He used negative coordinates freely, although it was Isaac Newton who unequivocally used two (oblique) axes to divide the plane into four quadrants, as shown in the ) solved special cases of the basic problems of calculus: finding tangents and extreme points (differential calculus) and arc lengths, areas, and volumes (integral calculus).
François Viète introduced the first systematic algebraic notation, using letters to represent known and unknown numerical quantities, and he developed powerful general methods for working with algebraic expressions and solving algebraic equations.
With the power of algebraic notation, mathematicians were no longer completely dependent upon geometric figures and geometric intuition to solve problems.
And really, all those calculations that the computer is doing is based off geometric and mathematical principles that have been proved either with the use of geometric tools or by some other method.
Now, you may be wondering just what tools are part of your geometric tool box.
What they did have was good old geometry with basic geometric tools used to draw geometric figures and perform the math of geometry.
With just two of these tools, you can draw and solve just about any geometric problem you come across. If you didn't have a computer but you did have your geometric tools, then you could potentially draw up a working blueprint for a house.
Your angles would be spot on, and your distances would be on point.
You could do this all without the use of a computer program that measures and gives you angles at the push of a button.
Newton divided cubics into 72 species, a total later corrected to 78.
Do you think you could build the pyramids if you didn't have any modern tools or calculators? The Egyptians didn't have modern tools or calculators when they built it.