Question: What was the year of birth of the mathematician that is credited with developing infinitesimal calculus and using Jean Picard's measurement of earth to create his theory of universal gravitation?

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Pierre de Fermat: Pierre de Fermat (] ; (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the "Parlement" of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.  In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory.  He made notable contributions to analytic geometry, probability, and optics.  He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' "Arithmetica".

Isaac Barrow: Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus.  His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve.  Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form.

API-Calculus: API Calculus is a program that solves calculus problems using operating systems within a device that solves calculus problems.  In 1989 the PI- Calculus was created by Robin Milner and was very successful throughout the years.  The PI Calculus is an extension of the extension of the process algebra CCS, a tool that has algebraic languages that are specific to processing and formulating statements.  The PI Calculus provides a formal theory for modeling systems and reasoning about their behaviors.  In the PI Calculus there are two specific variables such as name and processes.  But it was not until 2002 when Shahram Rahimi decided to create an upgraded version of the PI- Calculus and call it the API Calculus.  Milner claimed the detailed characteristics of the API Calculus to be its "Communication Ability, Capacity for Cooperation, Capacity for Reasoning and Learning, Adaptive Behavior and Trustworthiness."  The main purpose of creating this mobile advancement is to better network and communicate with other operators while completing a task.  Unfortunately, the API Calculus is not perfect and has faced a problem with its security system.  The language has seven features that was created within the device that the PI Calculus does not have.  Since this program is so advanced by the way the software was created and the different abilities that are offered in the program, it is required to be converted to other programming languages so it can be used on various devices and other computing languages.  Although the API Calculus is currently being used by various other programming languages, modifications are still being done since the security on the API Calculus is causing problems to users.

Guillaume de l'Hôpital: Guillaume François Antoine, Marquis de l'Hôpital (] ; 1661 – 2 February 1704) was a French mathematician.  His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞.  Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his treatise on the infinitesimal calculus, entitled "Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes".  This book was a first systematic exposition of differential calculus.  Several editions and translations to other languages were published and it became a model for subsequent treatments of calculus.

Leonhard Euler: Leonhard Euler ( ; ] ; ] ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer who made important and influential discoveries in many branches of mathematics like infinitesimal calculus and graph theory while also making pioneering contributions to several branches such as topology and analytic number theory.  He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.  He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.

Law of Continuity: The Law of Continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler.  It is the principle that "whatever succeeds for the finite, also succeeds for the infinite".  Kepler used it to calculate the area of the circle by representing the latter as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely-many triangles with infinitesimal bases.  Leibniz used the principle to extend concepts such as arithmetic operations, from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus.  A mathematical implementation of the law of continuity is provided by the transfer principle in the context of the hyperreal numbers.

John Wallis: John Wallis ( ; 3 December 1616 – 8 November 1703) was an English mathematician who is given partial credit for the development of infinitesimal calculus.  Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court.  He is credited with introducing the symbol ∞ for infinity.  He similarly used 1/∞ for an infinitesimal.

Jean Picard: Jean-Félix Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand.  He died in Paris, France.  He was the first person to measure the size of the Earth to a reasonable degree of accuracy in a survey conducted in 1669–70, for which he is honored with a pyramid at Juvisy-sur-Orge.  Guided by Maurolycus's methodology and Snellius's mathematics for doing so, Picard achieved this by measuring one degree of latitude along the Paris Meridian using triangulation along thirteen triangles stretching from Paris to the clocktower of Sourdon, near Amiens.  His measurements produced a result of 110.46 km for one degree of latitude, which gives a corresponding terrestrial radius of 6328.9 km.  The polar radius has now been measured at just over 6357 km.  This was an error only 0.44% less than the modern value.  This was another example of advances in astronomy and its tools making possible advances in cartography.  Picard was the first to attach a telescope with crosswires (developed by William Gascoigne) to a quadrant, and one of the first to use a micrometer screw on his instruments.  The quadrant he used to determine the size of the Earth had a radius of 38 inches and was graduated to quarter-minutes.  The sextant he used to find the meridian had a radius of six feet, and was equipped with a micrometer to enable minute adjustments.  These equipment improvements made the margin of error only ten seconds, as opposed to Tycho Brahe's four minutes of error.  This made his measurements 24 times as accurate.  Isaac Newton was to use this value in his theory of universal gravitation.

Isaac Newton: Sir Isaac Newton {'1': ", '2': ", '3': ", '4': "} ( ; 25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution.  His book "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics.  Newton also made pathbreaking contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

History of the philosophy of field theory: Field theory, the study of dynamical fields in physics, was originally a powerful mathematical formulation of Newtonian mechanics.  The success of Newtonian physics since the publication of the "Principia" provided a strong framework with which to investigate the motion and forces associated with electricity and magnetism.  Charles-Augustin de Coulomb showed in 1785 that the repulsive force between two electrically charged spheres obeys the same (up to a sign) force law as Newton's law of universal gravitation: the force between two bodies is directed along the line separating the bodies and its magnitude is proportional to the product of their charges (for gravitation, their masses) divided by the square of their distance apart.  André-Marie Ampère then showed in 1823 that the force between infinitesimal lengths of current-carrying wires similarly obeys an inverse-square law such that the force is directed along the line of separation between the wire elements.

Supporting paragraphs: Jean Picard Isaac Newton
Answer: 1642