Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite ix
... FIGURES - THEOREMS ERRONEOUSLY ATTRIBUTED TO PYTHA- GORAS AND HIS SCHOOL - CONCLUSIONS FROM THE FOREGOING EXAMINA- TION ESTIMATE OF THE STATE OF GEOMETRY , circ . 480 B.C. - THE THEORY OF PROPORTION - THE ANCIENTS REGARDED PROPORTION ...
... FIGURES - THEOREMS ERRONEOUSLY ATTRIBUTED TO PYTHA- GORAS AND HIS SCHOOL - CONCLUSIONS FROM THE FOREGOING EXAMINA- TION ESTIMATE OF THE STATE OF GEOMETRY , circ . 480 B.C. - THE THEORY OF PROPORTION - THE ANCIENTS REGARDED PROPORTION ...
Seite 3
... figures [ the regular solids ] . After him , Anaxagoras of Clazomenae contributed much to geometry , as also did Oenopides of Chios , who was somewhat junior to Anaxagoras ; and Plato has relating to it , which are scattered in ancient ...
... figures [ the regular solids ] . After him , Anaxagoras of Clazomenae contributed much to geometry , as also did Oenopides of Chios , who was somewhat junior to Anaxagoras ; and Plato has relating to it , which are scattered in ancient ...
Seite 7
... figure , so that some of them could be found by means of others in a manner strictly rigorous . This was a phenomenon quite new in the world , and due , in fact , to the abstract spirit of the Greeks . In connection with the new impulse ...
... figure , so that some of them could be found by means of others in a manner strictly rigorous . This was a phenomenon quite new in the world , and due , in fact , to the abstract spirit of the Greeks . In connection with the new impulse ...
Seite 14
... figures , that we do not find amongst them any trace of the doctrine of proportion , and that Greek writers say that this part of their mathe- matical knowledge was derived from the Babylonians or Chaldaeans.22 Bretschneider also ...
... figures , that we do not find amongst them any trace of the doctrine of proportion , and that Greek writers say that this part of their mathe- matical knowledge was derived from the Babylonians or Chaldaeans.22 Bretschneider also ...
Seite 16
... figures and solids plays the principal part ; there are no theorems properly so called ; everything is stated in the form of problems , not in general terms but in distinct numbers , e . g . - to measure a rectangle the sides of which ...
... figures and solids plays the principal part ; there are no theorems properly so called ; everything is stated in the form of problems , not in general terms but in distinct numbers , e . g . - to measure a rectangle the sides of which ...
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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.