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Part of the Earth to us, and not fall headlong into the Sky. This last has created a Scruple not only with the Vulgar, but even with some Men of Letters; which I could scarce have believed, had I not heard them confess, that tho they could not deny the Spherical Figure of the Earth for many urgent Reasons; yet they could not remove this one Objection out of their Minds; not to mention the Taunts and Scoffs of St Augustine, and other Fathers upon this Subject. There and such like Reasons are soon confuted by any one: and that the highest Mountains have scarce any Proportion to the Semidiameter of the Earth, we shall afterwards demonstrate (g).

THEREFORE, since the spherical Figure of the Earth is plainly proved and demonstrated, we ought to make ourselves acquainted with those Definitions and Properties which are applied to, and found in the Sphere, or Globe, by Geometricians, and accommodate them to the Earth ; as the Center, the Diameter, the Axis and Poles, the greater and leffer Circles of the Sphere, &c. (b).

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(g) The highest Mountains 2. Because the Superficies of are so inconsiderable to the Se. the Earth is globular, the Head midiameter of the Earth ; that of a Traveller goes a longer they alter the figure of it no Journey than his Feet: and more than Duft upon the Sur: he who rides on Horseback, goes face of our common Globes, as a longer Journey than he who is proved below, Ch. 9. Prop. 7. walks the same Way on Foot.

(h) Tacquet (Lib. i. Cbap 2. So, likewise, the upper Part of his. Affronomy) has drawn of the Mast of a Ship goes some very neat Coonsequences more Way than the lower; viz. from the roundness of the Earth; Because they move in Part of a which we shall here transcribe 'larger Circle.. froni Dr Clarke's Notes upon Ro. 3. If a Man goes the whole hault's Physics. Vol. ii. Pag. 5. Circumference of the Earth's

1. If any part of the Earth's Orb; the Journey which his Superficies were plane, Men Head travels exceeds that of could no more stand upright his Feet, by the Circumference upon it, than upon the side of of a Circle whose Radius is the a mountain.

Man's height. -..

WHO it was that first found out the Earth's spherical Figure, lies hid in the dark Ruins of Antiquity. Certainly the Opinion is very ancient (i); for when Babylon was taken by Alexander, Eclipses were there found calculated and foretold, for many Years before Christ: which could not be done without the Knowledge of the Earth's Figure. Nor can Thales the Grecian be thought to have been ignorant of it, by his foretelling an Eclipse.

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Ć HA P. IV.
Of the Menfuration and Magnitude of the Earıb.

H E Mensuration of the Earth is founded upl on the Solution of these three Problems. 1. To measure the Diameter or Semidiameter, and also the Circuit or Periphery, 2. To find the Area

or

4. If a Vefsel full of Water Water at the foot of a Moun. be raised perpendicularly, some tain than at the Top; and more of the Water would continually in a Cellar than in a Chamber. run over, and yet the Vessel To which may be added, lastwould be always full. viz. Be- ly, that two Threads upon which cause the Superficies of the two Steel Balls hang perpenWater is continually depreled dicularly (or two Walls of a into Part of a larger Sphere.. House raised by a Plumb Line)

5. If a Vefsel full of Water are not parallel to each other, were carried directly downwards but Parts of two Radius's which tho' none of it run over, yet meet at the Center of the Earth. the Vessel would not be full, (i) Ptolemy, inibis Almagelt, viz. Because the Superficies of tells the Times of three Lunar the Water is continually raised Eclipses, observed by the Babyinto Part of a less Sphere. Ionian Astronomers. The first

6. Whence it follows, that on the 19th of March 721 the same Vessel will hold more Years before Chrift: The next

on

or Extent of the Superficies. 3. To coinpute the Solidity, Mass, or Magnitude. These have such a Relation among themselves, that one being known the rest are obtained by Geometrical Propositions, fupposing the Earth a Sphere; as is shewn in Chap. 2. ,

THIS Proposition has been esteemed so advan. tageous and useful, that it hath employed and exercifed the greatest Genius's for many Ages: so that whole Volumes have been writ only upon this Subject. Wherefore I thought it would not unacceptable to the Students in Geography, to give a short' History of the Mensuration of the Earth.

DIOGENES Laërtius highly commends A. naximander, a Disciple of Thales, for that, beside other Astronomical Inventions, he first discovered the Perimeter or Circuit of the terraqueous Globe. This Anaximander lived about 550 Years before the Birth of our Saviour: and Authors mention no other Measure but his, to be used by the Mathematicians of fucceeding Ages, even 'till the Time of Eratosthenes ; so that it is (very likely) his Measure, which Aristotle mentions in the end of his second Book De Cælo. “ Mathematicians, says he, who " have attempted to measure the Earth say it is « 400,000 Furlongs round.”. Hence we have the Dimensions of the Earth according to Anaximander. But besides this one Testimony of Diogenes Laërtius, we are entirely in the dark by what. Invention, Ar

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on the 8th of March 720 Years Day became presently as dark
before Christ; and the third " as the Night; which Change
on September 1, 710 Years be. " had been predi&ted by Thales
fore the same Æra And Heo to the Ionians.” This was
rodotus (in his History, Lib. 1, about 594 Years before Christ;
Seet. 74. Pag. 30.) says, That which shews us that the Phiç
after the War had been car- losophers in these early Times
« ried on six years between the were not ignorant of the true
« Medes and Lydians ; as they Figure of the Earth.
were going to battle, the

tifice,

tifice, or Method, Anaximander found out this Measure. Therefore Eratosthenes (who attempted it next after him, and lived about 200 Years before Christ; being perfectly skilled in Menfuration, and other Parts of Mathematics) is justly celebrated and esteemed by all, as the first and most accurate Meafurer of the Earth. He discovered the Perimeter of it to be about 250000 Furlongs; or, as others say, 252.000; which are, as Pliny tells us, 31.500.000 Roman Paces, equal to 31.500 Miles of 1000 Paces each.

STRABO relates the Contents of three Books of Geography that had been writ by Eratosthenes, which are now loft, thro’ the Injury of Time. Cleomedes also mentions the Method he used in measuring the Earth ; which we shall explain afterwards. However, this Measure of Eratosthenes was judged by several Mathematicians (and first by Hipparchus about 100 Years after) to deviate something from the Truth: tho' Hipparchus himself has not left us his Method of Mensuration; but only added 25.000 Furlongs to Eratostbenes's Perimeter. After him Posidonius (an excellent practical Astronomer, and also well skilled in Philosophy; a little before Christ, in the Time of Cicero and Pompey) set about it, and found, by his Mensuration, the Circumference of the Earth to be 240.000 Furlongs, as Cleomedes tells us. But Strabo differs from him, and says it was 180.000: whence there arose great Doubts and Difputes about the Cause of this Difference. It is true, Strabo's Method is delivered in few Words, and is in Fact much nearer the Truth than the other : but because Cleomedes both read and taught Posidonius's Geography, we shall explain his Method hereafter.

NEVERTHELESS, the Dimensions of Eratosthenes were made use of by many; even 'till the Time of Ptolemy. And he, in the year of Christ 144, used 180.000 Furlongs as the Perimeter, and

affirmed

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thod,

vith the a the peri thoshehtors;

affirmed it to be most agreeable to the Truth; infomuch that this Invention was, by Theon, ascribed to him. We gather also from the Writings of Ptolemy, that Marinus, a famous Geographer, by whose Writings he himself was very much instructed, had attempted something in this Matter.

PTOLEMY (in Lib. I. Chap. 3, of his Geography) tells us, that he also had tried this Method, not the same way with his Predeceffors; but in Places of different Meridians: thoʻ he does not tell us how much he found the Perimeter to be, but con-; tents himself with the Measure he had received from Marinus and his Predecessors, viz. 180.000 Furlongs.

AFTERWARDS, when the Cultivation of 'Arts by degrees disappeared in Greece, nothing was done in this Business; neither did the Romans trouble themselves about it. · BUT the Arabs and Saracens having wrested the Glory of Empire and Arts out of the Hands of the Grecians, did not neglect this part of Mathematics. For (as Snellius tells us from Abulfeda, an Arabian Geographer, who flourished about the Year of Christ 1300, and whose Writings were published at Rome) about the 800 Year of the Christian Æra, Maimon King of Arabia, or Calif of Babylon, being a great Student in Mathematics, como inanded Ptolemy's Great Constru£tion to be translated from the Greek into Arabic, which is, by the Ara. bians, called Prolemy's Almagest. This Maimon hay. ing summoned together several learned Mathematicians commanded them to search into the Earth's Perimeter. For performing of which they made ufe. of the Planes of Zinjan or Mefopotamia ; and measuring from North to South under the same Meridian 'till they had decreased the Elevation of the Pole one Degr. they found the length of their journey to be 56 Miles, or 561; from whence we find the

Perimeter

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