Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
Im Buch
Ergebnisse 1-5 von 26
Seite x
... MEAN PROPORTIONALS BETWEEN TWO GIVEN STRAIGHT LINES - PROBABLE RELATION OF THIS PROBLEM TO THE PYTHAGOREAN COSMOLOGY - ITS INFLUENCE ON THE DEVELOPMENT OF GEOMETRY - THE TRISECTION OF AN ANGLE - THE QUADRATRIX - HIPPIAS OF ELIS - METHOD ...
... MEAN PROPORTIONALS BETWEEN TWO GIVEN STRAIGHT LINES - PROBABLE RELATION OF THIS PROBLEM TO THE PYTHAGOREAN COSMOLOGY - ITS INFLUENCE ON THE DEVELOPMENT OF GEOMETRY - THE TRISECTION OF AN ANGLE - THE QUADRATRIX - HIPPIAS OF ELIS - METHOD ...
Seite 40
... mean proportional between the whole line and the other segment ( Euclid , VI . , 30 ) , or so that the rect- angle under the whole line and one part shall be equal to the square on the other part ( Euclid , II . , 11 ) . To effect this ...
... mean proportional between the whole line and the other segment ( Euclid , VI . , 30 ) , or so that the rect- angle under the whole line and one part shall be equal to the square on the other part ( Euclid , II . , 11 ) . To effect this ...
Seite 41
... mean proportionals , and afterwards they inquire how between two given straight lines two mean proportionals may be found . But Hippocrates of Chios is reported to have been the first inventor of geome- trical reduction ( άraywyń ) ...
... mean proportionals , and afterwards they inquire how between two given straight lines two mean proportionals may be found . But Hippocrates of Chios is reported to have been the first inventor of geome- trical reduction ( άraywyń ) ...
Seite 43
... mean proportional between two given lines , or the construction of a square which shall be equal 64 Aristoteles , Analyt . Prior . , I. , c . xxiii . , 41a , 26 , and c . xliv . , 50a , 37 , ed . Bekker . Euclid has preserved this proof ...
... mean proportional between two given lines , or the construction of a square which shall be equal 64 Aristoteles , Analyt . Prior . , I. , c . xxiii . , 41a , 26 , and c . xliv . , 50a , 37 , ed . Bekker . Euclid has preserved this proof ...
Seite 44
... proportion , the first is to the third as the square on the first is to the square on the second ; and also on the solution of the problem , to find a mean proportional between two given straight lines . Now , we shall see later that ...
... proportion , the first is to the third as the square on the first is to the square on the second ; and also on the solution of the problem , to find a mean proportional between two given straight lines . Now , we shall see later that ...
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.