Mathematical Questions and Solutions, from the "Educational Times.", Τόμος 71

F. Hodgson, 1899

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Σελίδα 46 - AC\ Construct the square BG on the side BC, the square AH on the side AB, and the square AI on the side AC ; from A draw AD perpendicular to BC, and prolong it to E : then will DE be parallel to BF ; draw AF and HC. In the triangles HBC and ABF, we have HB equal to AB, because...
Σελίδα 100 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Σελίδα 25 - BA', BC, coupent AC en B, , B2; CB', ÇA' coupent BA en C,, C2; enfin AC', AB' coupent CB en Ar, A2. Les enveloppes de BiC2, CiAa, A,B2 sont des hyperboles touchant deux des côtés de ABC et ayant pour asymptote le troisième côté; ces courbes ont pour tangente commune la droite de Lemoine de ABC (p. 11—13). J 2 f . M. STUYVAERT. Sur une réussite. Dans « urnes, numérotées de 1 à «, sont placées au hasard « boules numérotées. De l'urne 1 on tire la boule qui s'y trouve et qui porte...
Σελίδα 86 - A and B are two points on the same side of a straight line CD ; find the point P in CD for which AP + PB is least. Give a proof.
Σελίδα 68 - Draw a circle passing through two given points and touching a given line. (Points 1" and 1 • 5" from line and 2" apart.) 34. Draw a circle passing through two given points and cutting a given circle in the extremities of a diameter. (Circle 1-6
Σελίδα 46 - Conies, second edition, page 436, in which the above is described as the ortho-centroidal circle.] 13892. (PW FLOOD.) — Inscribe a triangle in a given segment of a circle, having the sum of the perpendicular and segment of base a maximum.
Σελίδα 47 - Provo that the centre of this ellipse is at the centroid of the triangle, and that one focus of it is the symmedian point of its own pedal triangle with regard to the original triangle. [This seems the easiest way of obtaining the fundamental property of STEINES' s foci.] Solution by the Rev.
Σελίδα 56 - Find three numbers (each less than 10,000) whose squares are in arithmetical progression, so that the ratio of the greatest to the least may be (i.) as great as possible, and (ii.) as small as possible.
Σελίδα 57 - AE, and the median AF, then, if DE = 3EF, the sides of the triangle will be in arithmetical progression.

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