1. The problem statement, all variables and given/known data On pages 65-66 of Calculus An Intuitive And Physical Approach, Mr. Kline discusses Inclinations of lines. In illustration 3A-7 he uses the substitution method to create a proof. But there is one step that I think he leaves out. He shows the equation tan A = tan(180 - B) = -tan(B). I understand that angle A = (180 - B) So I understand the first part of the equation. But what I want to know is what he does to the number 180 in the second part of the equation. 2. Relevant equations tan(A) = tan(180 - B) = -tan(B) 3. The attempt at a solution After researching Ptolomey's table of Chords and Rene Descartes, I know that negative numbers were not used in early mathematics. I also know that Euclid himself never considered negative numbers. I've heard that Fermat and Issac Newton were some of the first people to use negative numbers. But this still doesn't completely explain what happens to the number 180 in the second part of the equation.