Yoder places Huygens's work in the context of his time by examining his relationship with other scientists and the priority disputes that sometimes motivated his research. Joella Yoder details the creative interaction that led Huygens to invent a pendulum clock that theoretically beat absolutely uniform time, to measure the constant of gravitational acceleration, to analyze centrifugal force, and to create the mathematical theory of evolutes. This case study examines the interrelationship between mathematics and physics in the work of one of the major figures of the Scientific Revolution: the Dutch mathematician, physicist, and astronomer, Christiaan Huygens (1629-1695). Finally, the role of Huygens in the rise of applied mathematics is addressed. The reception of Huygens' masterpiece, the Horologium Oscillatorium of 1673 and the place of evolutes in the history of mathematics are also analyzed. A discussion of Huygens' relationship with other scientists and the priority disputes that sometimes motivated his research help place his work in the context of the period. She also describes the way that each of these important discoveries arose from the interaction of Huygens' mathematics and physics. Professor Yoder offers a detailed account of the discoveries that Huygens made at the end of 1659, including the invention of a pendulum clock that theoretically kept absolutely uniform time, and the creation of a mathematical theory of evolutes. With a system of three circles it is readily seen that thereĪre six centres of similitude, viz.This case study examines the interrelationship between mathematics and physics in the work of one of the major figures of the Scientific Revolution, the Dutch mathematician, physicist, and astronomer, Christiaan Huygens (1629-1695). Which has for its base the distance between the centres of theĬircles and the ratio of the remaining sides equal to the ratio of the It may be shown to be the locus of the vertex of the triangle Of similitude as diameter is named the “circle of similitude.” The circle on the line joining the internal and external centres “internal centre.” It may be readily shown that the externalĪnd internal centres are the points where the line joining theĬentres of the two circles is divided externally and internally in Rise to the “external centre,” the transverse tangents to the Tangents to the two circles, the direct common tangents giving Of two circles may be defined as the intersections of the common 2=0 as the equation to theĬentres and Circle of Similitude.-The “centres of similitude” Should be made to the article Geometry: Euclidean, for aĭetailed summary of the Euclidean treatment, and the elementary Triangles, quadrilaterals and regular polygons. With the circle in its relations to inscribed and circumscribed Relating to the circle, and certain lines and angles, which heĭefines in introducing the propositions. and II.Įuclid devotes his third book entirely to theorems and problems “distance.” Having employed the circle for the constructionĪnd demonstration of several propositions in Books I. The possibility of describing a circle for every “centre” and ![]() Three definitions the centre, diameter and the semicircle areĭefined, while the third postulate of the same book demands ![]() Within the figure are equal to one another.” In the succeeding 15) as a “plane figure enclosedīy one line, all the straight lines drawn to which from one point Its simplicity specially recommending it as an object for study.Įuclid defines it (Book I. The circle was undoubtedly known to the early civilizations, 4 theĬlear figure is sometimes termed a “lens.” ABD, isĬircles a “lune,” the shaded portions in fig. 2), is termed an “arc” Īnd the plane figure enclosed by a chord and arc, e.g. DEF, is termed a “secant” if it touches the circle, e.g.ĭG, it is a “tangent.” Any portion of the circumference Line drawn from an external point to cut the circle in two points,Į.g. AB, is a “diameter” Īny other line similarly terminated, e.g. “circumference.” Any line through the centre and terminatedĪt both extremities by the curve, e.g. 1) the constant distance, e.g.ĬG, the “radius.” The curve itself is sometimes termed the ![]() The fixed point in the preceding definition is The form of a circle is familiar to all and we proceed to defineĬertain lines, points, &c., which constantly occur in studying Moves so that its distance from a fixed point is constant. Κρίκος), a plane curve definable as the locus of a point which word is κιρκος, generally used in the form
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