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Arithmetic

(1,608 words)

Author(s): Epple, Moritz
1. General The techniques of arithmetic and the media required are among the earliest cultural achievements of humankind. In many places (e.g. southern Mesopotamia at the end of the 4th millenium BCE), the introduction of writing was associated directly with the techniques of written arithmetical calculation and bookkeeping. Where arithmetical theory emerged, as in ancient Greece, practical calculation naturally remained in use as well; in many cases it had its own separate history, concealed in part by the history of academic mathematics [3]. The latter also includes the te…
Date: 2017-02-14

Equation

(845 words)

Author(s): Epple, Moritz
1. BeginningsEven though the equality of quantities and figures or numbers and ratios is a relationship that had been in use in the mathematical sciences since their beginnings, solving equations, that is, the symbolically expressed equality of two algebraic expressions containing known and unknown quantities, did not become a focus of mathematical problem solving until around 1600 – with the advent of symbolic algebra and the analytic geometry dependent on it. Even earlier, though (building on s…
Date: 2018-02-14

Differential geometry

(828 words)

Author(s): Epple, Moritz
A key aspect of the renewal of mathematics in the 17th century was the combination of geometric themes with symbolic/calculatory techniques related to the infinitesimal, that is, the infinitely small (Analysis, mathematical; Infinitesimals). This enabled a new way of conducting geometry, the most appropriate term for which in the 17th century is infinitesimal geometry and which from the 18th century onwards - the century of the elaboration of differential calculus - developed further as differential geometry.The main subjects of differential geometry in the 17th and…
Date: 2018-02-14

Analysis situs

(765 words)

Author(s): Epple, Moritz
At the end of the 17th century,  analysis situs (“analysis of the location”) or geometria situs (“geometry of the location”) came into use as an early term for the field of mathematics we today call topology, a new field initially developed very slowly during the 18th and 19th centuries (see Mathematical sciences). Alongside the mathematical theory of probability, its was the most important field of mathematics to be developed totally from the ground up in the Early Modern era, without any roots in antiquity.At the same time as modern analysis (Analysis, mathematical) was c…
Date: 2017-02-14

Geometry

(3,588 words)

Author(s): Epple, Moritz
1. Historical development: overview From Greek antiquity onwards, the cultures of the Mediterranean considered geometry - the study of figures on the plane and in space - to be the epitome of an exact science, relying on strict proofs based on precisely formulated assumptions. Geometry moreover represented science’s most powerful language for expressing relations of size, trumping the arithmetica universalis. Its domain extended from direct measurement of spatial proportions through astronomy and optics to the art of construction.The early modern era witnessed a remar…
Date: 2018-11-28

Hydrodynamics

(977 words)

Author(s): Epple, Moritz
1. GeneralDue to its complexity, the mathematical and physical description of the motion of fluids was one of the areas of the mathematical sciences that demanded the application of the most advanced techniques in mathematics, while in the context of the time, there was a productive interaction between problems in hydraulics, experimental study, theoretical analysis and the possibility of effective computation.Moritz Epple2. From the 15th to the 17th century Hydraulic engineering, which had shaped the cities of antiquity, gained great sig…
Date: 2018-11-28

Geodesy

(1,134 words)

Author(s): Epple, Moritz
1. Traditions and beginnings in the 16th century The process of measuring of the earth, supported by optical, astronomical and mathematical tools and procedures, was an important component of the new European natural sciences of the 16th and 17th century. This practise was closely tied to maritime navigation and was of economic, military and political significance. As such it served both as a field of application and a driver for innovation in the natural sciences.Modern geodesy had its origins in the manufacturing of maps and globes (Cartography). This practise was k…
Date: 2018-11-28

Ballistics

(1,069 words)

Author(s): Epple, Moritz
Ballistics (the science of the behavior of projectiles) was one of the disciplines that played a key role in the emergence of the new science of the 16th and 17th centuries. It provided both a motivation and one of the trickiest applications for mechanics as a mathematical science of motion. It was also related, not always straightforwardly, with early modern weaponry and artillery.Two concepts of the motion of a projectile were in competition. First, it was possible to see the phenomenon as the motion of a body through a continuous medium. Alternativel…
Date: 2017-02-14