
He was also the first to consider the difficult problems involved in equations of mixed differences, and to prove that an equation in finite differences of the first degree and the second order might always be converted into a continued fraction.
In the first degree there is a strong persuasion of the propriety of the impression made; the second and third degrees are produced by comparisons of the impression with others associated with it, and an analysis of itself.
