## The Works of ArchimedesIntroduction: 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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Apollonius applied approximations Archimedes axis base called centre of gravity circle circumscribed complete cone conics conoid construction contained cubic curve cylinder described diameter difference direction distance divided draw drawn ellipse equal equation expression figure fluid follows frustum geometrical given gives greater Greek height Hence hyperbola inscribed intersection Join latter lemma length less magnitude manner means Measure meet method obtain original Pappus parabola paraboloid parallel particular passing perpendicular placed plane polygon portion position possible problem produced proof Prop proportional Proposition proved pyramid radius ratio rectangle reference remaining respectively result right angles says sector segment side similar Similarly solid solution solved sphere spheroid spiral square straight line Suppose surface Take taken tangent term touch triangle turn vertex volume whence

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Page 121 - Hence all prisms are to one another in the ratio compounded of the ratios of their bases, and of their altitudes. For every prism is equal to a parallelopiped of the same altitude with it, and of an equal base (2.

Page xlviii - Y3 inscribed regular figures of sixteen sides, &r. the preceding process gives the proof that circles are to one another as the squares on their diameters.

Page 259 - G, it follows that (A -)- B) will remain stationary in the fluid. Therefore the force which causes A by itself to sink must be equal to the upward force exerted by the fluid on B by itself. This latter is equal to the difference between (G -)- H) and G.

Page 255 - Proposition 3 Of solids those which, size for size, are of equal weight with a fluid will, if let down into the fluid, be immersed so that they do not project above the surface but do not sink lower.

Page 257 - Proposition 6 If a solid lighter than a fluid be forcibly immersed in it, the solid will be driven upwards by a force equal to the difference between its weight and the weight of the fluid displaced.

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