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On The Equilibrium Of Planes
''On the Equilibrium of Planes'' ( grc, Περὶ ἐπιπέδων ἱσορροπιῶν, translit=perí epipédōn isorropiôn) is a treatise by Archimedes in two volumes. The first book contains a proof of the law of the lever and culminates with propositions on the centre of gravity of the triangle and the trapezium. The second book, which contains ten propositions, examines the centres of gravity of parabolic segments. According to Pappus of Alexandria, Archimedes' work on levers caused him to say: "Give me a place to stand on, and I will move the Earth" ( grc, δός μοί ποῦ στῶ καὶ κινῶ τὴν γῆν, translit=dṓs moi poû stṓ kaí kinô tḗn gên, links=no), though other ancient testimonia are ambiguous regarding the context of the saying. Overview The lever and its properties were already well known before the time of Archimedes, and he was not the first to provide an analysis of the principle involved. The earlier '' Mechanical Problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes
Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time,* * * * * * * * * * Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Heath, Thomas L. 1897. ''Works of Archimedes''. Archimedes' other mathematical achievements include deriving an approximation of pi, defining ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrature Of The Parabola
''Quadrature of the Parabola'' ( el, Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his Alexandrian acquaintance Dositheus. It contains 24 propositions regarding parabolas, culminating in two proofs showing that the area of a parabolic segment (the region enclosed by a parabola and a line) is \tfrac43 that of a certain inscribed triangle. It is one of the best-known works of Archimedes, in particular for its ingenious use of the method of exhaustion and in the second part of a geometric series. Archimedes dissects the area into infinitely many triangles whose areas form a geometric progression. He then computes the sum of the resulting geometric series, and proves that this is the area of the parabolic segment. This represents the most sophisticated use of a ''reductio ad absurdum'' argument in ancient Greek mathematics, and Archimedes' solution remained unsurpassed until the development ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simon Stevin
Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He also translated various mathematical terms into Dutch, making it one of the few European languages in which the word for mathematics, '' wiskunde'' ('' wis'' and '' kunde'', i.e., "the knowledge of what is certain"), was not a loanword from Greek but a calque via Latin. He also replaced the word ''chemie'', the Dutch for chemistry, by '' scheikunde'' ("the art of separating"), made in analogy with '' wiskunde''. Biography Very little is known with certainty about Simon Stevin's life, and what we know is mostly inferred from other recorded facts. E. J. Dijksterhuis (1970) ''Simon Stevin: Science in the Netherlands around 1600'', The Hague: Martinus Nijhoff Publishers, Dutch original 1943, 's-Gravenhage The exact birth date and the date and place of his death ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernardino Baldi
Bernardino Baldi (5 June 1553 – 10 October 1617) was an Italian mathematician, poet, translator and priest. Baldi descended from a noble family from Urbino, Marche, where he was born. He pursued his studies at Padua, and is said to have spoken about sixteen languages during his lifetime, though according to Tiraboschi the inscription on his tomb limits the number to twelve. The appearance of the plague at Padua forced him to return to his native city. Shortly afterwards he was called to act as tutor to Ferrante Gonzaga, from whom he received the rich abbey of Guastalla. The oldest biography of Nicolaus Copernicus was completed on 7 October 1588 by him.On the revolutions, Foundations of natural history, Band 1, p.335, Nicolaus Copernicus: Complete Works, Edward Rosen, Johns Hopkins University Press, 1992. He held office as abbot for 25 years, and then returned once again to Urbino. In 1612 he was employed by the duke as his envoy to Venice. Baldi died at Urbino on 12 October ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guidobaldo Del Monte
Guidobaldo del Monte (11 January 1545 – 6 January 1607, var. Guidobaldi or Guido Baldi), Marquis del Monte, was an Italian mathematician, philosopher and astronomer of the 16th century. Biography Del Monte was born in Pesaro. His father, Ranieri, was from a leading wealthy family in Urbino. Ranieri was noted for his role as a soldier and also as the author of two books on military architecture. The Duke of Urbino, Duke Guidobaldo II, honoured him with the title Marchese del Monte so the family had only become a noble one in the generation before Guidobaldo. On the death of his father Guidobaldo inherited the title of Marchese. Guidobaldo studied mathematics at the University of Padua in 1564. While there he became a friend of the great Italian poet Torquato Tasso. In fact Guidobaldo may have known Tasso before they studied at Padua together, for Tasso was almost exactly the same age as Guidobaldo and had been educated at the court of the Duke of Urbino, with the duke's s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics). Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. Classical mechanics The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry and conserved quantities during the dynamical evol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science In The Renaissance
During the Renaissance, great advances occurred in geography, astronomy, chemistry, physics, mathematics, manufacturing, anatomy and engineering. The collection of ancient scientific texts began in earnest at the start of the 15th century and continued up to the Fall of Constantinople in 1453, and the invention of printing allowed a faster propagation of new ideas. Nevertheless, some have seen the Renaissance, at least in its initial period, as one of scientific backwardness. Historians like George Sarton and Lynn Thorndike criticized how the Renaissance affected science, arguing that progress was slowed for some amount of time. Humanists favored human-centered subjects like politics and history over study of natural philosophy or applied mathematics. More recently, however, scholars have acknowledged the positive influence of the Renaissance on mathematics and science, pointing to factors like the rediscovery of lost or obscure texts and the increased emphasis on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vitruvius
Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled '' De architectura''. He originated the idea that all buildings should have three attributes: , , and ("strength", "utility", and "beauty"). These principles were later widely adopted in Roman architecture. His discussion of perfect proportion in architecture and the human body led to the famous Renaissance drawing of the '' Vitruvian Man'' by Leonardo da Vinci. Little is known about Vitruvius' life, but by his own descriptionDe Arch. Book 1, preface. section 2. he served as an artilleryman, the third class of arms in the Roman military offices. He probably served as a senior officer of artillery in charge of ''doctores ballistarum'' (artillery experts) and ''libratores'' who actually operated the machines. As an army engineer he specialized in the construction of '' ballista'' and '' scorpio'' artillery war machines for siege ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for this is the ''law of the lever.'' Machine components designed to manage forces and movement in this way are called mechanisms. An ideal mechanism transmits power without adding to or subtracting from it. This means the ideal machine does not include a power source, is frictionless, and is constructed from rigid bodies that do not deflect or wear. The performance of a real system relative to this ideal is expressed in terms of efficiency factors that take into account departures from the ideal. Lever The lever is a movable bar that pivots on a fulcrum attached to or positioned on or across a fixed point. The lever operates by applying forces at different distances from the fulcrum, or pivot. The location of the fulcrum determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hero Of Alexandria
Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He is often considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition. Hero published a well-recognized description of a steam-powered device called an ''aeolipile'' (sometimes called a "Hero engine"). Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. He is said to have been a follower of the atomists. In his work ''Mechanics'', he described pantographs. Some of his ideas were derived from the works of Ctesibius. In mathematics he is mostly remembered for Heron's formula, a way to calculate the area of a triangle using only the lengths of its sides. Much of Hero's original writings and designs have been lost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frustum
In geometry, a (from the Latin for "morsel"; plural: ''frusta'' or ''frustums'') is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid. In the case of a pyramid, the base faces are polygonal, the side faces are trapezoidal. A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise it is an oblique frustum. If all its edges are forced to become of the same length, then a frustum becomes a prism (possibly oblique or/and with irregular bases). In computer graphics, the viewing frustum is the three-dimensional region which is visible on the screen. It is formed by a clipped pyramid; in particular, ''frustum culling'' is a method of hidden surface determination. In the aerospace industry, a frustum is the fairing between two stages of a multistage rocket (such as the Saturn V), which is shaped like a truncated cone. Elements, special cases, and related concepts A frust ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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