{"product_id":"volume-ii-basic-euclidean-geometry-9798231094943","title":"Volume II: Basic Euclidean Geometry","description":"\u003cp\u003e • Author(s): Franz Rothe\u003cbr\u003e • Publisher: Franz Rothe\u003cbr\u003e • Publisher Imprint: Franz Rothe\u003cbr\u003e • BISAC: Geometry - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe present second volume starts with Euclidean geometry, and the text gets a more educational and even more elementary flavour. \u003c\/p\u003e\u003cp\u003eHere I start with Thales theorem about the angle in a semicircle, and continue with Euclid's related theorems about angles in a circle.\u003cbr\u003eThe most simple parts of the Euclidean geometry are given in detail, as well as the later parts about similarity, and finally area in \u003c\/p\u003e\u003cp\u003eEuclidean geometry with the theorem of Pythagoras and trigonometry, and the measurement of the circle. \u003c\/p\u003e\u003cp\u003eToo, the lens equation from geometrical optics is treated.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003eIn several sections is recalled the strictly modern view of the first volume, beginning with Hilbert's axioms from the Foundations of Geometry. \u003c\/p\u003e\u003cp\u003eAfter some discussion of logic and axioms in general, we go on with a short section about incidence geometries in two dimensions.\u003cbr\u003eThe theorems from neutral geometry which have been proved in the first volume and are needed again, are cited.\u003cbr\u003eThe relation of analytic and synthetic geometry is treated on Hilbert's rigorous account.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46398433755287,"sku":"9798231094943","price":1769.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9798231094943.webp?v=1769044775","url":"https:\/\/atlanticbooks.com\/products\/volume-ii-basic-euclidean-geometry-9798231094943","provider":"Atlantic Books","version":"1.0","type":"link"}