1. The Gulph of Mexico, between North and South America.

2. The Gulph of Bengal, between Indoftan and Malacca.

3. The Bay [of Siam] between Malacca and Cambodia.

4. The White Sea, between Lapland and Muscovy.

5. The Lantchidol Sea, between New-Holland and New-Guinea.

6. The Gulph between Nuyt's Land, and Van Diemen's Land.

7. Hudson's Bay; between New-France and New-Denmark.

3. Streights.

1. THE Streights of Magellan, which join the Atlantic to the Pacific Ocean. These are longer than any of the rest.

2. THE Streights of La Maire near those of Magellan, and of the fame ufe.

3. THE fuppofed Streights of Anian, which join the Pacific to the Tartarian Ocean.

4. DAVIS's Streights which join [ Baffin's Bay] to the Atlantic, near which are Forbishers's Streights.

5. THE Streights of Waygats, which join the Icy Sea, perhaps, to the Tartarian Ocean, if the Ice do not interpofe.

6. THE Streights of Gibralter, Atlantic to the Mediterranean Sea.

which join the

7. THE Streights of Denmark, or the Sound, join the Atlantic to the Baltic.

8. THE Streights of Babelmandel, at the mouth of the Arabian Gulph.

9. THE Streights of Ormus, at the mouth of the Perfian Gulph.

10. THE

10. THE Hellefpont and Bofphorus, which join the Archipelago to the Euxine or Black Sea.

WHETHER the Cafpain Sea be a Lake or a broad Bay, which is joined to the main Ocean by fome fubterraneous Streights, is not fettled among Geographers,

CHA P. XIII.

Of the Ocean, and certain Properties of it's

Parts.

PROPOSITION I.

The Surface of the Ocean, and of all other Liquids, is round and spherical: Or the Surface of the watery Part joined to the Surface of the dry Part, do both together make up the Superficies of the terraqueous Globe.

TH

HE Truth of this Theorem is proved from the Arguments ufed in Chapter iii. to prove the spherical Figure of the Earth, for they hold as well here as there; but because those Proofs are chiefly built upon the Phænomena that are reafonably fuppofed to proceed from fuch a Figure, that is, rather from the Effects than the Caufe; we fhall propofe, in this Place, a Demonstration which is wholly founded upon natural Caufes, and by which Archimedes proved the Superficies of all liquid Bodies to be spherical: in order to which he

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took

took for granted the three following Poftulata: 1, That the Earth hath a Center, and is therefore fpherical. 2. That it is the Nature of all Liquids, whose Parts are continued and lie at equal Distances from the Center, that the Parts lefs preffed are expelled from their Places by thofe that are more preffed, as is manifeft from Experience, 3. That every Part of the Liquid is preffed by that Part which is above it, perpendicularly, towards the Center of the Earth, if the whole be defcending, or is preffed by any other Body. Befides thefe Poftulata, Archimedes uses a Geometrical Propofition which is not found demonftrated any where in the Elements; and therefore he demonftrates it himself, which is this: If a Superficies be cut by feveral Planes, all paffing thro' one Point, and each Section be the Periphery of a Circle, whofe Center is that one Point, then will the Superficies be fpherical, and that Point the Center of the Sphere; as is eafily demonftrated.

LET the Superficies of any Body be cut by the Plane IF KEP (Fig. 16.) thro' D, and let the Perimeter of the Section IF KEP be circular, having D for it's Center; alfo let every other Section, made thro' D, have circular Perimeters, and D for their Center. It is to be fhewn, that the Superficies of this Body is fpherical, and that D is it's Center; i. e. that all the Points in the Superficies are equidiftant from D. For we may imagine feveral right Lines to be drawn from Ď to other Points of the Superficies, and we must prove them to be all equal. We may fuppofe a Plane to pafs thro' any of them drawn from D to the Superficies, and alfo thro' DF (for two right Lines cutting one another, or meeting, are in the fame Plane by Euclid Lib. ii. Prop. 2.) and the Periphery of the Section will be circular by the Hypothefis; therefore, the fuppofed Line

2

drawn

drawn will be equal to DF, and fo will all other Lines drawn from D to the Superficies be in like manner equal to DF (a). Hence we prove the Superficies to be spherical, having D for it's Center (b). This being premised, the Superficies of all Liquids are thus demonftrated to be fpherical. Let us fuppofe a Liquid at Reft, in the form of EFGH, (Fig. 17.) and let the Earth's Center be D, and imagine this Liquid to be cut by a Plane paffing thro' D, fo as the Section may be reprefented in the Superficies by EFGH. We are first to prove that this Line EFGH is circular, or an Arch of the Periphery of a Circle, whofe Center is D. If it were poffible not to be circular, then would two Lines, drawn from D to it, be unequal. Let the unequal Lines DE, DG be drawn, viz. let DG be greater than DE, also let the one be the leaft, and the other the greatest that can be drawn from D. Then draw another right Line DF to EFGH, bifecting the Angle GDE, fo as to be longer than DE, but fhorter than DG. With this DF as a Radius updefcribe in the fame Plane the Arch IF KH, which will cut the Line D E produced in the Point I, and the Line DG on this Side G, in the Point K.

on the Center D,

With this DF as a

LIKEWISE with the Radius DL, fomething lefs than DE, upon the Center D, describe the Arch LMN within the Liquid in the fame Plane IFKH. Then are the Parts of the Liquid within the Arch L M N continued, and at equal distances from the Center D: but the Parts between M N are more preffed than thofe between LM, having above them a greater Quantity, and therefore a greater Weight of Water.

(a) By the Definition of a Circle Chap. ii. Article 3.

(6) By the Definition of a Globe Chap. fi. Article 12.

N 4

J

AND

SECT. IV. AND the Parts of the Liquid within LM, being lefs preffed, are driven out of their Places by thofe within M N which take them up, and put the Liquid in Motion, But it was before fuppofed to lie in this Form at Reft, and ftill: So that the Liquid, by this, will be both at Rest and in Motion, which is inconfiftent. Wherefore the right Lines, drawn from D to EFGH, are not unequal, but equal; and fo the Line E F G H is an Arch of a Circle, whofe Center is D. The fame may be demonftrated in all Planes cutting the Superficies of the Liquid, and paffing thro D, viz, that the Section is an Arch of a Circle whofe Center is D. Therefore fince, in the Superficies of Liquids, all Planes paffing any how thro' D, are found to produce circular Sections, it will follow, from the foregoing Propofition, that the Superficies of all Liquids is fpherical; having the Point D, that is, the Center of the Earth, for their Center; as will more manifeftly appear from the Proof of the following Proposition,

PROPOSITION II.

The Sea is not higher than the Land, and therefore the Earth and Water are almost every where of the fame Altitude, high Mountains excepted,

THE Truth of this is demonftrated by the preceeding Propofition. For if the Superficies of the Ocean be fpherical, and have the fame Center with the Superficies of the Earth, and alfo if the Sea, near the Shore, be no higher than the Land, neither will the middle of the Ocean be elevated above the Earth, because both their Surfaces make up the Superficies of one and the fame Sphere. But fome perhaps will not believe the former Propofition, by Reafon of the affumed Hypothefis;

2

therefore