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
URELY the Man, who, frft in hollow Wood,
Tempted, adventurous, the briny Flood,

In

In harden'd Oak his fearless Heart did hide,
And Ribs of Iron arm'd his Side.

He not th' impetuous Winds contending Roar
Did dread; nor Billows beating on the Shore.
What Form of Death could ever him affright,
Who, unconcern'd, with stedfast Sight,

Could view the Surges rifing Mountain steep,
And Monsters rolling in the liquid Deep
Could through the numerous Ranks of Ruin go,
With ftormy Winds above, and Rocks below,
Without the Magnet's Aid, his Courfe to fhow?
The Northern Polar Star his only Guide,
Which from his Sight the Clouds did often hide.
Mighty Advantages in their Employ,
Our Modern Navigators do enjoy,

'Bove what the Antients had, we all muft own,
Since the Magnetic Needle's Ufe was known 5.
Nor only this, but the learn'd Labours view
Of Wright, Mercator, Wallis, Halley, too :
Whofe Praife to future Ages may fome Wit,
In Numbers equal to their Fame tranfmit.
YET in the Sailing we Mercator's call,
*Two Cafes ftill remain (if not by all)
By moft as unfurmountable are thought,
Nor to the common Rules can e'er be brought ;
Yet does the Noble Analytic Art,

In order thereunto fome help impart,
To the Ingenious then I will apply,
In Algebra who vers'd their Skill may try,
And to the World unfold the Mystery.

}

* 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
To footh my Cares, and Nature's Works admire :
Here the Carnation and the bafhful Rofe,
Their Virgin Blushes to the Sun disclose :
There the chaft Lilly rifes to the Light,
Unveils her fnowy Breaft, and charms the Sight.
Here a Maandring Rivulet gently flows,
And a new Heaven in its fair Bofom fhows,
Inviting by its Murmurs foft Repose.
Two lofty Trees within the Garden stand
(Upright and freight) which o'er the reft command:
Between each Tree when meafur'd on the Ground
In a ftreight Line, juft forty Yards are found,
The higher Tree does fixty Yards contain,
Thirty the lower, (both ftand on a Plain :)
Betwixt the Trees a Fountain plac'd must be
But fo; that when from it to th' Apex of each Tree..
Two Lines are drawn, the Angle they contain,
Muft be the greateft poffible it can.
He who by Fluxions refolves this Question true,
And gives a Geometrick Conftruction too,
To him I'll own that Thanks are justly due.

*

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.

-