# Mathematical tools: Abacus, Slide rule, Analytical Engine, Calculator, Straightedge, Nomogram, Location arithmetic, Napier's bones

## Source: Wikipedia

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 65. Chapters: Abacus, Slide rule, Analytical Engine, Calculator, Straightedge, Nomogram, Location arithmetic, Napier's bones, Mechanical calculator, Differential analyser, Rod calculus, Counting rods, Suanpan, Stepped Reckoner, Curta calculator, Mathematical table, Planimeter, Compass, Jeton, Genaille-Lucas rulers, Graph paper, Integrator, Protractor, Otis King, Arithmetic rope, Chisanbop, Coggeshall slide rule, Calculating machine, Steinhaus longimeter, Shadow square, Counting board, Oxford Set of Mathematical Instruments, Mate Tusanga, Geometry template. Excerpt: Location arithmetic (Latin arithmeticæ localis) is a technique to do binary arithmetic using a chessboard-like grid. John Napier termed the technique in his treatise Rabdology, from the way that positions of counters on the board represented numbers. Using simple moves of counters on the board, Napier showed ways to multiply, divide and even find the square roots of binary numbers. He was so pleased by his discovery that he said in his preface ... it might be well described as more of a lark than a labor, for it carries out addition, subtraction, multiplication, division and the extraction of square roots purely by moving counters from place to place. Binary notation had not yet been standardized, and Napier used what he called location numerals to represent binary numbers. Roughly speaking, it used alphabets to stand for various powers of two. He used a to represent 1, b for 2, c for 4, d for 8, e for 16 and so on. To represent a number as a location numeral, express it as a sum of powers of two and replace the powers by the letters. For example 87 = 1 + 2 + 4 + 16 + 64 = abcegA location numeral can similarly be converted back into standard notation: abdgkl = 1 + 2 + 8 + 64 + 512 + 1024 = 1611He permitted letters to repeat, so the same number could be represented in m...

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