Qu E TI on the Tenth by J. T. Or minded am to breathe in purer Air ; To him I'll own that Thanks are justly due. 00000000050001000009099900 QUESTION the Eleventh, by J. T. says, That the Comet which appeared in the Year 1686, (which he supposes to move in a Parabolic Trac jettory,) its Perihelium Distance from the Sun was 32,5, fuch Parts as the mean Distance of the Earth from the ********************* * i e. The greatest Angle that can be formed by two right Lines drawn from any point in the line of Diffure, so the Vertices of the said Tree, 28 Arithmetical Questions to be Answered. Sun is 1000. Suppose now the COMET to be in such a Part of its Orbit G, that the Area GPS is equal to 492916 za fuch Square Parts ; and letting fall the Semiordinate G B upon the Axis, its required to draw the Line B M to such a Point of the Curve, so that the Angle contained by the Line B M, and a Tangent drawn to the Point M, ('wiz, the Angle B M R) may be a maximum. To the above I will add, two more Questions which were some Years ago proposed 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 folu'd when it is brought to an Equation, wherein there is only one unknown Quantity, yet in fome Cafes it is otherwise, viz. when it happens to be an Exponential Equation as 3C = b. we then are obliged to have recourse to other Methods, the common Rules of Algebra here failing us. The first of the Questions I have limited, by fixing ir 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 answer'd by seve ral directly, without guessing it by repeated Trials, QUESTION QUESTION the Twelfth. 2534:09 This is d.gg. L.O. IN some Ladies was drinking of Tears [ of May. 3 The Area o'th'End of the Room I here show, [80 Sq. Feet ] 2000 2.21. L. Diary QU E'S T ion the Thirteenth. Gentleman as he did ride, Near to a pleasant Common Side, ONE of the Damsels straight reply'd, shall soon be fatisty'd ; E } But, But, if for One of us you do 0000000000000000000000000 QUESTION the Fourteenth, by J. T. IT is required to find a Curve, the Sub-Normal of which is equal to an invariable Line. a. I Mould here have concluded, had not a small Treatise wrote by one T. Baxter, accidentally fallen into my Hands; in which he pretends to sày (not indeed to prove, for there is not a Demonstration in the whole Book) that he has found out the Quadrature of the Circle in finite Terms, viz. that if the Diameter be equal to 1; the Circumference is 3.0625. the chief Reason, if I may so call jt which he gives for his Affertion is, that there may be several Figures different in Form, yet equal with Regard to their Areas; and if so, why may not a Circle and * Square be also. This though it be very true in fome particular Cafes, cannot be affirmed of Universals ; we grant that a Square whose Side is 12. is exactly equal to à Rectangle, one of whose Sides is 16, and the other 9. Or that a Parabola, the Absciffa of which is 60, and the corresponding Ordinate 40, is equal to a Rectangle, one of whofe Sides is 80, and the other 20, because they are demonstrable ; but we cannot say the fame of a Circle and a Square. Again, fupposing it were poffible to find the Ratio of a Circle's Diameter to its Circumference in finite Terms, yet furely Mr. Baxter, has not found it ; who says they are in Proportion as I. to 3.0625 this will appear falie to any one who con sults Page 348, of Ward's, Young Mathematicians Guide, where he proves, A B Dd That if a regular Polygon of 258280326 Sides be inscribed in a Circle, whose Radius is Unity, its Periphery will be equal to 6.28318530717958 : But the Circumference of the Circle must neceffarily be greater than that of its infcribed Polygon, confequently the Diameter of a Circle is to its Circumference as I to 3.14159265358979 nearly. I shall annex to this another Demonstration, which is deduced from the Principles of Fluxions. Let AD= x; and CD be the Sine of 30 Degrees = g (=.5) Radius equal to Unity, (for í fuppose that every one who knows what a Circle is, knows also that the side of a regular Hexagon infcrib’d in a Circle is equal to the Radius ; but the right Sine C D is cqual to half the Side of the Hexagon confequently = .5) now by the Property of the Circle yy which in Fluxions is 2.4 -- 2xx = 2y; and x =gy : This Squared will give XXC نو و و =? • Equal to 3 (because 230 + 1 уу by the Equation of the Curve 2x* -- ** = 99.). The Fluxion of the Arch AC is = oc? t you? |