Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
Im Buch
Ergebnisse 1-5 von 38
Seite ix
... 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 NOT MERELY AS A BRANCH OF ...
... 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 NOT MERELY AS A BRANCH OF ...
Seite x
... ATTRIBUTED TO HIPPO- CRATES - PROBABLE ORIGIN OF HIS DISCOVERY CONCERNING THE QUADRA- TURE OF THE LUNE - THOUGH THE PRINCIPAL GEOMETER OF THIS PERIOD , THE JUDGMENT OF THE ANCIENTS ON HIM WAS NOT ALTOGETHER FAVOUR- ABLE - SUGGESTED ...
... ATTRIBUTED TO HIPPO- CRATES - PROBABLE ORIGIN OF HIS DISCOVERY CONCERNING THE QUADRA- TURE OF THE LUNE - THOUGH THE PRINCIPAL GEOMETER OF THIS PERIOD , THE JUDGMENT OF THE ANCIENTS ON HIM WAS NOT ALTOGETHER FAVOUR- ABLE - SUGGESTED ...
Seite xi
... ATTRIBUTED TO PLATO - STRONG PRESUMPTION AGAINST ITS BEING GENUINE - PLATO'S SOLUTION — THE GEOMETRICAL THEOREMS USED IN IT WERE KNOWN TO 153-179 ARCHYTAS - RECAPITULATION , CHAPTER VII . THE SUCCESSORS OF EUDOXUS - II . DEINOSTRATUS ...
... ATTRIBUTED TO PLATO - STRONG PRESUMPTION AGAINST ITS BEING GENUINE - PLATO'S SOLUTION — THE GEOMETRICAL THEOREMS USED IN IT WERE KNOWN TO 153-179 ARCHYTAS - RECAPITULATION , CHAPTER VII . THE SUCCESSORS OF EUDOXUS - II . DEINOSTRATUS ...
Seite 8
... attributed to the Greeks the discovery of truths which were known to the Egyptians . See , in relation to the distinction between abstract and concrete science , and its bearing on the history of Greek Mathematics , amongst many ...
... attributed to the Greeks the discovery of truths which were known to the Egyptians . See , in relation to the distinction between abstract and concrete science , and its bearing on the history of Greek Mathematics , amongst many ...
Seite 10
... attributed to Thales ( 6 ) —it follows that the sum of the angles at the base of the right - angled tri- angle is equal to the vertical angle , and that therefore the 11 Proclus , ed . Friedlein , p . 65 . 12 This is unquestionably the ...
... attributed to Thales ( 6 ) —it follows that the sum of the angles at the base of the right - angled tri- angle is equal to the vertical angle , and that therefore the 11 Proclus , ed . Friedlein , p . 65 . 12 This is unquestionably the ...
Andere Ausgaben - Alle anzeigen
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.