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Q. 21. L. Diary

IN

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QUESTION the Twelfth.

N the North Latitude of Fifty Three,
As I with fome Ladies was drinking of Tea
The Room it was pleasant, and the First Day
[of May..

I happen'd to applaud their bright Genius and Wit,
Yet thought Mathematicks for them not fo fit;!)
But nettl'd at this was a learned brisk Lafs,
And the Sun fhining plain on a Specular Glafs,
Toth Top o'th' Eaft Corner of the Room came the Rays,
Let's fee by your Learning? fhe answering prays;
This Glafs is i'th' Middle o'th' Wall I do find,

Horizontally plac'd, which stands to th' South Wind.
The Area o'th End of theRoom Ihere fhow, [80Sq. Feet]
The whole Room's Dimenfions from hence I wou'd know
With the Time of the Day? But I'll tell you below,
That the Height of the Sun is exactly the fame
As his Azimuth, I truly do find by the Beam.
A Difh of the Beft fhall then be your due,
If you to this Quere a Solution give true.

QUESTION the Thirteenth.

A Gentleman as

Gentleman as he did ride,

Near to a pleasant Common Side,
Some Shepherdeffes chanc'd to meet
Driving their Flocks, whom he did greet:
GOD fpeed you well, and may you be
As happy as you're fair, quoth he !
Profper your Flocks, and may they thrive,
Tell me how many Sheep you drive.
ONE of the Damfels ftraight reply'd,
Sir you fhall foon be fatisfy'd ;
For if the Flock we should divide
Amongst us equally, each fhare

Is twice the Number we Maids are ;
E

}

But,

But, if for One of us you do

Count one Sheep, for the next count Two ;
For the Third, Four; for the Fourth, Eight;
So doubling at each Maid aright :

At the laft Maid, the Sum would be
As many as the Sheep you fee :
From what I've faid, I make no doubt,
You foo will find the Numbers out.

QUESTION the Fourteenth, by J. T.

IT

T is required to find a Curve, the Sub-Normal of which is equal to an invariable Line. a.

I should here have concluded, had not a fmall Treatife wrote by one T. Baxter, accidentally fallen into my Hands; in which he pretends to fay (not indeed to prove, for there is not a Demonftration 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 Reafon, if I may fo call it which he gives for his Affertion is, that there may be feveral Figures different in Form, yet equal with Regard to their Areas; and if fo, why may not a Circle and Square be alfo. This though it be very true in fome particular Cafes, cannot be affirmed of Univerfals ; we grant that a Square whofe Side is 12. is exactly equal to Rectangle, one of whofe Sides is 16, and the other 9. Or that a Parabola, the Abfciffa of which is 60, and the correfponding Ordinate 40, is equal to a Rectangle, one of whofe Sides is 80, and the other 20, because they are demonftrable; but we cannot fay the fame of a Circle and a Square. Again, fuppofing 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 fays they are in Proportion as 1. to 3.0625 this will appear falie to any one who con fults Page 348, of Ward's, Young Mathematicians Guide, where he proves,

a

That

That if a regular Polygon of 258280326 Sides be infcribed in a Circle, whofe 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 1 to 3.14159265358979 nearly. I fhall annex to this another Demonitration, which is deduced from the Principles of Fluxions. Let A D = x; and CD be the Sine of 30 Degrees = y (= .5) Radius equal to Unity, (for I fuppofe that every one who knows what a Circle is, knows alfo that the Side of a regular Hexagon infcrib'd in a Circle is equal to the Radius; but the right Sine CD is equal to half the Side of the Hexagon confequently .5) now by the Property of the Circle 2.30 -yy which in Fluxions is

2x -- 2xx = 2yy; and x =

=

: Equal to

3030 2x + I

=

I

وو

by the Equation of the Curve 2xxx = yy.) The

Fluxion of the Arch A C is = Vi

40

112

1152

+

2816

&c. equal to the Length of the Arch A Č. Now if we take only five Terms of the Series without carrying it further on, we shall find A C equal to .523585 and this multiplyed by 12, because the Arch A C is a twelfth Part of the Periphery, will give 6.2830, &c. equal to the Circumference of that Circle, whofe Diameter is 2. which is as I to 3.1415 before found. It is wonderful to me, that Men fhould take fuch Notions into their Heads, and then endeavour to propagate them for Truths without a more mature Examination; had Mr. Baxter lived in the 11th or 12th Centuries, when Ignorance was in its Meridian, perhaps his Opinion might have been fwallowed by fome; but in an Age like ours, where even Sir Isaac Newton's Word would not be taken without a Demonftration, in a Mathematical Theorem he muft expect no Followers: I am informed that Mr. Baxter was advised by some of his Friends, not to print this Treatife, but he perfifted in it, which fhews how much Men are bigotted to their own Sentiments, and proves the Truth of the old Proverb, Amor fui cecus. But further, it is to be observed, that Mr. Baxter is only the Second Inventor of the Quadrature of the Circle; for a certain Frenchman has, feveral Years ago publifhed in the Memoirs of the Royal Academy of Sciences that after Five and Twenty Years Study, he had found out the Ratio betwixt the Diameter and Periphery in finite Terms. Before I leave off, I must take Notice of a Scheme which I have seen, fubfcribed 1. Hemingway, which was defigned (I do fuppofe) for a Confutation of Mr. Baxter's Affertion, but he alfo runs into a great Error, and is no more likely to convince Mr. Baxter, than the other is to perfuade him for he requires that we grant him thofe very Things which he ought to have demonftrated, and which he

does

2

does afterwards in a blind Manner Attempt, even when he has made them Poftulata.

I SHALL fay no more, for I believe the Author will have (to his Coft) a fufficient Conviction of his Error by the Sale of his Book.

تو

BECAUSE the finding the Fluent of this Fluxion

I

-yy at Page the 32d is difficult, I will give you the Operation at full Length for the Satisfaction of thofe who are but Beginners in this Study.

AND First

I

will ftand thus.