N O M Y< 
358 ASTRO 
Sun at S, the elongation is nothing, the planet being then 
in its inferior conjundtion. As the planet moves from E 
tojy, its elongation increafes ; for, when it is at y, it ap¬ 
pears in the line AjyP, while the Sun appears in the line 
ASQj, fo that PAQ^will be its elongation. When the 
A 
Q 
planet is arrived at x, it appears jn the line AxV, which 
is a tangent to its orbit; and then its elongation is VAQj, 
which is the greateft that can be on that fide the Sun ; for, 
after this, the elongation decreafes. When the planet is 
at K, its elongation is PAQ^ when at G, it is nothing, 
becaufe it is then in its fuperior conjundtion; as the pla¬ 
net moves on from G, its elongation again increafes ; for, 
when it comes to C, it appears in the line ACR, and its 
elongation is RAQ^_ When the planet comes to H, 
a line drawn from the Earth through the planet is a tan¬ 
gent to the orbit, and the elongation is TAQj. the great- 
eft it can have when it is on the other fide of the Sun; for, 
after this, the elongation again decreafes. Hence it is 
clear, that the inferior planets can never appear far from 
'the Sun, but muft always accompany it in its apparent 
motion through the ecliptic. And when we fee either 
■Venus or Mercury, it is either in the evening in the weft, 
foon after the fun has fet; or in a morning, a little before 
the Sun rifes. 
When the inferior planets are palling from their greateft 
elongation, on one fide of the Sun, through their fuperior 
conjundtion, to their greateft elongation on the other fide, 
their motion, as viewed from the Earth, is diredt. In 
order to explain this propofition, we (hall firft fuppofe the 
Earth to be at reft at A, in the preceding figure, and cor- 
redt this fuppofition afterwards, by (hewing that the appa¬ 
rent motion of Venus, or Mercury, feen from the Earth, is 
the fame in this refpeCt, whether the Earth moves in its 
orbit, or refts at A. The propofition to be explained is 
this : that as Venus, for inftance, moves from x, its greateft 
elongation on one fide of the Sun, through G its fuperior 
conjifhdtion to H its greateft elongation on the other fide, 
it will appear to a fpedtator upon the Earth, to move from 
weft to eaft according to the order of the figns; that is, its 
geocentric motion will bediredt. 
The planets move round the Sun from weft to eaft, and 
confequently, if there were a fpedtator at the Sun, they 
would appear to him to move through the zodiac, accord¬ 
ing to the order of the figns ; or, in other words, the helio¬ 
centric motion of Venus is diredt. Now, if the Sun and 
the Earth A, are both on the fame fide of the planet, a 
fpedta.tor at the Earth is in the fame fituation, with refpedt 
to the planet and its motion, as if he had been at the Sun: 
for, whilft the planet is moving from x, through G, to F, 
a fpedtator either at A or S is on the concave fide of the 
planet’s orbit* and confequently the planet will appear to 
move in the fame maqner from either; but the apparent 
motion of the planet, when feen front the Sun, is diredh 
and confequently its motion when feen front the Earth 
will alfo be diredt. For, when Venus is at x, it appears 
to a fpedtator on the Earth at A, to be in the line AxV, or 
is feen among the (tars at V ; when Venus has moved to K, 
it is feen among the fixed (tars at P; w hen ir has moved to 
G, it is in its fuperior conjundtion; when it has moved to 
C, it appears among the fixed (tars at R ; and, when it is 
come to H, it appears among tire fixed (tars at T. Thus 
whilft Venus has moved in its orbit from x, its greateft 
elongation on one fide of the Sun, through G its fuperior 
conjundtion, to H its greateft elongation on the other fide, 
it appears to have defcribed the arc VPQjdT in the con¬ 
cave fphere of the heavens; but the letters wKGCH lie 
from weft to eaft, becaufe they lie in the fame direction 
that the planet moves round the Sun ; and the letters 
VPQ_RT lie in the fame diredtion with wKGCH. There¬ 
fore, as the planet feems to a fpedtator on the Earth to de- 
fcribe the arc VPQJtT, its apparent motion feen from the 
Earth is diredt, or from weft to eaft. 
The fecond propofition is this: that while the inferior 
planets move from their greateft elongation on one fide of 
the Sun, through their inferior conjundtion, to their great¬ 
eft elongation on the other fide, their geocentric motion is 
retrograde. Or, in other words, whilft Venus is moving 
from its greateft elongation H, through its inferior con¬ 
jundtion E, to its other greateft elongation x, it appears 
to a fpedtator upon the Earth at A to move backwards, or 
from eaft to weft, contrary to the order of the figns. 
A fpedtator at the Sun is on the concave fide of the pla¬ 
net’s orbit, viewing it from within fide. But, whilft Ve¬ 
nus is moving from its greateft elongation H on one fide; 
through E its inferior conjundtion, to x its greateft elonga¬ 
tion on the other (ide, a fpedtator upon the Earth is on the 
convex fide of its orbit, viewing it from without. There* 
fore, if a fpedtator at the Sun S would fee the planet move 
oneway, a fpedtator at the Earth A will fee it move the 
contrary way ; or the geocentric motion will be contrary to 
its heliocentric motion, and therefore retrograde; for, as 
feen from the Sun, its motion is always diredt. That two 
fpedtators, one at the Earth, the other at the Sun, as they 
are on contrary tides of the arc HE.r, will lee the planet 
apparently move contrary ways; which may be rendered 
more plain by the following familiar conlideration : if two 
men (land with their faces towards each other, and a ball 
is rolled along between them upon the ground, this ball 
will move from the right hand of one of the men towards 
his left, and from the left hand of the other towards his 
right. In like manner, if one man is at the earth A, and 
the other at the Sun S, then whilft the planet is deferibing 
the arc HEx, which is between them, it will appear to 
move from the right hand of the man at S towards his 
left, and from the left hand of the man at A towards his 
right. Whilft the motion of Venus is diredt, or while it 
is deferibing the arc xGH, it appears to move from V to 
T, among the fixed ftars. But, after it has been carried 
in its orbit from H to Qj, it appears in the line A.zR, and 
is feen among the fixed ftars at R. When it comes to E, 
it appears at and, when at y, its apparent place in the 
heavens is at P. Thus as the planet paffes from its great¬ 
eft elongation H on one fide of the Sun, through its infe¬ 
rior conjundtion E, ,to its greateft elongation xon the other 
fide, it apparently runs back from T to V, or its motion 
is retrograde. 
The third propofition is, that Venus is ftationary, or has 
no apparent motion for fume time, when it is at its great¬ 
eft elongation; that is, when it is at H or x, and its appa¬ 
rent place is either at T or V. For, when either of the 
inferior planets, Venus for inftance, is at its greateft elon¬ 
gation H or^, a line drawn from the Earth "through the 
planet, as AHT, or AxV, is a tangent to the orbit. Now 
though a right line touches a circle but in one point, yet 
fome part of the circle greater than a point is fo near to 
the tangent, as not to be diftinguifhed from it. Confe- 
quently, while the planel is deferibing this arc, no other 
change 
