Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite x
... ELEMENTS , 99 OF STATE OF HELLAS DURING THE PERSIAN WARS - PRE - EMINENCE OF ATHENS- THE ELEATIC SCHOOL AND THE ATOMIC PHILOSOPHY - HIPPOCRATES CHIOS - NOTICES OF HIM AND OF HIS WORK - WAS THE FIRST WRITER OF AND FIRST SQUARED THE LUNE ...
... ELEMENTS , 99 OF STATE OF HELLAS DURING THE PERSIAN WARS - PRE - EMINENCE OF ATHENS- THE ELEATIC SCHOOL AND THE ATOMIC PHILOSOPHY - HIPPOCRATES CHIOS - NOTICES OF HIM AND OF HIS WORK - WAS THE FIRST WRITER OF AND FIRST SQUARED THE LUNE ...
Seite xii
... ELEMENTS EUCLID WAS MOST INDEBTED TO THE PYTHAGOREANS , THEAETETUS AND EUDOXUS - WHAT PORTIONS OF THE ELEMENTS ' ARE DUE TO EACH OF THESE SOURCES ? -THE PRINCIPAL PART OF THE ORIGINAL WORK OF EUCLID HIMSELF IS CONTAINED IN THE TENTH ...
... ELEMENTS EUCLID WAS MOST INDEBTED TO THE PYTHAGOREANS , THEAETETUS AND EUDOXUS - WHAT PORTIONS OF THE ELEMENTS ' ARE DUE TO EACH OF THESE SOURCES ? -THE PRINCIPAL PART OF THE ORIGINAL WORK OF EUCLID HIMSELF IS CONTAINED IN THE TENTH ...
Seite 4
... Elements . Plato , who lived after them , contributed to the pro- gress of geometry , and of the other mathematical sciences , through his study of these subjects , and through the mathematical matter introduced in his writings ...
... Elements . Plato , who lived after them , contributed to the pro- gress of geometry , and of the other mathematical sciences , through his study of these subjects , and through the mathematical matter introduced in his writings ...
Seite 5
... Elements , and generalized many parti- cular propositions . Athenaeus of Cyzicus [ or Cyzicinus of Athens ] about the same time became famous in other mathematical studies , but especially in geometry . All these frequented the Academy ...
... Elements , and generalized many parti- cular propositions . Athenaeus of Cyzicus [ or Cyzicinus of Athens ] about the same time became famous in other mathematical studies , but especially in geometry . All these frequented the Academy ...
Seite 6
... Elements . ' * Procli Diadochi in primum Euclidis Elementorum librum commentarii . Ex recognitione G. Friedlein . Lipsiae , 1873 , pp . 64-68 . CHAPTER I. THALES . The founder of Greek Geometry . 6 Greek Geometry from Thales to Euclid .
... Elements . ' * Procli Diadochi in primum Euclidis Elementorum librum commentarii . Ex recognitione G. Friedlein . Lipsiae , 1873 , pp . 64-68 . CHAPTER I. THALES . The founder of Greek Geometry . 6 Greek Geometry from Thales to Euclid .
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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.