The Gentleman's Mathematical Companion, Volume 1

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William Davis, John Hampshire
Davis and Dickson, 1809 - Mathematics
1827 includes "Appendix. A regular list of all the enigmas, charades, rebuses and anagrams, from the commencement."

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Page 25 - casteth down imaginations, [reasonings,] and every high thing that exalteth itself against the knowledge of God, and bringeth into captivity every thought to the obedience of Christ.
Page 63 - DQ conftant to each fixed value of n, therefore the angle QRm being equal to DPQ, will alfo be conftant, whether the inclination of the plane be variable or not ; and hence the angles of the direction with the plane for the draught to be made with the greateft advantage, are found for different values of n as follows : NB The direction, or angle QRm, is to be taken below the plane for the fufpending, and above the plane for the moving force.
Page 72 - AD orVB; now (excluding friction) if that part of the arch which touches Pb was removed, it is evident QbbP would immediately begin to defcend along Qb with a force reprefented by VB or AD ; but this defcent is prevented by that part of the arch which touches Pb-; and therefore the force of that arch, in the direction HA, muft be fuch as to be equivalent to DA in the direction DA or BV ; but no force greater or lefs than HA will be equivalent to DA in the direction DA, and there, fore HA is the real...
Page 66 - AB reprefents the preffure that the body would exert againfl the common inclined plane ; take DK to DP as AB in the foregoing figure to AC, or as the fecant of the inclination of the angular plane with its bafe to radius ; let Dq be the n part of DK, and join Kq ; then RM drawn any how to meet Kq in M, gives RM for the meafure of the whole force in that direction; and it is the moving or fufpending force, according as Dq is taken upwards or downwards in the line AB. It is evident that Kq is parallel...
Page 66 - AMP * be half the feftion perpendicular to trie horizon, and to the axis of the folid which forms the curvilineal plane on which the body is moved; AP the axis ; PM the ordinate, and MS a tangent to the curve at the point M; alfo let RM reprefent the weight or...
Page 67 - Corollary I. Becaufe Mn 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 the planes are inclined to the horizon, the frictions of the...
Page 70 - A of a lever, moveable about an axis whofe center is ' ' ' * d and radium dn ; and let N be the fuftaining force acting at B : now it is evident that the preffure on the axis d differs fo little from the weight, that it may be fafely taken for it without any confiderable error, except in fome remarkable cafes, which may be allowed for from what has been faid already ; and therefore the friction which ought in ftrictnefs to be taken as the n part of the preflure, will here be taken as the n part...
Page 68 - ... upon the threads like a body fuftained on an inclined plane by a force parallel to its bafe ; and as the force to overcome both the •weight and the...
Page 69 - Likewil'e the friction is the fame, 'whether the cylinder be fixed, and the body AB moved round the axis MR by a force Qc applied at c ; or whether the point c be fixed with AB fattened to Cc, and the cylinder be revolved in a * circle whofe center is c, fo as always to retain its...

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