# Archimedes Sentence Examples

The word parabola was used by

**Archimedes**, who was prior to Apollonius; but this may be an interpolation.**Archimedes**died at the capture of Syracuse by Marcellus, 212 B.C. In the general massacre which followed the fall of the city,**Archimedes**, while engaged in drawing a mathematical figure on the sand, was run through the body by a Roman soldier.This theorem is called generally the principle of

**Archimedes**.As stated first by

**Archimedes**, the principle asserts the obvious fact that a body displaces its own volume of water; and he utilized it in the problem of the determination of the adulteration of the crown of Hiero.If, therefore, the walls of the enclosure held the gas that is directly in contact with them, this equilibrium would be the actual state of affairs; and it would follow from the principle of

**Archimedes**that, when extraneous forces such as gravity are not considered, the gas would exert no resultant force on any body immersed in it.AdvertisementThe founder of the mathematical school was the celebrated Euclid (Eucleides); among its scholars were

**Archimedes**; Apollonius of Perga, author of a treatise on Conic Sections; Eratosthenes, to whom we owe the first measurement of the earth; and Hipparchus, the founder of the epicyclical theory of the heavens, afterwards called the Ptolemaic system, from its most famous expositor, Claudius Ptolemaeus.Although the heliocentric system is not mentioned in the treatise, a quotation in the Arenarius of

**Archimedes**from a work of Aristarchus proves that he anticipated the great discovery of Copernicus.This subject was investigated by

**Archimedes**, who, by his "method of exhaustions," derived the principal results.With

**Archimedes**(287-212 B.C.) a notable advance was made.Further, in comparing the labours of

**Archimedes**and Vieta, the effect of increased power of symbolical expression is very noticeable.AdvertisementTo compare it on this score with the fundamental proposition of

**Archimedes**, the latter must be put into a form similar to Snell's.At Pavia in 1494 we find him taking up literary and grammatical studies, both in Latin and the vernacular; the former, no doubt, in order the more easily to read those among the ancients who had laboured in the fields that were his own, as Euclid, Galen, Celsus, Ptolemy, Pliny, Vitruvius and, above all,

**Archimedes**; the latter with a growing hope of some day getting into proper form and order the mass of materials he was daily accumulating for treatises on all his manifold subjects of enquiry.Another group of polyhedra are termed the " Archimedean solids," named after

**Archimedes**, who, according to Pappus, invented them.This has come down to us through a Latin version of an Arabic manuscript; it cannot, however, have been written by

**Archimedes**in its present form, as his name is quoted in it more than once.**Archimedes**concluded from his measurements that the sun's diameter was greater than 27' and less than 32'; and even Tycho Brahe was so misled by his measures of the apparent diameters of the sun and moon as to conclude that a total eclipse of the sun was impossible.'AdvertisementFollowing

**Archimedes**, Fagnano desired the curve to be engraved on his tombstone.He published the first Italian translation of Euclid (1543), and the earliest version from the Greek of some of the principal works of

**Archimedes**(1543).Ptolemy's Almagest, the works of Apollonius,

**Archimedes**, Diophantus and portions of the Brahmasiddhanta, were also translated.**Archimedes**' problem of dividing a sphere by a plane into two segments having a prescribed ratio,was first expressed as a cubic equation by Al Mahani, and the first solution was given by Abu Gafar al Hazin.**Archimedes**'s process of unending cycles of arithmetical operations could at best have been expressed in his time by a " rule" in words; in the 16th century it could be condensed into a " formula."AdvertisementThe problem he set himself was the exact converse of that of

**Archimedes**.His first contribution 3 was a variation of the method of

**Archimedes**.The Bryozoa were also abundantinsomeregions (Polypora, Fenestella), including the remarkable form known as

**Archimedes**.With Ricci's assistance, he rapidly mastered the elements of the science, and eventually extorted his father's reluctant permission to exchange Hippocrates and Galen for Euclid and

**Archimedes**.The first four books, of which the first three are dedicated to Eudemus, a pupil of Aristotle and author of the original Eudemian Summary, contain little that is original, and are principally based on the earlier works of Menaechmus, Aristaeus (probably a senior contemporary of Euclid, flourishing about a century later than Menaechmus), Euclid and

**Archimedes**.AdvertisementFor revenge,

**Archimedes**devised a fiendish computational problem that involved truly immense numbers.**Archimedes**the numerical analyst Here we summarize the main points in the paper by Phillips with the above title.**Archimedes**(287-212 BC Greece) is reputed to have used powerful lodestones to pull the nails out of enemy ships thus sinking them.This has been discredited because it is not mentioned by Polybius, Livy or Plutarch; but it is probable that

**Archimedes**had constructed some such burning instrument, though the connexion of it with the destruction of the Roman fleet is more than doubtful.Propositions I-II are preliminary, 13-20 contain tangential properties of the curve now known as the spiral of

**Archimedes**, and 21-28 show how to express the area included between any portion of the curve and the radii vectores to its extremities.On

**Archimedes**himself, see Plutarch's Life of Marcellus.**Archimedes**, the famous mathematician, had a celestial globe of glass, in the centre of which was a small terrestrial globe.The fundamental principles of hydrostatics were first given by

**Archimedes**in his work H€pi rwv o ovpEvwv, or De its quae vehuntur in humido, about 250 B.C., and were afterwards applied to experiments by Marino Ghetaldi (1566-1627) in his Promotus**Archimedes**(1603).Rectification and quadrature of the circle have thus been, since the time of

**Archimedes**at least, practically identical problems. Again, since the circumferences of circles are proportional to their diameters - a proposition assumed to be true from the dawn almost of practical geometry - the rectification of the circle is seen to be transformable into finding the ratio of the circumference to the diameter.The conclusion from these therefore was that the ratio of circumference to diameter is 34 This is a most notable piece of work; the immature condition of arithmetic at the time was the only real obstacle preventing the evaluation of the ratio to any degree of accuracy whatever.5 No advance of any importance was made upon the achievement of

**Archimedes**until after the revival of learning.The preface treats of Greek sciences, geometry, the discovery of specific gravity by

**Archimedes**, and other discoveries of the Greeks, and of Romans of his time who have vied with the Greeks -- Lucretius in his poem De Rerum Natura, Cicero in rhetoric, and Varro in philology, as shown by his De Lingua Latina.In the Quadrature of the parabola

**Archimedes**finds the area of a segment of a parabola cut off by any chord.But to borrow Mr.

**Archimedes**exclamation, Eureka!According to one story,

**Archimedes**was puzzled till one day, as he was stepping into a bath and observed the water running over, it occurred to him that the excess of bulk occasioned by the introduction of alloy could be measured by putting the crown and an equal weight of gold separately into a vessel filled with water, and observing the difference of overflow.When Cicero was quaestor in Sicily (75 B.C.), he found the tomb of

**Archimedes**, near the Agrigentine gate, overgrown with thorns and briers.Lessing' in 1773, which purports to have been sent by

**Archimedes**to the mathematicians at Alexandria in a letter to Eratosthenes.**Archimedes**maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direction; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium.As the molten metal is run in, the upward thrust on the outside mould, when the level has reached PP', is the weight of metal in the volume generated by the revolution of APQ; and this, by a theorem of

**Archimedes**, has the same volume as the cone ORR', or rya, where y is the depth of metal, the horizontal sections being equal so long as y is less than the radius of the outside FIG.Like another

**Archimedes**, he requested that the logarithmic spiral should be engraven on his tombstone, with these words, Eadem mutata resurgo.Further, Copernicus could not have known of Aristarchus's doctrine, since

**Archimedes**'s work was not published till after Copernicus's death.These latter formulae are due to

**Archimedes**.The third volume includes, however, some theological treatises, and the first part of it is occupied with editions of treatises on harmonics and other works of Greek geometers, some of them first editions from the MSS., and in general with Latin versions and notes (Ptolemy, Porphyrius, Briennius,

**Archimedes**, Eutocius, Aristarchus and Pappus).Since the area of a circle equals that of the rectilineal triangle whose base has the same length as the circumference and whose altitude equals the radius (

**Archimedes**, KIKXou A ir, prop.i), it follows that, if a straight line could be drawn equal in length to the circumference, the required square could be found by an ordinary Euclidean construction; also, it is evident that, conversely, if a square equal in area to the circle could be obtained it would be possible to draw a straight line equal to the circumference.The theorem for angle-bisection which Vieta used was not that of

**Archimedes**, but that which would now appear in the form I - cos 0 = 2 sin e 20.Then, by the principle of

**Archimedes**, W = Vwo; or wo = W/V.Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by

**Archimedes**, and finds, by a method recalling that of**Archimedes**, the surface and volume of a sphere.At the Marchese's request he wrote, in 1588, a treatise on the centre of gravity in solids, which obtained for him, together with the title of "the

**Archimedes**of his time," the honourable though not lucrative post of mathematical lecturer at the Pisan university.From the time of

**Archimedes**there had existed a science of equilibrium, but the science of motion began with Galileo.**Archimedes**contributed to the knowledge of these curves by determining the area of the parabola, giving both a geometrical and a mechanical solution, and also by evaluating the ratio of elliptic to circular spaces.He discovered a simpler method of quadrating parabolas than that of

**Archimedes**, and a method of finding the greatest and the smallest ordinates of curved lines analogous to that of the then unknown differential calculus.