Renaissance mathematicians did not have some of the basic tools for solving problems, notably proper logarithmic tables, analytic geometry, and differential calculus. Nevertheless major progress was made in algebra and geometry. Before the 14th century, algebraic problems were expressed mostly in narrative language, as in a literary text. Most numbers and expressions were written out, hindering visualization of the problem. Then during the early 14th century European mathematicians began to learn the Hindu-Arabic method for writing out their problems in a sort of shorthand, which included the symbolic letters of today’s algebra. The familiar notations used in algebra were a Renaissance invention. in mathematics in general, the Arabic base 10 system of arithmetic was adapted by Europeans during this time. Advancements in geometry were important for art, as human proportions were better represented and linear perspective was applied to painting (see chapter 3). The new geometric knowledge also contributed to improvements in surveying, navigation, and cartography (see chapter 9). Trigonometry began to be understood, and multiple-angle formulas were used for the trigonometric functions. The combination of rediscovered ancient Greek sources and increasingly sophisticated commercial problems requiring computation created new opportunities for mathematicians to experiment and learn.
World History
