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Topic: Feuerbach point

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	KARL WILHELM FEUERBACH
		The point of tangency with the incircle is the Feuerbach point, and the three tangency points with the excircles form the Feuerbach triangle.
		Feuerbach was born to a distinguished German family, sufficiently many of whom exhibited both genius and mental illness for there to be a book on this subject (below).
		Feuerbach held mathematics positions at the Gymnasiums in Erlangen, and after a period of imprisonment, in Hof, and in 1828, after a relapse of his illness, again in Erlangen.
	faculty.evansville.edu /ck6/bstud/feuerba.html (279 words)

	Darij Grinberg
		The Mitten point of a triangle, defined as the perspector of the medial and excentral triangles, is shown to be the radical center of a variable circle triad.
		The point L is known as the Feuerbach point of triangle ABC.
		The note is on a new proof that the midpoints of the sides, the feet of the altitudes and the midpoints between the vertices and the orthocenter of a triangle lie on one circle.
	de.geocities.com /darij_grinberg (4615 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		THESES ON FEUERBACH Karl Marx -- 1845 I The chief defect of all hitherto existing materialism (that of Feuerbach included) is that the thing, reality, sensuousness, is conceived only in the form of the _object or of contemplation_, but not as _sensuous human activity, practice_, not subjectively.
		VII Feuerbach, consequently, does not see that the "religious sentiment" is itself a social product, and that the abstract individual whom he analyses belongs to a particular form of society.
		IX The highest point reached by contemplative materialism, that is, materialism which does not comprehend sensuousness as practical activity, is contemplation of single individuals and of civil society.
	marx.eserver.org /1845-feuerbach.theses.txt (605 words)

	Triangle
		The three perpendicular bisectors meet in a single point, the triangle's circumcenter; this point is the center of the circumcircle, the circle passing through all three vertices.
		The remaining three points for which it is named are the midpoints of the portion of altitude between the vertices and the orthocenter.
		It touches the incircle (at the Feuerbach point) and the three excircles.
	www.brainyencyclopedia.com /encyclopedia/t/tr/triangle.html (2205 words)

	Feuerbach - MSN Encarta
		Ludwig Andreas Feuerbach was born in Landshut and educated in Berlin and Erlangen.
		According to Feuerbach, people and their material needs should be the foundation of social and political thought.
		An individual and his or her mind, he held, are products of their environment; the whole consciousness of a person is the result of the interaction of sensory organs and the external world.
	encarta.msn.com /encyclopedia_761567631/Feuerbach.html (253 words)

	Ludwig Andreas Feuerbach (Stanford Encyclopedia of Philosophy)
		Feuerbach argues that Hegel's speculative metaphysics of "pure spirit" really must be understood as the culmination of movement that originated in the speculative theology of the Middle Ages when the naïve notion of a personal deity was conceptualized as an infinite, omniscient, omni-benevolent, necessary being.
		Feuerbach's notion that sensuousness is the unique way in which persons related to the world is at once his most distinctive idea and the most difficult to render intelligible, not to speak of precise.
		Feuerbach had concluded from this that one of the most important philosophical and cultural tasks of his generation was to revise the way human beings thinking about the relationship of mind to nature because it was the notion of "spirit" that was crucial to both idealism and Christianity.
	plato.stanford.edu /entries/ludwig-feuerbach (13292 words)

	Triangle (Site not responding. Last check: 2007-11-06)
		[[Nine point circle demonstrates a symmetry where six Points lie on the same circle.]] The midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine point circle.
		The radius of the Nine point circle is half that of the circumcircle.
		The center of the Nine point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter.
	triangle.iqnaut.net (1965 words)

	The Philosophy Resource Center: The Causal Closure of Physics: An Explanation and Critique, by Kile Jones
		Feuerbach's aphorism that humans created God in their own image can easily be inverted: God made humans in his image and therefore they-by virtue of their theomorphic nature-project out a God who is personal, like them.
		Feuerbach himself acknowledge his Atheism: "If therefore my work is negative, irreligious, atheistic, let it be remembered that atheism-at least in the sense of this work-is the secret of religion itself."[22] The philosophical trajectory of Feuerbach is the elevation of humankind and the reduction of anything considered "divine" to the hopes and aspirations of humankind.
		Feuerbach challenges the religious experientialist's to take a further look and question whether they have made God in their own image, whether things seem to good to be true, and whether they can provide any warrant for their theology.
	radicalacademy.com /studentrefphil_kjones2.htm (3374 words)

	THE DEBATE BETWEEN FEUERBACH AND STIRNER: AN INTRODUCTION
		Feuerbach presented a theory of knowledge which was based on the sense-immediate intuition of particulars; yet his epistemology was also as abstract, mediated and universal as that of Hegel.
		Feuerbach had no right to talk of a "common human potentiality" in view of the fact that some individuals have so outstripped their fellows in capacity that they are "Unique." Here Stirner used Uniqueness to refer to a distinction due to a level of excellence.
		Feuerbach is, to be sure, not a materialist (Stirner never said he was, but described him only as a materialist who bears the properties of idealism); he is not a materialist, for while he imagines that he is talking about actual men, he says nothing about them.
	www.nonserviam.com /egoistarchive/stirner/articles/gordon.html (4540 words)

	Feuerbach biography
		Feuerbach was a geometer who discovered the nine point circle of a triangle.
		The nine point circle which is described here had also been described in work of Brianchon and Poncelet the year before Feuerbach's paper appeared.
		The point where the incircle and the nine point circle touch is now called the Feuerbach point.
	www-history.mcs.st-and.ac.uk /history/Biographies/Feuerbach.html (401 words)

	Thèses sur Feuerbach - K. Marx & F. Engels
		Feuerbach veut des objets concrets, réellement distincts des objets de la pensée; mais il ne considère pas l'activité humaine elle-même en tant qu'activité objective.
		Feuerbach part du fait que la religion rend l'homme étranger à lui-même et dédouble le monde en un monde religieux, objet de représentation [3], et un monde temporel [4].
		Feuerbach, que ne satisfait pas la pensée abstraite, en appelle à l'intuition sensible; mais il ne considère pas le monde sensible en tant qu'activité pratique concrète de l'homme.
	www.marxists.org /francais/marx/works/1845/00/kmfe18450001.htm (839 words)

	Reference.com/Encyclopedia/Incircle and excircles of a triangle
		The point where the nine-point circle touches the incircle is the Feuerbach point.
		The Gergonne point of a triangle is the symmedian point of its contact triangle.
		The Gergonne triangle is also calld the excentral triangle, and the points of intersection of the interior angle bisectors of ABC with the segments BC,CA,AB are the vertices of the incentral triangle.
	www.reference.com /browse/wiki/Gergonne_point (754 words)

	German Ideology_background
		Feuerbach is famous for a work called the Essence of Christianity, in which he argued, consistently with Hegel, that one's religion is a product of the culture and set of ideas shared by those in one's society; a religion reflects the spirit of one's age.
		Feuerbach criticizes them, and tries to show how their religion is indeed a human creation, one that reflects their particular 'spirit'.
		On Feuerbach's view, Marx implies, all we need to do to be liberated from religion, and to achieve ultimate freedom, is to think new thoughts-to think away religion, perhaps (although Feuerbach actually is not an atheist).
	www.fau.edu /~tunick/courses/knowing/Hegel_Feuerbach.html (1064 words)

	Marx's ``Theses on Feuerbach'' A Summary (Site not responding. Last check: 2007-11-06)
		Feuerbach, Marx writes, has moved from ``abstract thinking'' to ``sensuous contemplation'' (§5), but this move, for Marx, is not far enough.
		What Feuerbach fails to recognize, in Marx's view, is that religious sentiment and human essence or human nature are themselves social products (§7), and that society is ``essentially practical,'' which is to say, society consists primarily in the intercourse of people on a practical basis.
		In Feuerbach's conception, society can only be understood as a collection of individuals (§9), whereas, once practical activity is properly accounted for, society can be understood as ``associated humanity,'' which is more closely connected in their shared engagement in practical activity for human ends (§10).
	thm.askee.net /articles/thesesonfeuerbach (497 words)

	Feuerbach biography
		Karl Feuerbach's father Paul J A Ritter von Feuerbach who was a professor of law and wrote the Bavarian criminal code.
		Feuerbach was a geometer who discovered the nine point circle of a triangle.
		The nine point circle which is described here had also been described in work of Brianchon and Poncelet the year before Feuerbach's paper appeared.
	www-history.mcs.st-andrews.ac.uk /Biographies/Feuerbach.html (401 words)

	PlanetMath: nine-point circle
		The nine point circle also known as the Euler's circle or the Feuerbach circle is the circle that passes through the feet of perpendiculars from the vertices
		These three triples of points make nine in all, giving the circle its name.
		Cross-references: inscribed, Euler line, circumcenter, center, circumcircle, radius, points, orthocenter, line segments, Euler, sides, midpoints, properties, triangle, vertices, perpendiculars, passes through, circle
	planetmath.org /encyclopedia/FeuerbachCircle.html (180 words)

	Feuerbach biography
		Of his 8 children 5 sons were to be awarded a doctorate, 3 of them becoming a professor, the most famous being the philosopher (without ever being professor) Ludwig A Feuerbach (1804-72) who was one of the very influential critics of religion and thus of great importance for Marx and marxism.
		The nine point circle which is described here had also been described in work of Brianchon and Poncelet the year before Feuerbach's paper appeared.
		The point where the incircle and the nine point circle touch is now called the Feuerbach point.
	www.gap-system.org /~history/Biographies/Feuerbach.html (401 words)

	Feuerbach’s Religious Illusion
		In Feuerbach’s own words: "Man—this is the mystery of religion—projects his being into objectivity, and then again makes himself an object to this projected image of himself thus converted into a subject." What the devout mind worships as God is accordingly nothing but the idea of the human species imagined as a perfect individual.
		Feuerbach’s "felicity principle," as Harvey calls it, assumes that the point of being religious is to secure one’s well-being both here and hereafter.
		Feuerbach was too good an interpreter of religion to overlook the phenomenon of self-abnegation, which he read as a subtle form of self-love.
	www.religion-online.org /showarticle.asp?title=77 (3362 words)

	normblog: The Feuerbach XI
		The Feuerbach XI This may be the most esoteric item ever posted at normblog.
		Any reader who was ever seized by a passion to uncover the truth, who has felt the force of a tantalizing hypothesis when it has taken possession of his or her soul, will understand why I can do no other, by considering this.
		Sceptics will point out that there have been many Test match captains, but they (the sceptics) should note that Marx links 'ensemble' to 'relations', thereby telling us that we're looking for a captain with a family member in the same team.
	normblog.typepad.com /normblog/2005/10/the_feuerbach_x.html (2370 words)

	Feuerbach's Theorem: A Proof
		Feuerbach's Theorem states that the 9-point circle is tangent internally to the incircle of a triangle and externally to its excircles.
		S is the external center of similitude of the two excircles, while A is their internal center of similitude.
		The same holds for the projections P, B', C', S of the four points onto BC.
	www.cut-the-knot.org /Curriculum/Geometry/FeuerbachProof.shtml (578 words)

	Incidence in Feuerbach's Theorem: What Is It About?
		According to Feuerbach's theorem, the 9-point circle of a triangle touches its incircle and the three excircles.
		The point of tangency of the incircle and the 9-point circle is known as the Feuerbach point N. Let the base triangle be ABC, and denote the points of tangency in question F
		The point is X(12) in Kimberling's Encyclopedia of Triangle Centers, a harmonic conjugate of X(11), the Feuerbach Point F
	www.cut-the-knot.org /Curriculum/Geometry/FeuerbachIncidence.shtml (173 words)

	Theses on Feuerbach
		Feuerbach starts out from the fact of religious self-alienation, of the duplication of the world into a religious world and a secular one.
		Feuerbach, consequently, does not see that the “religious sentiment” is itself a social product, and that the abstract individual whom he analyses belongs to a particular form of society.
		The highest point reached by contemplative materialism, that is, materialism which does not comprehend sensuousness as practical activity, is contemplation of single individuals and of civil society.
	www.marxists.org /archive/marx/works/1845/theses/theses.htm (636 words)

	Jónas Hallgrímsson: Feuerbach's Nihilism
		In the manuscript of Jónas's translation, he has written the Danish phrase "Nihilisme Feuerbachs" ("Feuerbach's Nihilism") in the margin to the right of the first strophe, probably intending it as a title.
		The point of Feuerbach's lines (in Feuerbach's context) is that it is the total dissolution of each unique individual in nothingness that guarantees the freshness, originality, and brilliant colors of subsequent individuals when they arise from that nothingness.
		In "Feuerbach's Nihilism," this emphasis is thrown into high relief by the fact that Jónas borrows several key terms from the creation story in the Poetic Edda, specifically from the account of how life was bestowed upon the male and female ancestors of the human race.
	www.library.wisc.edu /etext/jonas/Nihilisme/Nihilisme.html (957 words)

	The Feuerbach Circle of a Triangle
		Several interesting points and lines can be constructed, and they all move as you drag about a vertex A, B, or C of the triangle.
		The point N divides HZ in the ratio one to three and it is the center of the Feuerbach circle which passes through A', B', C', D, E, F, Q, R, S.
		As it goes through nine special points it is also known as the nine point circle.
	www.math.ruu.nl /people/vdkallen/compalg/Geometry/feuerbach.html (644 words)

	TRIANGLE CENTERS
		He noted that the bisectors met in a single point and decided to repeat the experiment on an extremely obtuse triangle.
		Thereafter, points now called nine-point center, symmedian point, Gergonne point, and Feuerbach point, to name a few, were added to the literature.
		In the 1980s, it was noticed that these special points share some general properties that now form the basis for a formal definition of triangle center
	faculty.evansville.edu /ck6/tcenters (197 words)

	Quelques exemples de thèmes pour des clubs de mathématiques
		Aire balayées par une droite passant par tous les points d'un contour et un point intérieur ou extérieur au contour.
		Courbes à construire point par point : trisectrice de Mac-Laurin, anguinéa, versiera.
		Plusieurs points étant donnés, trouver un lieu qui soit « le plus proche possible » de tous ces points.
	www.animath.fr /UE/sujetsclub.html (528 words)

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