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Home > History and Archaeology > History > Geschichte Unserer Abendlandischen Philosophie (2, PT. 1); Entwicklungsgeschichte Unserer Spekulativen, Sowohl Philosophischen ALS Religiosen Ideen Von Ihren Ersten Anfangen Bis Auf Die Gegenwart
Geschichte Unserer Abendlandischen Philosophie (2, PT. 1); Entwicklungsgeschichte Unserer Spekulativen, Sowohl Philosophischen ALS Religiosen Ideen Von Ihren Ersten Anfangen Bis Auf Die Gegenwart

Geschichte Unserer Abendlandischen Philosophie (2, PT. 1); Entwicklungsgeschichte Unserer Spekulativen, Sowohl Philosophischen ALS Religiosen Ideen Von Ihren Ersten Anfangen Bis Auf Die Gegenwart


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About the Book

Das historische Buch konnen zahlreiche Rechtschreibfehler, fehlende Texte, Bilder, oder einen Index. Kaufer konnen eine kostenlose gescannte Kopie des Originals (ohne Tippfehler) durch den Verlag. 1862. Nicht dargestellt. Auszug: ... in wachsenden ungeraden Summenzahlen (2-H3a+(2+3)a + ('2 + 5) a etc. herumlegt, bis diese Summen zusammen dem Produkte 2 ab gleich werden, hier fur a = l also: (2 + 1)1+O + 3)1=8 x 1 = 2 (1.4; so dass demnach in den Quadratzahlen des rechtwinkligen Dreiecks b2 + c1 = h1 nur ein verkurzter Ausdruck fur die Binomial-Formel: az + 2ab-(-bz = (a + b)2 versteckt sei. Diese einfache Entdeckung, mit den aus den verschiedenen Zahlenwerthen fur die Dreiecksseiten entstehenden Zahlenreihen und ihren Gesetzen, war nun der fruchtbare Quell aller seiner weiteren zahlentheoretischen Untersuchungen. Der nachste Theil der Formel. der Wert h fur die Hypotenuse, ergibt sich eben so leicht. Wenn h ein Binom b2 _ aa = a + c ist, c aber =-. so brauchte er diesen Werth 2a jjj _ ai fur c nur in a + c einzufugen und erhielt: h zr a +--, -8--a2 b2 + 2a2--a bz + aa, ', oder, wenn a =: t: 2a 2a 2a----: in Zahlen: --_ = 5. Ganz auf demselben Wege 2 2 und durch dieselbe Verfahrungsweise ist aber auch die zweite, dem Plato oder Archytas zugeschriebene Formel entstanden, da sie mit der ersten, wie wir gesehen haben, ganz identisch ist. Dass aber Pythagoras mit den Operationen der Gleichungen, den eigentlichen algebraischen Operationen, schon vertraut war, werden wir weiter unten noch genauer sehen. Die oben aufgestellten Satze bestatigen sich also vollkommen. Mit der Grundlegung einer geometrischen und arithmetischen Theorie der rechtwinkligen Dreiecke beschaftigte sich Pythagoras, und fur diese Theorie gaben offenbar die Eigenschaften des einfachsten rechtwinkligen Dreiecks mit den Seitenzahlen 3, 4, a und der Flachenzahl 6 den Ausgangspunkt; dieses Dreieck diente als Schema fu'r die Formeln, indem di...


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Product Details
  • ISBN-13: 9781235365133
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 198
  • Spine Width: 11 mm
  • Width: 189 mm
  • ISBN-10: 1235365131
  • Publisher Date: 01 Jan 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 363 gr

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Geschichte Unserer Abendlandischen Philosophie (2, PT. 1); Entwicklungsgeschichte Unserer Spekulativen, Sowohl Philosophischen ALS Religiosen Ideen Von Ihren Ersten Anfangen Bis Auf Die Gegenwart
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Geschichte Unserer Abendlandischen Philosophie (2, PT. 1); Entwicklungsgeschichte Unserer Spekulativen, Sowohl Philosophischen ALS Religiosen Ideen Von Ihren Ersten Anfangen Bis Auf Die Gegenwart
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Geschichte Unserer Abendlandischen Philosophie (2, PT. 1); Entwicklungsgeschichte Unserer Spekulativen, Sowohl Philosophischen ALS Religiosen Ideen Von Ihren Ersten Anfangen Bis Auf Die Gegenwart

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