Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite x
... CUBE - REDUCED BY HIPPOCRATES TO THE FINDING OF TWO MEAN PROPORTIONALS BETWEEN TWO GIVEN STRAIGHT LINES - PROBABLE RELATION OF THIS PROBLEM TO THE PYTHAGOREAN COSMOLOGY - ITS INFLUENCE ON THE DEVELOPMENT OF GEOMETRY - THE TRISECTION OF ...
... CUBE - REDUCED BY HIPPOCRATES TO THE FINDING OF TWO MEAN PROPORTIONALS BETWEEN TWO GIVEN STRAIGHT LINES - PROBABLE RELATION OF THIS PROBLEM TO THE PYTHAGOREAN COSMOLOGY - ITS INFLUENCE ON THE DEVELOPMENT OF GEOMETRY - THE TRISECTION OF ...
Seite xi
... CUBE - HE DISCOVERED THE THREE CONIC SECTIONS - PASSAGE FROM THE ' REVIEW OF MATHEMATICS ' OF GEMINUS QUOTED - HYPOTHESIS OF BRETSCHNEIDER AS TO THE WAY IN WHICH MENAECHMUS WAS LED TO THE DISCOVERY OF THE CONIC SECTIONS-- COMPARISON OF ...
... CUBE - HE DISCOVERED THE THREE CONIC SECTIONS - PASSAGE FROM THE ' REVIEW OF MATHEMATICS ' OF GEMINUS QUOTED - HYPOTHESIS OF BRETSCHNEIDER AS TO THE WAY IN WHICH MENAECHMUS WAS LED TO THE DISCOVERY OF THE CONIC SECTIONS-- COMPARISON OF ...
Seite 38
... cube . " 60 59- Hankel says it cannot be ascertained with precision how far the Pythagoreans had penetrated into this theory , namely , whether the construction of the regular pentagon and ordinate dodecahedron was known to them ...
... cube . " 60 59- Hankel says it cannot be ascertained with precision how far the Pythagoreans had penetrated into this theory , namely , whether the construction of the regular pentagon and ordinate dodecahedron was known to them ...
Seite 39
... cube , and the octahedron - were certainly known to the Egyptians , and are to be found in their archi- tecture . There remain , then , the icosahedron and the dodecahedron . Let us now examine what is required for the construction of ...
... cube , and the octahedron - were certainly known to the Egyptians , and are to be found in their archi- tecture . There remain , then , the icosahedron and the dodecahedron . Let us now examine what is required for the construction of ...
Seite 40
George Johnston Allman. known . It was also known from the formation of the cube that three squares could be placed in a similar way with a common vertex ; and that , further , if three equal and regu- lar hexagons were placed round a ...
George Johnston Allman. known . It was also known from the formation of the cube that three squares could be placed in a similar way with a common vertex ; and that , further , if three equal and regu- lar hexagons were placed round a ...
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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.