New series of The mathematical repository, Volume 1

Couverture
W. Glendinning, 1806
 

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Page 314 - BC is to the radius (or the fine of the right angle at A) as the fine of the fide AC to the fine of the angle B. And, in like manner, the fine of BC is to the fine of the angle A...
Page 167 - In any triangle, the double of the square of a line drawn from the vertex to the middle of the base, together with double the square of the half base, is equal to the sum of the squares of the other two sides.
Page 209 - Two bodies whose weights are known, lying on a smooth horizontal plane, are connected by a flexible line passing through a small ring fixed at a given point between them ; in this position a given velocity is Communicated to one of them in a direction perpendicular to the line that joins their centers, and the other is made to move directly towards the ring. Investigate the motion of the projected body, and find the angle described when the other body arrives at the ring. Evening Problems.
Page 185 - Leslie published 4 an Experimental Inquiry into the Nature and Propagation of Heat,' a work which, as we have already had occasion to observe, contained some very interesting results, together with sundry disquisitions on topics not very immediately connected with the subject, nor always well understood by the author. In one of these, he recommended Hume's ' Essay on necessary Connexion, as a model...
Page 57 - Arithmetical progreffion fuch, that the fum of every two of them may be a fquare number.
Page 64 - ... and velocity of a body at any point; being given, it is required to determine the nature of the curve it will defcribe. Let r ~ diflance of the point at which the body is pro...
Page 66 - V* * equation'to a conic feflion ; which will be a hyperbola, parabola, or ellipfis-, according as m is greater, equal to, or lefs than unity; that is, according as the velocity with which the body is projected in a direction perpendicular to the horizon, is greater, equal to, or lefs than that acquired by falling from an infinite height.
Page 54 - Sc!:o!ium, it will be evident, that the body will move in the curve VW, to which VP is a tangent, continually defcending towards the circle abd, but will never arrive at it in any finite number of revolutions. This circle is therefore an afymptote to the trajeftory. In the fame manner if...
Page 57 - Laftly, when m is greater than unity, it may be determined by the firft theorem, what proportion the velocity in the curve bears to that velocity, towards which it continually approaches as the body recedes indefinitely from the centre. For, if y be fuppofed infinite, then v...
Page 60 - ... powers of the diftance reciprocally; it is required to determine the equation of the orbit it will defcribe, &c. Suppofe the whole force...

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