A History of Greek Mathematics, כרך 2Clarendon Press, 1921 |
תוכן
| 81 | |
| 91 | |
| 97 | |
| 104 | |
| 110 | |
| 197 | |
| 235 | |
| 245 | |
| 252 | |
| 259 | |
| 273 | |
| 283 | |
| 292 | |
| 385 | |
| 395 | |
| 428 | |
| 440 | |
| 462 | |
| 476 | |
| 484 | |
| 514 | |
| 518 | |
| 556 | |
| 563 | |
| 570 | |
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
Apollonius Archimedes Archimedes's axes axis base bisected Book centre of gravity chap chord circle circumference circumscribed commentary cone conic contained curve cylinder diameter Diophantus Dioptra draw drawn earth ellipse equal equation equivalent Eratosthenes Eucl Euclid Eutocius follows formula frustum Geminus geometry given in position given ratio gives greater Greek Heron Hipparchus hyperbola inscribed figure intersection lemmas length loci means meet method method of exhaustion Metrica moon obtained ordinates Pappus Pappus's parabola parallel parallelogram perpendicular plane Posidonius problem Proclus produced proof Prop propositions proved Ptolemy radius rectangle regular polygon respectively right angles says sector segment semicircle sides similar solid solution sphere spherical spheroid spiral square stades straight line surface tangent Theon Theon of Alexandria theorem treatise triangle vertex weight whence
קטעים בולטים
עמוד 17 - Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit...
עמוד 21 - I am persuaded, no less useful even for the proof of the theorems themselves; for certain things 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.
עמוד 82 - ... stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.
עמוד 21 - ... his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.
עמוד 50 - Or, to take a case yet stronger, when it is affirmed, that " the area of a circle is equal to that of a triangle having the circumference for its base, and the radius for its altitude...
עמוד 398 - But in synthesis, reversing the process, we take as already done that which was last arrived at in the analysis and, by arranging in their natural order as consequences what before were antecedents, and successively connecting them one with another, we arrive finally at the construction of what was sought; and this we call synthesis.
עמוד 3 - universe" is the name given by most astronomers to the sphere whose centre is the 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 as you have heard from astronomers.
עמוד 94 - ... so far as to give a most complete investigation of the positions of rest and stability of a right segment of a paraboloid of revolution floating in a fluid, the intelligent reader cannot fail to be struck by the remarkable range of subjects and the mastery of treatment.
עמוד 388 - ... a certain geometrical forethought we may thus infer. They would necessarily think that the figures must all be adjacent one to another and have their sides common, in order that nothing else might fall into the interstices and so defile their work. Now there are only three rectilineal figures which would satisfy the condition, I mean regular figures which are equilateral and equiangular, inasmuch as irregular figures would be displeasing to the bees. For equilateral triangles and squares and...
עמוד 3 - His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit...