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189)
Atmosphere. And, in order to give an easy Example, let the Tangent IFE perpendicular to PC subtend the Arc IME of sixty Degrees. And then, As y [[superscript]] e [[/superscript]] Versed Sine of [[strikethrough]] 9 ^ [[insertion]] ° [[/insertion]] 0° [[/strikethrough]] 30°, Is to y [[superscript]] e [[/superscript]] Radius; So will be MF or 132", To MC or CO, the apparent Semidiameter of the Moon, which would be found of 16' 25" 1/4. And to the Apparent Semidiameter, which returns frequently, the following Example is accommodated. 
4. About the Pole P [[underlined]] of the Equator, [[/underlined]] draw the Parallel Circle [[underlined]] to it [[/underlined]] DO, which cuts the apparent Limb MEL in O. And in the Spherical Triangle PCO, the three Sides will be given; PC = 63°; CO = 16' 25" 1/4; and OP = DP = 63° 12' 1" 1/4. And therefore the Angle CPO will be found of 12' 31",916. In which Calculation it appears how much my Two Methods, by Versed Sines, are preferable to the common Trigonometrical Rules. 
5. And As the Radius, Is to the Sine of OP; So are 751",916 contained in the Arc DO (as well as in the Angle DPO) To 671",17, or to 11' 11",17 = DO expressed in Parts of a Great Circle.
6. Now let us suppose that the Observations be made at Land, and even in Royal Observatories, and with the best Instruments of all Sorts; and that all the required [[underlined]] Data [[/underlined]] be perfectly known: That so we may better perceive what the Errors and Uncertanties arising barely from the Neglect of the horizontal Refraction in the Atmosphere of the Moon, may amount to, both in the Longitude and

Transcription Notes:
edited for insertion and superscript tags -megshu