Paul Kinion
This paper provides the second known solution to da Coi’s quartic, a problem posed and partially solved in Girolamo Cardano’s Ars Magna. The objective was to test a method for solving polynomial equations. First, horizontally shift the polynomial to “center” it. That is, move it to a polynomial with 0 as the second leading coefficient. Second, with the advantage of symmetry, solve the centered equation. Third, shift the solutions back to the original polynomial. Da Coi’s quartic is a 500-year-old story problem that leads to solving a fourth-degree polynomial. The method yielded the two exact real answers as reported in The Scrubby Plant, 2026. Here we illustrate the method with an alternate solution. The goal is to find the mathematical stumbling block that made the solution to da Coi’s problem so elusive. Non-mathematical reasons are also explored. The focus on solving quartics has been approximation, here we simply solve them.