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every Degree of the Meridian therefrom to the Poles ; such are the Tropics, and Polar Circles.

XLI. The Latitude of a Place is its Distance from the Equator reckoned in Degrees and Minutes on the Arch of the Meridian ; thus the Latitude of Z is the Arch of the Meridian Æ Z, equal to 51° 32'.

XLII. The Declination of the Sun, Moon, or Stars, is the same as the Latitude of Places ; being only their Distance North or South from the Equinoctial, in Degrees and Minutes.

XLIII. The Poles of the Ecliptic are two Points 23° 29' distant from the Poles of the World ; as G and T.

XLIV. The Latitude of the Sun, Moon, and Stars, is their Distance from the Ecliptic towards either of its Poles, in Degrees and Minutes, counted in a proper Circle of Latitude.

XLV.,Circles of Latitude or Longitude are Great Circles concurring and intersecting each other in the Poles of the Ecliptic ; and cross the Ecliptic at Right Angles ; as T YG.

XLVI. The Longitude on the Terrestrial Globe is counted in Degrees and Minutes on the Equator, from West to East. So that the Longitude of a Place is an Arch of the Equator contained between the First or General Meridian, and the Meridian passing thro' the said Place.

XLVII. The Longitude of the Sun, Moon, or a Star, is its Distance counted in the Ecliptic from the first Minute of Aries y, according to the Order of the Signs, to the Place where the Circle of Longitude, passing thro' the Star, intersects the Ecliptic.

XLVIII. The Altitude of the Sun, or Stars, is the Arch of an Azimuth (in Degrees and Minutes) contained between the Center of the Sun or Star, and the Horizon.

XLXIX. Afcen

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XLIX. Ascension and Descension is the Rising and Setting of the Heavenly Bodies above or below the Horizon.

L. Right Ascension is the Number of Degrees and Minutes in the Equinoctial ( from the B-ginning of Aries ) which cometh to the Meridian with the Center of the Sun or Star, or any Point of the Ecliptic.

LI. Oblique Ascension is the Arch of the Equinoctial contained between the 'Beginning of r and the Horizon at the moment the Sun, Star, or any. Part of the Ecliptic riseth ; on the contrary,

LII. Oblique Descension is that Degree and Minute of the Equinoctial that fetteth with the Sun, Moon, Star, &c.

LIII. Ascensional Difference, is the Difference between the Right and Oblique Ascension of the Sun, &c. or it is the Time which the Sun riseth or fetteth before or after Six a-Clock ; which, on the longest Day, is represented by the Arch of the Equinoctial, Ca.

LIV. The Amplitude of the Sun, or Stars, is the Distance of their Rising or Setting from the East or West Points of the Horizon, in Degrees and Minutes, toward the North or South Points thereof; and is represented by Cb, on the longest Day; and GD, on the shortest. The Amplitude of Rising is also called the Amplitude Ortive, and the Amplitude of Setting, the Occasive Amplitude.

These are the Fundamentals on ch the Substance of the following Tract of Spher. Geometry does depend. And that the Reader mig he better perceive the Meaning and Purport of each finition, I have hereto subjoin'd a few Schemes fo. heir Illustration, to which I have all along referred.

And though no Person can pretend to study this kind of Science without a previous Knowledge of those VOL. II.



Things, which are the subject Matter of the foregoing Définitions ; yet if he hath no other Expedient than bare reading of their Definitions, and viewing projected Schemes, he must have an exceeding happy Genius ever to acquire a perfect Notion of them by this Means only.

And therefore it behoves every one, who would make any tolerable Proficiency in this part of Knowledge, to qualify himself, as directed in the Preface to this Book, at least fo far as he is capable and hath Opportunity.

CH A P. 11.

Theorems serving to the Orthographical Pro

jection of the Sphere, called the Analemma.


THEOREM I. HE Rays of Light by which the Eye, placed at an infinite Distance, beholds an Object, differ infinitely little from Parallel Rays. Demonstration.


E Suppose any Object AB, be seen by an Eye first in C, then afterwards more remote

in D ;

By 21 Prop. 1 Lib. Euclid. the

Angle ACB, is greater than the Angle ADB; consequently, the Angles




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