of whofe Degrees draw occult Lines to D (and mark those that go thro' the 23 degr. 30 min. and 65 degr. 30 min.) the Line DB is as far from P as the Eye is from the Pole: and thro' P, as a Center, draw Circles thro' every Point of Interfection in the Line PC, which will be Parallels of Latitude's which may be counted on the Lines AP and CP 1, 2, 3, 4 from the Equator to the Pole; and you will fee the Latitude of each, and mark thereon the Tropic of Cancer, and the polar Circle at 23 degr. 30 min. and 66 degr. 30 min. there need only be coloured Lines at every fifth Meridian, the reft being occult, that there may be room for affixing the Names of Places.

AFTER the Parallels and Meridians are drawn it will be eafy to mark down the Places from the Tables of Latitude and Longitude; finding first their Longitude, and then the Parallel of their Latitude; and where thefe two cut one another is the Place.

IF the Ecliptic is alfo to be drawn, it must be done before the Names of Places are written; and it being an Ellipfis in the Projection, the feveral Points are to be found thro' which it paffeth; the first Point is where the firft Meridian cuts the Equator, viz. at the first of Aries, and the other Point in the oppofite Part of the Equator, which will be the firft of Libra; and the intermediate Point is where the Meridian thro' ninety Degrees cuts the Tropic. Thus we have the three Points thro' which a Portion of the Ellipfis paffes, which will be lefs than the half of an Ellipfis, for the other Points, as the first of Taurus, &c. there the Declination of thefe Points, and their right Afcenfions from the first Meridian muft be taken from the Tables here adjoined.

Declination.

THEN where 13 or 14 Degrees cuts the Parallel of 5 Degrees, or rather 6 Degrees, that Point will be the fifteenth of Aries; and where 27 cuts the Parallel of 11, there begins the first of Taurus 3 and where 42 cuts the Parallel of 16, there is the fifteenth of Taurus; and where the Meridian 106 cuts the Parallel 22 D. 41 M. there begins the fifteenth of Cancer; and where the Meridian 122 cuts the Parallel of 20, there the first of Leo begins; and fo for the reft: these Points being joined by a curve Line, we shall have a Portion of the Ellipfis for the North

Pa

of the Ecliptic, whofe Signs are eafily marked, taking the end of each Sign in the Tables to which you have it's Declination and Right Afcenfion, as we marked, 15 Degrees of Taurus; the first of Cancer, &c. Thus is the Map finifhed, that reprefents the northern Hemisphere.

'TIS plain from the Defcription and Conftruction, that the Method is eafy and pleasant; now for the Ufe and Advantage thereof. We said there is a three-fold end in conftructing Maps; the first of them is answered because the Latitude and Longitude of Places are thus fhown accurately: it shows alfo the Zones, or the Distance of Places from the Sun's Way. As for the fecond, viz. the proportionate bignefs of each Country; that is not fo truly fhown; for the nearer the Places are to the Equator, they are proportionably larger; yet the Difference is but fmall, becaufe of the great Distance the Eye is fuppofed to be at from them; and that fault is com

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pensed by marking down the better the Places near the Equator, thofe near the Pole being not much inhabited. As for the third end, viz. the Situation of Places, and their Distance, this cannot be known by these Maps; for the Lines on the Maps which denote thefe, are otherwife than they are on the Earth; but to know the Situation of Places with respect to any other, the Horizon of that Place must be drawn, as an Ellipfis, thus. Let there be counted from the Meridian of the Place ninety Degrees both Ways, and the rifing and continuance of the Sun above the Horizon may be known from that part of the Map which begins and ends at the two Points where the Horizon cuts the Equator; and the middle Point will be in the other Quadrant of the Meridian; as far from the Equator as the Place is from the Pole: which will fhow the North Point. The South Point we shall show how to find a little below, if more than a Hemifphere be shown in the Map, it not being in an Hemifphere only, except the Horizon of the Pole, which is the Equator. Thus then we have three Points for the Horizon; the other Points may be found eafier by the Globe, thus: Elevate it for the Latitude of the Place, and take the Point in each Parallel thro' which the firft Meridian paffes, and bring it to the Horizon, and mark the Degrees under the Meridian, and do fo for each Point in the first Meridian, and then count the Degrees for each Parallel from the Meridian of the Place on the Equator both ways; and where the Meridian cuts the Parallels anfwering them, you have the other Points thro' which the Horizon is to be drawn, by which you may judge nearly the Situation of other Places from the Place given.

THUS may almost the whole Earth be drawn in one Map, if either Pole, for Inftance, the South Pole, be taken for the Place of the Eye: and the primitive

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Circle inclofing the Map, may be any Parallel; for Example, if you take the antarctic Circle, if you would reprefent the Superficies between the North Pole and it in the Map, it wants only the lengthening out of the Meridian Lines in the former Conftruction, and Parallels drawn on the other Side of the Equator, and let the Ecliptic be drawn entire, and the Horizon if you please compleated.

BUT because the Parts, or Degrees, near the South Pole will be thus much larger than near the Equator, or in it, which is against the Truth of the Thing, 'tis better to divide the Map into two; one fhowing the North; the other the South Hemisphere.

THERE are few Maps drawn this way, tho' there are commonly two small ones of this kind added to the general right lined Maps, one reprefenting the Countries about the North, the other about the South Pole; which Readers may fee for the better understanding what is faid here: but these things are better understood from seeing them done than by Words.

The fecond Method; the Eye being in the Plane of the Equator.

THE preceding Method of defcribing Geographical Maps, neither shows the Magnitude and Situation of Places, nor is it fit to defcribe an Hemifphere, with Poles in it, and fo reprefent all Places in one Semicircle of the Meridian; and befides, 'tis not agreeable to our way of thinking, to have the Pole in the Center, which makes it more difficult to conceive the Map, and therefore another Method was found out; which is indeed more difficult than the former, but more fit to reprefent Places: and it also removes the Poles from the Equator.

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SECT. VI. TO understand this Method we must conceive the Earth's Surface divided into two Hemispheres, by an entire Circle of the first Meridian, and are to be exhibited in two Maps.

THE Eye is fuppofed in a Place of the Equator, ninety Degrees from the first Meridian; the Map in which it is reprefented is the Plane of the first Meridian; and the Hemifphere, which lies under that, in refpect of the Eye above it, is that which we would represent on the Plane, In which Projection the Equator becomes a ftrait Line, and that Meridian ninety Degrees from the first, becomes also a strait Line, the other Meridians, and all the Parallels of Latitude, and the Ecliptic be come Circles, because their Cones are cut by the Plane, or Map, in a fubcontrary Section; the explication of which depends on the Doctrine of Conic Sections; and is understood better by Sight than by Words.

THE Description is made thus: Having taken in the Map the Point E (Fig. 40) for a Center, defcribe a large or fmall Circle ABCD, as you would have your Map large or small. This represents the first Meridian, and it's oppofite; the Diameter BD reprefents the Meridian that is ninety Degrees from the firft, and B the one Pole, and D the other; and AC perpendicular to A D is the Equator; Let each Quadrant AB, BC, CD, DA, be divided into ninety Degrees. And to reprefent the Meridians and Parallels, or to find the Arches of the Meridians and Parallels, this must be done.

J. LET the Equator A C be divided into one hundred and eighty Degrees, for it represents only the half of the Equator, or AE, ÉC in ninety Degrees each: from the Point D draw ftrait Lines to every Degree of the two Quadrants ABC, or apply a Ruler to D, and to each Degree in the Se

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