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parallel, and terminating with the poles. 
They are called parallels of latitude, be- 
cause all places lying under the same pa- 
rallel, have the same, latitude. 
Parallels of latitude, in astronomy, are 
lesser circles of the sphere parallel to the 
ecliptic, imagined to pass through every de- 
gree and minute of the colures. They are 
represented on the globe by the divisions 
on the quadrant of altitude, in its motion 
round the globe, when screwed over the 
pole of the ecliptic. See Globe. 
Parallels of altitude, or Almucan- 
TARs, are circles parallel to the horizon, 
imagined to pass through every degree 
and minute of the meridian between the 
horizon and zenith, having their poles in the 
zenith. They are represented on the globe 
by the divisions on the quadrant of altitude, 
in its motion about thejjody of the globe, 
when screwed to the zenith. 
Parallels of declination, in astronomy, 
are the same with parallels of latitude in 
geography. 
Parallel sphere, that situation of the 
sphere, wherein the equator coincides with 
the horizon, and the poles with the zenith 
and nadir. In this sphere all the parallels of 
the equator become parallels of the ho- 
rizon, consequently, no stars ever rise or 
set, but all turn round in circles parallel to 
the horizon ; and the sun when in the equi- 
noctial, wheels round the horizon the whole 
day. After his rising to the elevated pole, 
he never sets for six months ; and after his 
entering again on the other side of the line, 
never rises for six months longer. This is 
the position of the sphere to such as live 
under the poles, and to wliom the sun is 
never above 23° 30' high. 
Parallel sailing, in navigation, is the 
sailing under a parallel of latitude. See 
NAVtGATION. 
PARALLELEPIPED, or Parallelo- 
piPED, in geometry, a regular solid com- 
prehended under six parallelograms, the 
opposite ones whereof are similar, parallel, 
and equal. All parallelepipeds, prisms, 
cylinders, &c. whose bases and heights are 
equal, are themselves equal. A diagonal 
plane divides a parallelepiped into two 
equal prisms ; so that a triangular prism is 
half a parallelepiped upon the same base, 
and of the same altitude. 
All parallelepipeds, prisms, cylinders, &c. 
are in a ratio compounded of their bases 
and altitudes ; wherefore, if their bases be 
equal, they are in proportion to their alti- 
tudes, and conversely, All parallelepipeds, 
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cylinders, cones, &c. are in a triplicate 
ratio, of their homologous sides, and also of 
their altitudes. 
Equal parallelepipeds, prisms, cones, cy- 
linders, &c. reciprocate their bases and al- 
titudes. 
PARALLELISM, the situation or qua- 
lity whereby any thing is denominated pa- 
rallel. See Parallel. 
Parallelism of the earth’s axis, in 
astronomy, that situation of the earth’s axis, 
in its progress through its orbit, whereby it 
is still directed towards the pole-star ; so 
that if a line be drawn parallel to its axis, 
while in any one position, the axis, in all 
other positions, will be always parallel to 
the .same line. 
This parallelism is the result of the cartli’s 
double motion, viz. round the sun, and 
round its own axis ; or its annual and 
diurnal motion ; and to it we owe the vi- 
cissitudes of seasons, and tlie inequality of 
day and night. 
Parallelism of the rows of trees. These 
are never seen parallel, but always inclining 
to each other towards the further eitreme. 
Hence mathematicians have taken occasion 
to inquire in what lines the trees must be 
disposed to correct this effect of the per- 
spective, and make the rows still appear 
parallel. The two rows must be such, as 
that the unequal intervals of aTy two oppo- 
site or correspondent trees may be seen 
under equal visual rays. 
PARALLELOGRAM, in geometry, a 
quadrilateral right-lined figure, whose oppo- 
site sides are parallel and equal to each 
other. It is generated by the equable mo- 
tion of a right line always parallel to itself. 
When it has all its four angles right, and 
only its opposite sides equal, it is called a 
rectangle or oblong. When the angles are 
all right, and the sides equal, it is called a 
square. If all the sides are equal, and the 
angles unequal, it is called a rhombus or lo- 
zenge ; and if the sides and angles be une- 
qual, it is called a rhomboides. 
In every parallelogram of what kind 
soever, a diagonal divides it into two equal 
parts ; the angles diagonally opposite are 
equal ; the opposite angles of the same side 
are together equal to two right angles ; and 
each two sides, together, greater than the 
diagonal. 
Two parallelograms on the same or equal 
base and of the same height, or between 
the same parallels, are equal ; and hence 
two triangles on the same base and of 
the same height, are also equal. Hence, 
