Greek Geometry from Thales to EuclidHodges, Figgis, & Company, 1889 - 237 Seiten |
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Seite 13
... line as diameter , which is the theorem in question . It may be noticed that this remark- able property of the ... given ; further , we have seen that Thales knew that , if the base is given , and the base angles not given sepa ...
... line as diameter , which is the theorem in question . It may be noticed that this remark- able property of the ... given ; further , we have seen that Thales knew that , if the base is given , and the base angles not given sepa ...
Seite 24
... line to the duad , a superficies to the triad , and a body to the tetrad ; 23 ( c ) The plane around a point is ... given right line when an area equal in content to some given one is described thereon ; but when the base of the ...
... line to the duad , a superficies to the triad , and a body to the tetrad ; 23 ( c ) The plane around a point is ... given right line when an area equal in content to some given one is described thereon ; but when the base of the ...
Seite 25
... given line lies without the described area , then the area is said to be in defect ( èλλeíπeiv ) . Euclid uses in this way , in his Sixth Book , the terms excess and defect . . . . The term applica- tion ( rapaßáλλew ) , which we owe to ...
... given line lies without the described area , then the area is said to be in defect ( èλλeíπeiv ) . Euclid uses in this way , in his Sixth Book , the terms excess and defect . . . . The term applica- tion ( rapaßáλλew ) , which we owe to ...
Seite 41
... line and the greater segment , the problem is reduced to the following : -To produce a given straight line so that the rectangle under the whole line thus pro- duced and the part produced shall be equal to the square on the given ...
... line and the greater segment , the problem is reduced to the following : -To produce a given straight line so that the rectangle under the whole line thus pro- duced and the part produced shall be equal to the square on the given ...
Seite 43
... line internally or externally so that the rectangle under the segments shall be equal to a given rectilineal figure ... given lines , or the construction of a square which shall be equal 64 Aristoteles , Analyt . Prior . , I. , c ...
... line internally or externally so that the rectangle under the segments shall be equal to a given rectilineal figure ... given lines , or the construction of a square which shall be equal 64 Aristoteles , Analyt . Prior . , I. , c ...
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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.