Greek Geometry from Thales to Euclid (Google eBook)

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Hodges, Figgis, & Company, 1889 - Geometry - 237 pages
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Page 10 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 240 - The Medical Language of St. Luke- : a Proof from Internal Evidence that "The Gospel according to St. Luke" and "The Acts of the Apostles" were written by the same Person, and that the writer was a Medical Man.
Page 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...
Page 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.
Page 240 - A TREATISE ON THE ANALYTICAL GEOMETRY OF THE POINT, LINE, CIRCLE AND CONIC SECTIONS.
Page 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...
Page 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...
Page 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.
Page 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.
Page 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.

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