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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. Theie 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 lesser Circles of the Sphere, &c. (b), :.

. . \ WHO

[g) The highest Mountains Sre so inconsiderable to the Semidiameter of the Earth; that they alter the Figure of it no more than Dust upon the Surface of our common Globes, as is proved below, Cb. 9. Prop. 7.

{b) Tacquet [Lib. l. Chap- 2. ,es-.Mt- Astronomy) has drawn some very neat Coonsequences ■from the roundness of the Earth; which we (hall here transcribe from Dr Clarke s Notes upon Rohault'< Pbyfics. Vol. ii. Pag. c. - t.. If any Part of the Earth's Superficies were plane, Men coutd no more, stand upright .upcfn it, than upon the side of a mountain.

2. Because the Superficies of the Earth is globular, the Head of a Traveller goes a longer Journey than his Feet: and he who rides on Horseback, goes a longer Journey than he who walks the fame Way on Foot. So, likewise,' the' upper Part of the Mail of a Ship goes more Way than the lower; viz. Because they move in Part of a. larger Circle.

3. If a Man goes the whole Circumference of the Earth's Orb; the Journey which his Head travels exceeds that of his Feet, by the Circumference of a Circle whose Radius is the Man's heigh;.

4- If

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 («') j 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 shales the Grecian be thought to have been ignorant of it, by his foretelling an Eclipse.

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Os the Mensuration and Magnitude os the Earth.

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

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4. Isa Vessel full os Water be raised perpendicularly, some of the Water would continually run over, and yet the Vessel w,ould be always full. viz. Betause the Superficies of the Water is continually depressed into Part of a larger Sphere.

5. If a Vessel full of Water were carried directly downwards tho* none of it run over, yet the Vessel would not be full, viz. Because the Superficies of the Water is continually raised into Part of a less Sphere.

6. Whence it follows, that the fame Vessel will hold more

Water at the Foot of a Mountain than at the Top; and more in a Cellar than in a Chamber.

To which may be added, lastly, that two Threads upon which, two Steel Balls hang perpendicularly {or two Walls of a House raised by a Plumb Line) are not parallel to each other, but Parts of two Radius's which meet at the Center of the Earth.

(/) Ptolemy, in his Almagest, tells the Times of three Lunar Eclipses, observed by the Babylonian Astronomers. The first on the 19th of March J21 Years before Christ: The next or Extent of the Superficies. 3. To compute the Solidity, Mass, or Magnitude. These have such a Relation among themselves, that one being known the rest are obtained by Geometrical Propositions, supposing the Earth a Sphere; as is shewn in Chap. 2.

THIS Proposition has been esteemed so advantageous and useful, that it hath employed and exercised 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 Laertius highly commends Anaximander, 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 succeeding 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 Ccelo. " Mathematicians, fays 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 Laertius, we are entirely in the dark by what Invention, Ar

on the 8th of March 720 Years "Day became presently as dark

before Christ; and the third "as the Night; which Change

on September r, 710 Years be- "had been predicted by Thales

fore the fame Æra. And He- "to the Ionians." This was

rodotus [in hi: History, Lib. 1. about 594. Years before Christ;

74. Pag. 30.)fays," That which sliews us that the Phi

"after the War had been car- losophers in these early Times

ried on fix years between the were not ignorant of the true

"Medes and Lydians; as they Figure of the Earth. "mere going te battle, the

tiflcc, tifice, or Method, Anaximan&er found out this Measure. Therefore Eratosthenes (who attempted it next after him, and lived about 200 Years before Christ; being perfectly skilled in Mensuration, and other Parts of Mathematics) is justly celebrated and esteemed by all, as the first and most accurate Measurer of the Earth. He discovered the Perimeter of it to be about 250000 Furlongs; or, as others fay, 252.000; whichare, as P/wy tells us, 31.500.000 Roman Paces, equal to 31.500 Miles of 1000 Paces each.

STRd BO relates the Contents of three Books of Geography that had been writ by Eratosthenes^ whichare now lost, 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 Hipparcbus about 100 Years after) to deviate something from the Truth: tho' Hipparcbus himself has not left us his Method of Mensuration •, but only added 2 5.000 Furlongs to Eratostbenes's Perimeter. After him Poftdonius (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, die Circumference of the Earth to be 240.000 Furlongs, as Cleomedes tells us. But Strabo differs from him, and fays it was 1 Jo.000: whence there arose great Doubts and Disputes 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 Pofidonius'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 X44, used 180.000 Furlongs as the Perimeter, and

affirmed affirmed it to be most agreeable to the'Truth; insomuch 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.

Pro LE MT (in Lib. i. Chap. 3, of his Geography) tells us, that he also had tried this Method, not the fame Way with his Predecessors; but irt Places of different Meridians: tho' he does not tell us how much he found the Perimeter to be, but contents himself with the Measure he had received from JMarims 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, commanded Ptolemy's Great Construction to be translated from the Greek into Arabic, which is, by the Arabians, Called Ptolemy's Almagest. This Maimon having summoned together several learned Mathematicians commanded them to search into the Earth's Perimeter. For performing of which they made use of the Planes of Zinjan or Mesopotamia; 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, p.r 56'a from whence we find the

... , Perimeter

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