Astronomy.

* J u p*ter 's Body from his Centre 5 asu red with a Micrometer,

The

! S tf ie n r ■.

'?hte ller i q *° he horned. At G one Half of the en-kid t() ^ Outface is turned to the Earth, and she is then&«tur e 6 dichotomized, and in her first Quarter or ghia-^arth^' Part more than half is turned to the

Hcijg’i^ 11 ^ then she is said to b e gibbous. At A herP°Jtti 0n Ur °iJied Hemisphere is seen, being then in Op-At st n °. the Sun ; and this is called the Full Moon.ke j s acr 6 . ls a gain gibbous, but on the other Part; at Cke ^ aitl dichotomized, and in her last Quarter ; at D£ °s ne d> as before ; and then becomes new again• PL Tr > re ^* e i s in Conjunction with the Sun.

^°’ ri irio- ^ he drawn perpendicular to the Line SLP e tp e A. 116 Centres of the Sun and Moon, and O Pp l,c ulatL >thh

121

ar to the Line T L joining the Centres ofthe a nd Moon, ’tis evident the Angle O L M intQl (j* of the Orbit, and P L N in the second,f 6 P r °P°rtional to the Quantity of the illuminatedHere^d towards the Earth ; and this Angle is every, e< l'Jal to the Angle ETL, which is called thej, of the Moon from the Sun.

Surf' to find what Quantity of the Moon’s visiblefid ert p e ls illustrated for any given Time, we are to con-tlie y. at the Circle of Illumination BFC is oblique to pj_ jjy.S ther ever y where (but at G and A) and therefore Fi ^se e itj Laws 0 f the Orthographic Projection (which’nto '^y Elements of all Geometry) it will be projectedthe yj Ellipse whose longest Axis is the Diameter of{‘he ® C, and the Semi-conjugate is EL — Co-^ers e j g. e Angle of Elongation FBP. Hence F P ~

of t C of the said Angle. But from the NatureV® Circle and Ellipse we have LP in a constantd'CuU o H P, wherever the Line P O is drawn perpen-stant n to P ; therefore also 2 LP ra P O has a con-•/ sl / 7 , at 'o to F P. But (by Euclid V. 12.) the Sumif >. toe Lines OP- Area of the Circle, is to the SumArea of the illuminated Part, asr the

>fal l th

>e Lines F P