The idea of the logarithm probably had its source in the use of... trigonometric formulas that transformed multiplication into addition and subtraction. ...[I]f one needed to solve a triangle using the law of sines, a multiplication and division were required. ...[C]alculations were long and errors... made. Astronomers realized... multiplication and division could be replaced by additions and subtractions. To accomplish this... sixteenth century astronomers used formulas... as 2 sin alpha sin beta = cos(alpha - beta) - cos (alpha + beta). ...A second source of the... logarithm was probably found in... algebraists as Stifel and Chuquet, who both displayed tables relating the powers of 2 to the exponents and showed that multiplication in one table corresponded to addition in the other. But because these tables had large gaps, they could not be used for necessary calculations. ...[T]wo men... independently, the Scot John Napier... and the Swiss Jobst Bürgi... came up with the idea of producing an extensive table... to multiply any... numbers... (not just powers of 2)... Napier published... first.

What It Means

This is a placeholder explanation generated by the low-overhead model. It interprets "The idea of the logarithm probably had its source in the use of... trigonometric formulas that transformed multiplication into addition and subtraction. ...[I]f one needed to solve a triangle using the law of sines, a multiplication and division were required. ...[C]alculations were long and errors... made. Astronomers realized... multiplication and division could be replaced by additions and subtractions. To accomplish this... sixteenth century astronomers used formulas... as 2 sin alpha sin beta = cos(alpha - beta) - cos (alpha + beta). ...A second source of the... logarithm was probably found in... algebraists as Stifel and Chuquet, who both displayed tables relating the powers of 2 to the exponents and showed that multiplication in one table corresponded to addition in the other. But because these tables had large gaps, they could not be used for necessary calculations. ...[T]wo men... independently, the Scot John Napier... and the Swiss Jobst Bürgi... came up with the idea of producing an extensive table... to multiply any... numbers... (not just powers of 2)... Napier published... first." in the context of "Victor J. Katz, A History of Mathematics: An Introduction (1993, 1998)" to mean that wisdom is timeless.