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Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
Transcendental anatomy, also known as philosophical anatomy, was a form of comparative anatomy that sought to find ideal patterns and structures common to all organisms in nature. [1] The term originated from naturalist philosophy in the German provinces, and culminated in Britain especially by scholars Robert Knox and Richard Owen , who drew ...
Two perspective triangles, with their perspective axis and center. Two figures in a plane are perspective from a point O, called the center of perspectivity, if the lines joining corresponding points of the figures all meet at O.
To a system of points, straight lines, and planes, it is impossible to add other elements in such a manner that the system thus generalized shall form a new geometry obeying all of the five groups of axioms. In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid.
The "definition" of line in Euclid's Elements falls into this category. [1]: 95 Even in the case where a specific geometry is being considered (for example, Euclidean geometry), there is no generally accepted agreement among authors as to what an informal description of a line should be when the subject is not being treated formally.
ʿAlāʾ al-Dīn Abū al-Ḥasan ʿAlī ibn Abī Ḥazm al-Qarashī (Arabic: علاء الدين أبو الحسن عليّ بن أبي حزم القرشي ), known as Ibn al-Nafīs (Arabic: ابن النفيس), was an Arab polymath whose areas of work included medicine, surgery, physiology, anatomy, biology, Islamic studies, jurisprudence, and philosophy.
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To draw the parallel (h) to a diameter g through any given point P. Chose auxiliary point C anywhere on the straight line through B and P outside of BP. (Steiner) In the branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions imposed on the traditional rules.