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i.

O R,

Entertainments

FOR THE

Ingenious of Both Sexes.

For the MONTHS of JANUARY, FEBRUARY and MARCH, 1735.

CONTAINING,

I. ENIGMA's.

II. MATHEMATICAL

QUESTIONS. Suited both to Beginhers, and alfo to fuch as have made, higher Advances in thofe STUDIES. Scribimus Indocti Doctique.

YORK Printed by THOMAS GENT: And Sold by J. WILFORD, behind the Chapter-Houfe in St. Paul's Church-Yard, LONDON: And by T. HAMMOND, in the Pavement, YORK, 1735 Price Six Pence.

D X

THE

PREFACE.

*****NE would think that the Mathematick Arts O need no Encomiums to recommend them to the World, but that they would be readily entertain'd

and embraced by all who have Leifure and Opportunity to get acquainted with fo useful a Part of Humane Learning: It must be confefs'd by all, that no Humane Knowledge whatfoever, can lay a more juft Claim to an unfbaken Evidence and Certainty, or boaft an higher Neceffity of its Demonftrations, or a greater Multitude of undeniable Truths, than the Mathematicks: So that Mr. LOCKE, did not without Reason fay, That he could wifh Perfons were more generally acquainted with 'em, not fo much to make them Mathematicians, as to make them reasonable Creatures.

Various and great are the Advantages which acerue to Mankind from this Science. Ope (not the least) of which, is the Knowledge of the true Figure of our own terreftrial Habitation. Divers of the Antients, and particularly LACTANTIUS, and fome Others of the Primitive Faibers, fuppofed the Figure of our World to be a large extended Circular Plain, founded upon a Bafis or Pedestal continued infinitely downwards. ANAXIMANDER, the Philofopher, fuppofed it to be Cylindrical like a Drum. But our modern Philofophers and Mathematicians do univerJally agree, that it is Globular or Spherical, which may be thus proped. The Shadow of the Earth (in every Lunar Eclipfe, in whatsoever Pofition it be) projected to the Moon appears Circular, from whence it neceffarily follows

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that the Earth from whence this Shadow proceeds, must be every Way Circular, that is Spherical.

But perhaps fome may object that the Section of Light and Shadow in Lunar Eclipfes is not caused by the Umbra of the Earth, but by that of its Atmosphere; and that we can only infer from hence the Sphericity of the Earth's Atmosphere. But then it is to be obferved, that the Atmosphere of the Earth in every Part of the World appears a Spherical Concave; and therefore, that the Earth, which is in all Places alike encompaffed by it, must be SphericoConvex.

I omit bere the Confideration of the Small Difference be tween the Equatorial and Polar Diameters arifing from the Centrifugal Force, which is inconfiderable in Respect of the whole Diameter of the Earth.

Befides, another Argument to prove the Spherical Figure of the Earth may be drawn from hence, that when we Travel from North to South, the Pole is depressed exactly in fuch Proportion, as the Figure of the Earth (if Spherical) would Require.

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Again, The Spherical Figure of the Earth is alfo certainly concluded from the Perpendicular Defcent of all heavy Bodies. For it is evidently manifeft, and what hath been alike obferved in all Regions whatsoever, that heary Bodies when lifted up, do fall down to the Surface of the Earth, in lines perpendicular thereto, or which is the fame Thing, to its Horizon, which is an irrefragable Proof of the Propofition: Since, as in all plain Figures, none can have its Perimeter every where perpendicular to the Radius, but a Circle; fo, none amongst Solids, but a Sphere, can have its Surface, or Horizon, perpetually and every where perpendicular to its Diameter.

The Spherical Figure of the Earth, may likewise be deduced from feveral other Phenomena; but what I have zention'd are fufficient, fo fhall not take up any more of my Readers Time therewith.

MARCH the 25th, 1735.

ADVER

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