Geschichte Der Mathematischen Wissenschaften (1-2) - Bookswagon
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Geschichte Der Mathematischen Wissenschaften (1-2)

Geschichte Der Mathematischen Wissenschaften (1-2)


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Dieses historische Buch kann zahlreiche Tippfehler und fehlende Textpassagen aufweisen. Kaufer konnen in der Regel eine kostenlose eingescannte Kopie des originalen Buches vom Verleger herunterladen (ohne Tippfehler). Ohne Indizes. Nicht dargestellt. 1873 edition. Auszug: ...ist daher DF--D e-f-g-(ergibt sich aus dem rechtwinkligen Dreieck D d F); da man nun das Verhaltniss dieser Momente, oder, was dasselbe ist, der Fluxionen der betreffenden Grossen hat, so kennt man auch das Verhaltniss von C G zur bekannten Strecke C g (welches dasselbe ist wie das von DF zu?f), und hieraus lasst sich der Punkt C bestimmen. Es sei nun AB = x, BD = y, Cg = l, und gS=z, so hat man die Proportion: 1: z = x: y y oder: z--Setze man nun di, das Moment von z, gleich o z (d. h. gleich dem Product der Geschwindigkeit oder Fluxion i. in die unendlichkleine Grosse o), so werden die Momente von x und y also D e und d e, beziehungsweise gleich sein xo und yo, woraus sich ergibt: Beispiel: Es sei die Gleichung vorgelegt: ax + bx2--y2 = 0 so gibt dieselbe uns (nach Prob. L): ax-f 2bxx--2yy = 0 oder: a + 2bx--2yz = 0 wenn fur x und y beziehungsweise 1 und z gesetzt wird. Die Operation mit dieser Gleichung zum zweiten Male vollzogen, gibt: 2bx--2zy--2yi=--0 oder: 2b--2 z2-2yz = 0, indem man wieder die betreffenden Substitutionen macht. a + 2bx Die erste Gleichung liefert uns den Werth fur z = b z2 die zweite denjenigen fur z =--. Diese Ausdrucke fur z und z in die obige Formel eingesetzt, geben uns den Krummungshalbmesser. Die heutige Formel fur den Krummungshalbmesser: gibt uns in der That denselben Werth wie das Newton'sche Verfahren. Wir sehen aus diesem Beispiele, wie Newton, obgleich er die Operation des Differentiirens zweimal anwandte, noch nicht zum Begriffe des zweiten Differentialquotienten gelangt war und daher zur Umgehung desselben einen Kunstgriff zu Hulfe nehmen musste, der seinen mathematischen Scharfsinn...


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Product Details
  • ISBN-13: 9781153489874
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 166
  • Spine Width: 9 mm
  • Width: 189 mm
  • ISBN-10: 1153489872
  • Publisher Date: 01 Jan 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 308 gr


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