30 DOCUMENT 23 SEPTEMBER 1896 " a2 - b2 + c2 29 cos ß = = TI = 0,8055 2ac 36 log cos ß = 9,9061 - 10 ß = 36° 20' a2 + b2 - c2 43 cos y = - = - 2ab 48 log cos y = 9,95226 - 10 y = 26° 23'. Berechnung der Seite a Da 2^a stumpf, so ist a = 2r . sin (180° - a) log a = log 20 + log sin (64° 43' 38")[4] = 1,30103 + 9,94884 - 10 = 1,24987 a = 17,77. AUFGABE 2.[5] Nennen wir den Abstand eines solchen Kreises aus dem gegebenen System vom Mittelpunkt p, so ist sein Radius = -Jr2 - p2. Seine Gleichung ist: (x - p)2 + r2 - p2 y2 = r2 - p2 x2 - 2px + p2 + y2 = r2 - p2 x2 - 2px + y2 = r2 - 2p2. [4] "64°" underlined twice. "Fehler im Ab- schreiben" and "Resultat richtig." are written in the left margin. [5] The problem, recorded with slight varia- tions by other examinees, is: Consider a circle of radius r, centered on the origin of a rectangular coordinate system. At each point along the x-axis, another circle is constructed, with center at this point and diameter deter- mined by the intersections of the perpendic- ular to the x-axis with the original circle. The circles so constructed are enveloped by an ellipse of semiaxes r and r^/2. When the dis- tance of the centers of the circles from the origin exceeds a certain maximum value, the circles cease to touch the envelope. Prove the last two statements and determine this maximum value.
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