David gave full play to his advantages in algebraic research and solved some geometric problems with algebraic methods. He gave some knowledge of algebraic equations involved in ruler and ruler drawing, and earlier transformed the famous bicubic problem ("Find the sides of a cube to make the volume of the cube twice that of a given cube") and the problem of angle trisection ("Divide any given angle into three equal parts") into the problem of solving cubic equations. In fact, only compasses and straightedge can't complete the accurate drawing of three famous geometric drawing problems-cubic problem, angle bisection problem and turning a circle into a square ("making a square to make it equal to a given circle area"). It was not until19th century that this impossibility was proved by mathematicians, and two thousand years have passed since these three questions were put forward.

In the book "Various Mathematical Solutions", David discussed some geometric drawing problems and gave the summation formula of infinite geometric series. The following formula for calculating pi was clearly given at the earliest:

This is the first analytic expression of π. David used a circle inscribed with a polygon of 3932 16 to make π accurate to 10 after the decimal point, which was the best pi value in Europe at that time. David's thought of solving geometric problems by algebraic method is of far-reaching significance to the later development of mathematics, because it embodies the fundamental spirit of analytic geometry.