... helped Kepler to refine his theory through mathematical method unintentionally. John Napier is famous for his discovery of logarithms. And the discovery of logarithms is also famous for helping Kepler. In the Biographical Encyclopedia of Astronomers, it was described that "His invention of logarithms with base e was announced in 1614. The invention was of great assistance to Johannes Kepler, and made possible ... ...

• Word Count: 1699
• Approx Pages: 7
• Has Bibliography
• Grade Level: Undergraduate

... finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula) and was the first to use power series with confidence and to revert power series with confidence and to revert power series. Newton's work on ... ...

• Word Count: 6149
• Approx Pages: 25
• Grade Level: Undergraduate

... (Chposky, 1988). Aiken's machine, called the Harvard Mark I, handled 23-digit numbers and could perform all four arithmetic operations (Dolotta, 1985). Also, it had special built-in programs to handled logarithms and trigonometric functions. The Mark I was controlled from prepunched paper tape. Output was by card punch and electric typewriter. It was slow, requiring 3 to 5 seconds for a multiplication, but it was ... ...

• Word Count: 2566
• Approx Pages: 10
• Grade Level: Undergraduate

... (Chposky, 1988). Aiken's machine, called the Harvard Mark I, handled 23-digit numbers and could perform all four arithmetic operations (Dolotta, 1985). Also, it had special built-in programs to handled logarithms and trigonometric functions. The Mark I was controlled from prepunched paper tape. Output was by card punch and electric typewriter. It was slow, requiring 3 to 5 seconds for a multiplication, but it was ... ...

• Word Count: 2566
• Approx Pages: 10
• Grade Level: Undergraduate

... with low standard errors (notwithstanding the ever-present problem of multicollinearity). It transpires that the rate of profit has a pronounced cyclical component and so proxying the sum of the weighted logarithms of w and r by a linear time trend (or their growth rates by a constant) biases the estimated coefficients of lnL and lnJ (McCombie, 2000-2001, Felipe and Holz, 2001, and Felipe and ... ...

• Word Count: 11086
• Approx Pages: 44
• Has Bibliography
• Grade Level: Undergraduate

... (Chposky, 1988). Aiken's machine, called the Harvard Mark I, handled 23-digit numbers and could perform all four arithmetic operations (Dolotta, 1985). Also, it had special built-in programs to handled logarithms and trigonometric functions. The Mark I was controlled from prepunched paper tape. Output was by card punch and electric typewriter. It was slow, requiring 3 to 5 seconds for a multiplication, but it was ... ...

• Word Count: 2571
• Approx Pages: 10
• Grade Level: Undergraduate

... (Chposky, 1988). Aiken's machine, called the Harvard Mark I, handled 23-digit numbers and could perform all four arithmetic operations (Dolotta, 1985). Also, it had special built-in programs to handled logarithms and trigonometric functions. The Mark I was controlled from prepunched paper tape. Output was by card punch and electric typewriter. It was slow, requiring 3 to 5 seconds for a multiplication, but it was ... ...

• Word Count: 2566
• Approx Pages: 10
• Grade Level: Undergraduate

... (Chposky, 1988). Aiken's machine, called the Harvard Mark I, handled 23-digit numbers and could perform all four arithmetic operations (Dolotta, 1985). Also, it had special built-in programs to handled logarithms and trigonometric functions. The Mark I was controlled from prepunched paper tape. Output was by card punch and electric typewriter. It was slow, requiring 3 to 5 seconds for a multiplication, but it was ... ...

• Word Count: 2510
• Approx Pages: 10
• Grade Level: Undergraduate