A Short History of Greek MathematicsUniversity Press, 1923 - 323 Seiten |
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Ahmes Alexandria algebraical Almagest Apollonius Arabic Archimedes Archytas Aristotle arithmetical astronomical Athens attributed Bretschneider calculation called Cantor Cantor Vorles centre century Chasles chord circle cited commentary cone conic contains cube curve Delambre described diameter Diophantus divided Egyptian equal equations Eratosthenes Eucl Euclid Eudemian summary Eudemus Eudoxus Eutocius evidence extant fact figure fractions Friedlein Geminus given number Greek geometry Hankel Heiberg Heron Hipparchus Hippocrates history of geometry Hultsch Hypsicles Iamblichus incommensurable inscribed invented isosceles later lemmas magnitudes Math mathematicians mathematics means Menaechmus mentioned method multiplied Nesselmann Nicomachus numbers Pappus perpendicular plane Plato Plutarch polygonal numbers porism problem Proclus proof Prop proportion propositions Ptolemy Pythagoras Pythagorean quoted ratio rectangle remains right angles says segment semicircle shews side similar solution sphere square number straight line Suidas symbolism Thales Theon theorem Torelli translation treatise triangle writer Zahlz καὶ περὶ
Beliebte Passagen
Seite 201 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 300 - He finds as a general law that a ray, passing from a rarer to a denser medium, is refracted towards the perpendicular : if...
Seite 58 - Archytas was a contempo- sec.ljaninotwithanyspecial problem. course, that most astronomers mean by 'the universe' the sphere of which the centre is the centre of the earth and the radius is a line drawn from the centre of the earth to the centre of the sun.
Seite 147 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A the given point in, it, and DCE the given rectilineal angle ; it is required to make...
Seite 55 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Seite 82 - This book has a completeness which none of the others (not even the fifth) can boast of: and we could almost suspect that Euclid, having arranged his materials in his own mind, and having completely elaborated the 10th book, wrote the preceding books after it, and did not live to revise them thoroughly.
Seite 135 - Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom and investigated its theorems in an immaterial and intellectual manner.
Seite 81 - Upon these two propositions follow several problems', to find medials, commensurable in line or in square, whose rectangle or square is of a given character : eg xxxiil. To find two medials commensurable only in square, such that their rectangle is medial and that the square of the greater exceeds the square of the less, by the square of a line either (a) commensurable or (b) incommensurable with the former. Two similar problems on lines incommensurable in square conclude the second part. All these...
Seite 15 - In any proportion, the product of the means is equal to the product of the extremes.
Seite 261 - Archimedes we find the Geometry of Measurements dealing with the quadrature of curvilinear plane figures and with the quadrature and cubature of curved surfaces, investigations which "gave birth to the calculus of the infinite conceived and brought to perfection successively by Kepler, Cavalieri, Fermat, Leibniz, and Newton.