THE Field is triangular; its three Sides known, viz. A B =62. BC: = 71. B And is to be divided into four equal Parts by two Lines, as QS, PR interfecting each other at right Angles. LE QUESTION the Fifth, by R. F. ET the tranfverfe Diameter of an Ellipfis be equal to 50 Feet, and the Conjugate 30. It's requir'd to inferibe therein the greatest Trapezoid poffible, two of whofe Sides fhall be Ordinates, rightly apply'd to the principal Axis, and in Proportion to one another as 5 to 3. Give QUESTION the Sixth, by R. F. Iven the Area of a Circle equal to 3848. 46 Square Feet, and therein let a Trapezium be infcribed, whofe Diagonals are given, viz. 62. and 64. Feet; and the Angle they form by their Interfection 104: -- Degrees requir'd to find the Sides of the Trapezium. QUESTION the Seventh, by J. T. SURELY In In harden'd Oak his fearless Heart did hide, He not th' impetuous Winds contending Roar Could view the Surges rifing Mountain steep, 'Bove what the Antients had, we all muft own, In order thereunto fome help impart, } * Viz. One Latitude, departure, and difference of Longitude, and One Latitude, diftance, and difference of Longitude. EXAMPLE. A Ship fets out from a Port in the Latitude of 54 Degrees North, and fails upon an unknown Course between the South and Weft, till her Departure be 44. 45 Miles, and her difference of Longitude 74. 17 Miles, requir'd her Course, diftance Run, and difference of Latitude. Again, a Ship fets out from a Place in the above mention'd Latitude, and fails in the fame Manner 80 Miles, and then finds her difference of Longitude to be 74 17 Miles, required her Courfe, Departure, and difference of Latitude. QUESTION QUESTION the Eighth, by R. F. IN the Oblique-angled Triangle A C F (vide the Figure below) there is given B S equal to 20 Poles and D G equal to 22; and H F equal to 16, ditto: And the Line B E drawn paralel to the Bafe A F bifects the Area of the Triangle; alfo the Line D Lis the fhorteft that can be drawn through the Point S, to terminate in the Sides F C, F A. Required the Sides of the Triangle. N. B. That C H and D G are Perpendicular to the Bafe A. F. 弟弟弟弟弟弟弟弟弟弟弟弟弟弟弟弟蕊蕊蕊蕊蕊蕊 QUESTION the Ninth, by J. T. IN a certain unknown Northern Latitude, the Declination of a Comet was obferv'd to be 38d: 32' Norther ly, and its Amplitude at fetting was found Four Points and a Halt, or 50d: 37 more Northerly, than the fetting Amplitude of Aldebaran, required the Latitude of the Place where thefe Obfervations were made. QUESTION QUESTION the Tenth by J. T. WHEN tir'd with Bufinefs, or perplex'd with Care, minded am to breathe in purer Air; I to my Garden ftraightway then retire * QUESTION the Eleventh, by J. T. DR. EDMUND HALLEY in his Cometography, fays, That the COMET which appeared in the Year 1686, (which he fuppofes to move in a Parabolic Trajectory,) its Perihelium Distance from the Sun was 325, fuch Parts as the mean Distance of the Earth from the 茶味 谢谢 ie. The greatest Angle that can be formed by two right Lines drawn from any Point in the Line of Diftance, to the Vertices of the faid Trees, Sun Sun is 1000. Suppofe now the COMET to be in such a Part of its Orbit G, that the Area GPS is equal to 492916 d fuch Square Parts; and letting fall the Semiordinate G B upon the Axis, its required to draw the Line B M to fuch a Point of the Curve, fo that the Angle contained by the Line B M, and a Tangent drawn to the Point M, (iz. the Angle B M R) may be a maximum. M R P S B To the above I will add, two more Questions which were fome Years ago propofed in the LADIES DIARY; the firit was there given unlimited, and the latter never had a true Algebraic Solution given to it hitherto; for though we commonly reckon a Question folv'd when it is brought to an Equation, wherein there is only one unknown Quantity, yet in fome Cafes it is otherwife, viz. when it happens to be an Exponential Equation as x= b. we then are obliged to have recourfe to other Methods, the common Rules of Algebra here failing The first of the Questions I have limited, by fixing it to a particular Latitude, and the latter of 'em will, I doubt not (now Algebra and the higher Geometry are better known and understood) be truly anfwer'd by seve ral directly, without gueffing it by repeated Trials. QUESTION us. - |