Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite vii
... proofs , and added some critical notes . Nor can I close this reference to DR . DAVIES without dwelling for a moment on his rare qualifications as a scholar , his disinterested love of learning , and the nobleness of his personal ...
... proofs , and added some critical notes . Nor can I close this reference to DR . DAVIES without dwelling for a moment on his rare qualifications as a scholar , his disinterested love of learning , and the nobleness of his personal ...
Seite xi
... PROOF OF THE PROPERTY OF THE QUADRATRIX ON WHICH THIS SECOND EMPLOYMENT OF THE CURVE DEPENDS - CRITICISMS OF SPORUS AND PAPPUS ON THE CURVE AND ON THIS USE OF IT - THEOREMS REQUIRED FOR , AND AXIOMS USED IN , THE PROOF OF THIS PROPERTY ...
... PROOF OF THE PROPERTY OF THE QUADRATRIX ON WHICH THIS SECOND EMPLOYMENT OF THE CURVE DEPENDS - CRITICISMS OF SPORUS AND PAPPUS ON THE CURVE AND ON THIS USE OF IT - THEOREMS REQUIRED FOR , AND AXIOMS USED IN , THE PROOF OF THIS PROPERTY ...
Seite xii
... 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 . THEAETETUS OF ATHENS ...
... 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 . THEAETETUS OF ATHENS ...
Seite 5
... proofs for the lax demonstrations of his predecessors . He lived in the times of the first Ptolemy , by whom , it is said , he was asked whether there was a shorter way to the knowledge of geometry than by his Elements , to which he ...
... proofs for the lax demonstrations of his predecessors . He lived in the times of the first Ptolemy , by whom , it is said , he was asked whether there was a shorter way to the knowledge of geometry than by his Elements , to which he ...
Seite 11
... proof given in the Elements of Euclid of the property of the circle ( III . , 31 ) , the discovery of which is attributed to Thales by Pamphila , and some writers have inferred hence that Thales must have known the theorem ( I. , 32 ) ...
... proof given in the Elements of Euclid of the property of the circle ( III . , 31 ) , the discovery of which is attributed to Thales by Pamphila , and some writers have inferred hence that Thales must have known the theorem ( I. , 32 ) ...
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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.