# 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.- 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. **Archimedes**perished in the confusion of the sack while he was calmly pursuing his studies (Liv.- 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. - Like another
**Archimedes**, he requested that the logarithmic spiral should be engraven on his tombstone, with these words, Eadem mutata resurgo. - 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. - The 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. - 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. - 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. - To compare it on this score with the fundamental proposition of
**Archimedes**, the latter must be put into a form similar to Snell's. - II) whose centre is 0, AC its chord, and HK the tangent drawn at the middle point of the arc and bounded by OA, OC produced, then, according to
**Archimedes**, AMC< HK, but > AC. In modern trigonometrical notation the propositions to be compared stand as follows: 2 tan 20 >2 sin 28 (**Archimedes**); tan 10+2 sin 3B>0> 3 sin B (Snell). - The most important are :- Euclid's Elements; Euclid's Data; Optical Lectures, read in the public school of Cambridge; Thirteen Geometrical Lectures; The Works of
**Archimedes**, the Four Books of Apollonius's Conic Sections, and Theodosius's Spherics, explained in a New Method; A Lecture, in which**Archimedes**' Theorems of the Sphere and Cylinder are investigated and briefly demonstrated; Mathematical Lectures, read in the public schools of the university of Cambridge. - 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. - But to borrow Mr.
**Archimedes**exclamation, Eureka! **ARCHIMEDES**(c. 287 -212 B.C.), Greek mathematician and inventor, was born at Syracuse, in Sicily.- When Cicero was quaestor in Sicily (75 B.C.), he found the tomb of
**Archimedes**, near the Agrigentine gate, overgrown with thorns and briers. - 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. - Lastly,
**Archimedes**is credited with the famous Cattle-Problem enunciated in the epigram edited by G. - Lessing' in 1773, which purports to have been sent by
**Archimedes**to the mathematicians at Alexandria in a letter to Eratosthenes. - - The editio princeps of the works of
**Archimedes**, with the commentary of Eutocius, is that printed at Basel, in 1544, in Greek and Latin, by Hervagius. **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.'- Following
**Archimedes**, Fagnano desired the curve to be engraved on his tombstone. - 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.- His assault seawards was made mainly on Achradina,1 but the city was defended by a numerous soldiery and by what seems to have been still more formidable, the ingenious contrivances of
**Archimedes**, whose engines dealt havoc among the Roman ships, and frustrated the attack on the fortifications on the northern slopes of Epipolae (Liv. **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. **Archimedes**gave his results in the treatise IIepi Ti j c aOaipas Kai roD KUXLvbpov: he left unfinished the problem of dividing a sphere into segments whose volumes are in a given ratio.- 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). - Pp. 313-339; Menge, Des
**Archimedes**Kreismessung (Coblenz, 1874). - 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. - Quam
**Archimedes**, we may direct our attention either to the infinite series of geometrical operations or to the corresponding infinite series of arithmetical operations. - APOLLONIUS OF PERGA [PERGAEUS], Greek geometer of the Alexandrian school, was probably born some twenty-five years later than
**Archimedes**, i.e. - 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. - The most important are :- Euclid's Elements; Euclid's Data; Optical Lectures, read in the public school of Cambridge; Thirteen Geometrical Lectures; The Works of
**Archimedes**, the Four Books of Apollonius's Conic Sections, and Theodosius's Spherics, explained in a New Method; A Lecture, in which**Archimedes**' Theorems of the Sphere and Cylinder are investigated and briefly demonstrated; Mathematical Lectures, read in the public schools of the university of Cambridge. - 280-264 B.C.), was described by
**Archimedes**in his Arenarius, only to be set aside Astronomisches aus Babylon (Freiburg im Breisgau, 1889). - 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. - 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.