The Works of ArchimedesUniversity Press, 1897 - 326 pagina's Introduction: I. Archimedes. II. Manuscripts and principal editions, order of composition, dialect, lost works. III. Relation of Archimedes to his predecessors. IV. Arithmetic in Archimedes. V. On the problems known as [neuseis] VI. Cubic equations. VII. Anticipations by Archimedes of the integral calculus. VIII. The terminology of Archimedes -- Works: On the sphere and cylinder, books I-II. Measurement of a circle. On conoids and spheroids. On spirals. On the equilibrium of planes, books I-II. The sand-reckoner. Quadrature of the parabola. On floating bodies, books I-II. Book of lemmas. The cattle-problem [including the solution of Wurm's problem by Amthor in Zeitschrift für math. u. phys. [Hist. litt. abth.] v. 25, 1880]. |
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A₁ AM² An² Apollonius Apollonius of Perga Archimedes axis bisecting centre of gravity chord circle circumference circumscribed figure cone conic sections conics conoid Conoids and Spheroids cubic equation cylinder or frustum described diameter draw drawn ellipse Euclid Eutocius fluid follows frustum geometrical given ratio greater Greek Heiberg Hence Hultsch hyperbola hyperboloid inscribed figure intersection Join lemma less magnitude meet method method of exhaustion middle point Pappus parabola parabolic segment paraboloid parallel perpendicular plane Plutarch polygon problem produced proof Prop proposition proved pyramid R₁ radius rectangle respectively revolution rhombus right angles sector segment ABB segmt semicircle side similar solid solution Sphere and Cylinder spheroid spiral square straight line Suppose surface tangent theorems trapezium triangle vertex whence δὲ ἐν καὶ περὶ τὰ τᾶς τὴν τῆς τὸ τοῦ τῷ τῶν
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Pagina v - Leibniz, and Newton." But whether Archimedes is viewed as the man who, with the limited means at his disposal, nevertheless succeeded in performing what are really integrations for the purpose of finding the area of a parabolic segment and a spiral, the surface and volume of a sphere and a segment of a sphere, and the
Pagina 233 - of which problem I have now discovered the solution. For it is here shown that every segment bounded by a straight line and a section of a right-angled cone [a parabola] is four-thirds of the triangle which has the same base and equal height with the segment, and for the demonstration
Pagina xvi - on such subjects, but, regarding as ignoble and sordid the business of mechanics and every sort of art which is directed to use and profit, he placed his whole ambition in those speculations in whose beauty and subtlety there is no admixture of the common needs of
Pagina 165 - If a straight line drawn in a plane revolve at a uniform rate about one extremity which remains fixed and return to the position from which it started, and if, at the same time as the line revolves, a point move at a uniform rate along the straight line beginning from the extremity which remains fixed, the point will describe a spiral
Pagina 255 - if let down into the fluid, be immersed so that they do not project above the surface but do not sink lower. If possible, let a certain solid EFHG of equal weight, volume for volume, with the fluid remain immersed in it so that part of it, EBCF, projects above the surface. Draw through 0, the
Pagina xlvii - proved by means of a certain lemma which he states as follows: "Of unequal lines, unequal surfaces, or unequal solids, the greater exceeds the less by such a magnitude as is capable, if added [continually] to itself, of exceeding any
Pagina 319 - IT is required to find the number of bulls and cows of each of four colours, or to find 8 unknown quantities. The first part of the problem connects the unknowns by seven simple equations ; and the second part adds two more conditions to which the unknowns must be subject.
Pagina xvii - Shall we not make an end of fighting against this geometrical Briareus who, sitting at ease by the sea, plays pitch and toss with our ships to our confusion, and by the multitude of missiles that he hurls at us outdoes the hundred-handed giants of
Pagina 189 - of gravity similarly coincide. 5. In figures which are unequal but similar the centres of gravity will be similarly situated. By points similarly situated in relation to similar figures I mean points such that, if straight lines be drawn from them to the equal angles, they make equal angles with the corresponding sides. 6. If magnitudes at certain distances
Pagina 221 - centre of the earth and whose radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account