Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite 13
... Montucla , and after him by Chasles and other writers on the History of Mathematics , to the school of Plato , " had been formed by Thales . 19 Montucla , Histoire des Mathématiques , Tome I. , p . 183 , Paris , 1758 . Chasles ...
... Montucla , and after him by Chasles and other writers on the History of Mathematics , to the school of Plato , " had been formed by Thales . 19 Montucla , Histoire des Mathématiques , Tome I. , p . 183 , Paris , 1758 . Chasles ...
Seite 46
... Montucla says that Pythagoras laid the foundation of the doctrine of Isoperimetry by proving that of all figures having the same perimeter the circle is the greatest , and that of all solids having the same surface the sphere is the ...
... Montucla says that Pythagoras laid the foundation of the doctrine of Isoperimetry by proving that of all figures having the same perimeter the circle is the greatest , and that of all solids having the same surface the sphere is the ...
Seite 60
... Montucla , which has been repeated since by recent writers on the history of mathematics , 20 that Hippocrates was expelled from a school of Pytha- goreans for having taught geometry for money.21 There is no evidence whatever for this ...
... Montucla , which has been repeated since by recent writers on the history of mathematics , 20 that Hippocrates was expelled from a school of Pytha- goreans for having taught geometry for money.21 There is no evidence whatever for this ...
Seite 92
... Montucla , however , and after him many writers on the history of mathematics , attribute to Hippias of Elis , a contemporary of Socrates , the invention of a transcendental curve , known later as the Quadratrix of Deinostratus , by ...
... Montucla , however , and after him many writers on the history of mathematics , attribute to Hippias of Elis , a contemporary of Socrates , the invention of a transcendental curve , known later as the Quadratrix of Deinostratus , by ...
Seite 93
... Montucla believes that there is some ground for this statement , for he says : ' Je ne crois pas que l'antiquité nous fournisse aucun autre géométre de ce nom , que celui dont je parle . ' Chasles , too , gives only a qualified assent ...
... Montucla believes that there is some ground for this statement , for he says : ' Je ne crois pas que l'antiquité nous fournisse aucun autre géométre de ce nom , que celui dont je parle . ' Chasles , too , gives only a qualified assent ...
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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.