Imágenes de página
PDF
ePub

Part of the Earth to us; and not fall headlong into the Sky. This laft has created a Scruple not only with the Vulgar, but even with fome Men of Letters; which I could scarce have believed, had I not heard them confefs, that tho' they could not deny the spherical Figure of the Earth for many urgent Reafons; 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. These and fuch like Reasons are foon 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, fince the spherical Figure of the Earth is plainly proved and demonftrated, 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).

(g) The highest Mountains are fo inconfiderable to the Semidiameter of the Earth; that they alter the Figure of it no more than Duft upon the Surface of our common Globes, as is proved below, Ch. 9. Prop. 7. (b) Tacquet (Lib. 1. Chap. 2. of his Aftronomy) has drawn fome very neat Coonfequences from the roundness of the Earth; which we fhall here tranfcribe from Dr Clarke's Notes upon Rohault's Phyfics. Vol. ii. Pag. 5.

1. If any Part of the Earth's Superficies were plane, Men could no more ftand upright upon it, than upon the fide of a mountain.

[ocr errors]

WHO

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 Horfeback, goes a longer Journey than he who walks the fame Way on Foot. So, likewife, the upper Part of the Mait 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 whofe Radius is the Man's height.

WHO it was that first found out the Earth's fpherical Figure, lies hid in the dark Ruins of Antiquity. Certainly the Opinion is very ancient (i); for when Babylon was taken by Alexander, Eclipfes were there found calculated and foretold, for many Years before Chrift: 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 Eclipfe.

CHA P. IV.

Of the Menfuration and Magnitude of the Earth.

T

HE Menfuration of the Earth is founded upon the Solution of these three Problems. 1. To meafure the Diameter or Semidiameter, and also the Circuit or Periphery. 2. To find the Area

4. If a Veffel full of Water be raised perpendicularly, fome of the Water would continually run over, and yet the Veffel would be always full. viz. Because the Superficies of the Water is continually depreffed into Part of a larger Sphere.

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

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

or

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, laftly, that two Threads upon which two Steel Balls hang perpendicularly (or two Walls of a Houfe raifed by a Plumb Line) are not parallel to each other, but Parts of two Radius's which meet at the Center of the Earth.

(i) Ptolemy, in his Almageft, tells the Times of three Lunar Eclipfes, obferved by the Babylanian Aftronomers. The first on the 19th of March 721 Years before Chrift: The next

on

or Extent of the Superficies. 3. To compute the Solidity, Mafs, or Magnitude. These have fuch a Relation among themselves, that one being known the rest are obtained by Geometrical Propofitions, fuppofing the Earth a Sphere; as is fhewn in Chap. 2.

THIS Propofition has been esteemed fo advan tageous and useful, that it hath employed and exercifed the greatest Genius's for many Ages: fo that whole Volumes have been writ only upon this SubWherefore I thought it would not unacceptable to the Students in Geography, to give a fhort Hiftory of the Menfuration of the Earth.

ject.

DIOGENES Laërtius highly commends Anaximander, a Difciple of Thales, for that, befide other Aftronomical 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 Eratofthenes: fo that it is (very likely) his Measure, which Ariftotle mentions in the end of his fecond Book De Calo. "Mathematicians, fays he, who "have attempted to meafure the Earth fay it is

[ocr errors]

400,000 Furlongs round." Hence we have the Dimenfions of the Earth according to Anaximander. But befides this one Teftimony of Diogenes Laërtius, we are entirely in the dark by what Invention, Ar

[blocks in formation]

tifice, or Method, Anaximander found out this Meafure. Therefore Eratofthenes (who attempted it next after him, and lived about 200 Years before Chrift; being perfectly skilled in Menfuration, and other Parts of Mathematics) is juftly celebrated and esteemed by all, as the first and most accurate Meafurer of the Earth. He difcovered the Perimeter of it to be about 250000 Furlongs; or, as others fay, 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 Eratofthenes, which are now loft, thro' the Injury of Time. Cleomedes alfo mentions the Method he used in measuring the Earth; which we fhall explain afterwards. However, this Measure of Eratosthenes was judged by feveral Mathematicians (and first by Hipparchus about 100 Years after) to deviate fomething from the Truth: tho' Hipparchus himself has not left us his Method of Menfuration; but only added 25.000 Furlongs to Eratofthenes's Perimeter. After him Pofidonius (an excellent practical Aftronomer, and alfo well skilled in Philofophy; a little before Chrift, in the Time of Cicero and Pompey) fet about it, and found, by his Menfuration, the Circumference of the Earth to be 240.000 Furlongs, as Cleomedes tells us. But Strabo differs from him, and fays it was 180.000: whence there arose great Doubts and Difputes about the Caufe 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 Eratofthenes were made use of by many; even 'till the Time of Ptolemy. And he, in the year of Chrift 144, used 180.000 Furlongs as the Perimeter, and affirmed

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

PTOLEMY (in Lib. 1. Chap. 3, of his Geography) tells us, that he also had tried this Method, not the fame Way with his Predeceffors; but in 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 Marinus and his Predeceffors, 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 whofe Writings were publifhed at Rome) about the 800 Year of the Chriftian Era, Maimon King of Arabia, or Calif of Babylon, being a great Student in Mathematics, commanded Ptolemy's Great Conftruction to be translated from the Greek into Arabic, which is, by the Arabians, called Ptolemy's Almageft. This Maimon having fummoned together feveral learned Mathematicians commanded them to fearch into the Earth's Perimeter. For performing of which they made ufe of the Planes of Zinjan or Mefopotamia; and meafuring from North to South under the fame 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

[ocr errors]
« AnteriorContinuar »