The Mathematical Repository, Band 2W. Glendinning, 1801 - 33 Seiten |
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alfo alſo altitude anfwered arch auxiliary fpring axis bafe becauſe bifecting cafe centre chord circumfcribing circumference cofine confequently conftruction cube curve defcribe demonftration diameter diff diftance draw drawn eafily ellipfis equal equation fame ratio fecond fegment femiarc fhall fhewn fides fimilar fince fluent fluxion folid whoſe baſe folution force fphere fquare friction fruftum ftraight line fuch fun's fuppofe furface given by pofition given circle given point given ratio gravity hence hyperbola infcribed circle interfect James Cunliffe John Surtees join lefs Lowry meeting the circle Meffrs muſt pafs parabola parallel perpendicular plane preffure Prob Prop propofer QUESTION radius rect rectangle refpectively reprefent right angles right lines SCHOLIUM ſpace ſquare Swale tangent thefe theref theſe Thornoby triangle trigonometry twice the fum velocity weight whence
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Seite 116 - ... occurred to them. 3. THE next thing to be mentioned, is alfo a matter of arbitrary arrangement, but one in which the Brahmins follow a method peculiar to themfelves. They exprefs the radius of the circle in parts of the circumference, and, fuppofe it equal to 3438 minutes, or 6oths of a degree. In this they are quite fingular. PTOLEMY, and the Greek mathematicians, after dividing the circumference, as we have already described...
Seite 208 - ... the common plane is to be taken ; and in the fecond, the inclined or angular one, confidered in the fourth Propofition : Wherefore if d be the diftance from the center of the axis to the middle of the threads of the fcrew, D the diftance of fame...
Seite 209 - Wd (tn—f} : ^n~t) D, where the letters exprefs the fame things as before, and the upper fign is for the moving, and the lower for the fufpending force. NB t is the natural tangent of the angle made by a line touching one of the threads, and a plane at right angles to the axis of the fcrew; or it is equal to the diftance of the refpe£tive edges of two threads, divided by the circumference of (Jie cylinder, out of which the fcrew is cut.
Seite 207 - MB or the fluxion of y is to Mm the fluxion of the curve, as MR or PN to RF or PQ, therefore if PN be a function of AP, PQ will be a fourth proportional to the fluxion of the ordinate, the fluxion of the curve AM, and this function ; wherefore if the curves HN and AM be given, the nature of the curve GQ will be known, and its area may be found by the common methods of quadratures. Corollary 2. It is evident that when...
Seite 210 - It has been already obferved, that a force afting perpendicular to the direction of a body in motion, does not alter the body's motion in that direction ; therefore if* we fuppofe DB to be an upright cylinder, and AB a body touching it in a line as in the figure, and retained clofe to it by an imaginary force, drawing it perpendicular towards the axis ; then if a force CP be applied to C, the center of gravity of AB, and be always fuppofed to...
Seite 117 - Thefe terms feem all to be derived from the \vordjya, which fignifies the chord of an arch, from which the> name of the radius, or fine of 90", viz.
Seite 118 - ... on, of that arch. The rule, when the fine of an arch is given, to find that of half the arch, is precifely the fame with our own : " The fine of an arch being given, find the co-fine, and thence the verfed fine, of the fame arch : then multiply half the radius into the verfed fine, and the fquare root of the produdl is the fine of half the given arch.
Seite 117 - ... and as the fraction of a minute is here more than a half, they took, as their conftant cuftom is, the integer next above, and called the radius 3438 minutes.