Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite ix
... THEOREM OF THE THREE SQUARES - CONSTRUCTION OF REGULAR POLYGONS AND OF THE REGULAR SOLIDS - DISCOVERY OF INCOMMENSURABLE QUANTITIES- THE APPLICATION OF AREAS THE DOCTRINE OF PROPORTION AND OF THE SIMILARITY OF FIGURES - THEOREMS ...
... THEOREM OF THE THREE SQUARES - CONSTRUCTION OF REGULAR POLYGONS AND OF THE REGULAR SOLIDS - DISCOVERY OF INCOMMENSURABLE QUANTITIES- THE APPLICATION OF AREAS THE DOCTRINE OF PROPORTION AND OF THE SIMILARITY OF FIGURES - THEOREMS ...
Seite x
... THEOREMS WHICH OCCUR IN IT - INFERENCES FROM IT AS TO ARCHYTAS'S KNOWLEDGE OF GEOMETRY - THE CONCEPTION OF GEOMETRICAL LOCI INVOLVED IN THIS SOLUTION - DIFFERENT OPINIONS AS TO ITS IMPOR- TANCE - CONSTRUCTION OF ARCHYTAS'S SOLUTION ...
... THEOREMS WHICH OCCUR IN IT - INFERENCES FROM IT AS TO ARCHYTAS'S KNOWLEDGE OF GEOMETRY - THE CONCEPTION OF GEOMETRICAL LOCI INVOLVED IN THIS SOLUTION - DIFFERENT OPINIONS AS TO ITS IMPOR- TANCE - CONSTRUCTION OF ARCHYTAS'S SOLUTION ...
Seite xi
... THEOREMS USED IN IT WERE KNOWN TO 153-179 ARCHYTAS - RECAPITULATION , CHAPTER VII . THE SUCCESSORS OF EUDOXUS - II . DEINOSTRATUS . DEINOSTRATUS - THE QUADRATRIX , ITS GENERATION AND CHARACTERISTIC PRO- PERTY - USE OF THIS CURVE TO ...
... THEOREMS USED IN IT WERE KNOWN TO 153-179 ARCHYTAS - RECAPITULATION , CHAPTER VII . THE SUCCESSORS OF EUDOXUS - II . DEINOSTRATUS . DEINOSTRATUS - THE QUADRATRIX , ITS GENERATION AND CHARACTERISTIC PRO- PERTY - USE OF THIS CURVE TO ...
Seite xii
... THEOREMS REQUIRED IN ITS PROOF AS GIVEN BY HYPSICLES- SIMPLE PROOF OF THE THEOREM OF ARISTAEUS -RETROSPECT - RELA- TION OF THE WORK DONE BY ARISTAEUS TO THAT OF ARCHYTAS AND HIS SUCCESSORS , 194-205 THE 6 6 CHAPTER IX . THEAETETUS ...
... THEOREMS REQUIRED IN ITS PROOF AS GIVEN BY HYPSICLES- SIMPLE PROOF OF THE THEOREM OF ARISTAEUS -RETROSPECT - RELA- TION OF THE WORK DONE BY ARISTAEUS TO THAT OF ARCHYTAS AND HIS SUCCESSORS , 194-205 THE 6 6 CHAPTER IX . THEAETETUS ...
Seite 3
... theorems from the immaterial and intellectual point of view ( άvλwç kaì voɛpwç ) ; he also discovered the theory of incommensurable quantities ( Tv ἀλόγων πραγματείαν ) , and the construction of the mundane figures [ the regular solids ] ...
... theorems from the immaterial and intellectual point of view ( άvλwç kaì voɛpwç ) ; he also discovered the theory of incommensurable quantities ( Tv ἀλόγων πραγματείαν ) , and the construction of the mundane figures [ the regular solids ] ...
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Häufige Begriffe und Wortgruppen
ancient Apollonius Archim Archimedes Archytas Aristaeus Aristotle arithmetic Athens attributed Book Bretsch Bretschneider Cantor circle Cobet cone conic sections construction cube curve Cyzicus Delian Democritus diameter Diog Diogenes Laertius discovery doctrine of proportion dodecahedron Dublin Egyptians Elements equal Eratosthenes Euclid Eudemus Eudoxus Eukl Eutocius extreme and mean figure Friedlein further Geom Gesch given line gnomon Greek Hankel Heiberg Hippias of Elis Hippocrates of Chios History of Geometry Hultsch Iamblichus Ibid incommensurable inscribed Laert lune Math mathematics mean proportionals mean ratio Menaechmus method Montucla Pappus parabola passage Paul Tannery pentagon perpendicular philosophy plane Plato Plutarch probably problem Proclus proof pupil Pyth Pytha Pythagoras Pythagoreans quadrant quadratrix quadrature rectangle referred regular solids right angles right-angled triangles says segments semicircle sides Simplicius solution solved square Tannery Thales Theaetetus theorem tion δὲ καὶ μὲν περὶ τὰ τὴν τῆς τὸ τὸν τοῦ τῶν
Beliebte Passagen
Seite 10 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Seite 145 - ... proclaim it as an authoritative dogma, silencing or disparaging all objectors — that Grecian speculation aspires. To unmask not only positive falsehood, but even affirmation without evidence, exaggerated confidence in what was only doubtful, and show of knowledge without the reality — to look at a problem on all sides, and set forth all the difficulties attending its solution — to take account of deductions from the affirmative evidence, even in the case of conclusions accepted as true...
Seite 219 - The Elements of Geometrie of the most auncient Philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, Citizen of London. Whereunto are annexed certaine Scholies, Annotations, and Inuentions, of the best Mathematiciens, both of time past, and in this our age.
Seite 40 - To divide a given straight line into two parts so that the rectangle contained by the whole and one part shall be equal to the square on the other part...
Seite 76 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Seite 135 - ... the gnomon NOL is equal to C; therefore also AX is equal to C. Wherefore to the straight line AB there is applied the parallelogram AX equal to the given rectilineal figure C, exceeding by the parallelogram PO, which is similar to D, because PO is similar to EL.
Seite 126 - State, they would some day emerge into light. Yes, he said, there is a remarkable charm in them. But I do not clearly understand the change in the order. First you began with a geometry of plane surfaces ? Yes, I said.
Seite 125 - ... solids in revolution, instead of taking solids in themselves; whereas after the second dimension the third, which is concerned with cubes and dimensions of depth, ought to have followed.