The Works of Archimedes

כריכה קדמית
Dover Publications, 1912 - 377 עמודים
 

מהדורות אחרות - הצג הכל

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קטעים בולטים

עמוד xlviii - Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be left some magnitude which will be less than the lesser magnitude set out.
עמוד 251 - 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.
עמוד clxx - If a straight line of which one extremity remains fixed be made to revolve at a uniform rate in a plane until it returns to the position from which it started, and if, at the same time as the straight line revolves, a point move at a uniform rate along the straight line, starting from the fixed extremity, the point will describe a spiral in the plane.
עמוד cxxxv - The two problems of the duplication of the cube and the trisection of an angle...
עמוד 253 - 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.
עמוד 17 - From this theorem, to the effect that a sphere is four times as great as the cone with a great circle of the sphere as base and with height equal to the radius of the sphere, I conceived the notion that the surface of any sphere is four times as great as a great circle in it; for, judging from the fact that any circle is equal to a triangle with base equal to the circumference and height equal to the radius...
עמוד 244 - First then I will set out the very first theorem which became known to me by means of mechanics, namely that Any segment of a section of a right-angled cone (ie a parabola) is four-thirds of the triangle which has the same base and equal height, and after this I will give each of the other theorems investigated by the same method. Then, at the end of the book, I will give the geometrical [proofs of the propositions]...
עמוד 14 - PROPOSITION 2 We can investigate by the same method the propositions that (1) Any sphere is (in respect of solid content) four times the cone with base equal to a great circle of the sphere and height equal to...
עמוד 6 - Are they equal or unequal ? For, if they are unequal, they will make the cone irregular as having many indentations, like steps, and unevennesses ; but, if they are equal, the sections will be equal, and the cone will appear to have the property of the cylinder and to be made up of equal, not unequal, circles, which is very absurd.
עמוד 9 - ... first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

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