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Printing Press
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Apian publishes work on Pascal's Triangle and the Fibonacci Sequence.
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Tartaglia publishes on Cubic Equations
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Nicolaus Copernicus bucks tradition by postulating and theorizing about the heliocentric universe, in which the sun (helios) not the Earth is the center of our galaxy.
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First appearance of the +/- symbols in text, as well as the = symbol, for mathematics.
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Cardano publishes Liber de Ludo Aleae, which studies probability.
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Kepler publishes his Laws of Planetary Motion, which both explain the movement of the planets within our solar system, but also back and prove Copernicus' theory of the Heliocentric Universe.
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John Napier publishes his work on logarithms, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.
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Santorio Santorini invents the Thermometer.
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Descartes applies algebra to geometry, making the maths more accessible and easy to understand to the average person.
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Evangelista Torricelli and Gasparro Berti invent the Barometer, used to measure barometric pressure.
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Hennig Brand discovers the element Phosphorus.
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Robert Boyle publishes his theory of corpusculation, which basically states that the individual atom of a particular element is at its bassist level, and cannot be further reduced without completely destroying the atom.
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Gottfried Wilhelm Leibniz publishes the first work on the subject of Calculus, the creation of which he shared credit with Sir Isaac Newton.