EQU 
jntrsduced by Des Cartes, who, by thus 
connecting together the two sciences of 
algebra and geometry, made them mutually 
assisting to each other, and so laid the 
foundation of the greatest improvements 
that have been made in every branch of 
them since that time. 
Equation of time, in astronomy and 
chronology, the reduction of the apparent 
time or motion of the sun, to equable, 
mean, or true time. The difference be- 
tween true and apparent time arises from 
two causes, the excen tricity of the earth’s 
orbit, and the obliquity of the ecliptic. See 
Time, equation of. 
EQUATOR, in geography, a great cir- 
cle of the terrestrial globe, equidistant 
from its poles, and dividing it into two equal 
hemispheres ; one north and the other south. 
It passes through the east and west points 
of the horizon, and at the meridian is raised 
as much above the horizon as is the com- 
plement of the latitude of the place. From 
this circle the latitude of places, whether 
north or south, begin to be reckoned in 
degrees of the meridian. All people liv- 
ing on this circle, called by geographers 
and navigators the line, have their days and 
nights constantly equal. It is in degrees of 
the equator that the longitude of places are 
reckoned; and as the natural day is mea- 
sured by one revolution of the equator, it 
follows that one hour answers to = 15 
degrees : hence one degree of the equator 
will contain four minutes of time; 15 mi- 
nutes of a degree w ill make a minute of an 
hour ; and consequently, four seconds an- 
swer to one minute of a degree. 
EQUATIONAL. See Observatory. 
EQUERRY, in the British customs, an 
officer of state, under the master of the 
horse. There are five equerries who ride 
abroad with his Majesty ; for which purpose 
they give their attendance monthly, one at 
a time, and are allow ed a table. 
EQUISETUM, in botany, English horse- 
tail, a genus of the Cryptogamia Filices 
class and order. Natural order of Filices 
or Ferns. There are seven species. They 
afe natives of most parts of Europe in 
w oods and shady piaces. 
EQUIANGULAR, in geometry, an epi- 
thet given to figures, whose angles are all 
equal : such are a square, an equilateral tri- 
angle, &c. 
EQUICRURAL, in geometry, the same 
with isosceles. See Isosceles Triangle. 
EQUIDIFFERENT numbers, in arith- 
metic, are of two kinds. 1. Continually 
EQU 
equidiffereht is when, in a series of three 
numbers, there is the same difference be- 
tween the first and second, as there is be- 
tween the second and third ; as 3, 6, 9. 
And 2. Discretely equidifferent, is when, in 
a series of four numbers or quantities, there 
is the same difference between the first 
and second as there is between the third 
and fourth: such are 3, 6, 7, 10. 
EQUIDISTANT, an appellation given 
to things placed at equal distance from 
some fixed point, or place, to which they 
are referred. 
EQUILATERAL, in general, something 
that hath equal sides, as an equilateral angle. 
Equilateral hyperbola, one whose trans- 
verse diameter is equal to its parameter ; 
and so all the other diameters equal to their 
parameters: in such an hyperbola, the 
asymptotes always cut one another at right 
angles in the centre. Its most simple equa- 
tion, witli regard to the transverse axis, is 
y 2 == x — a 2 ; and with regard to the con- 
jugate, y 2 ±r x 2 -j— a 2 , when a is the semi- 
transverse, or semiconjugate. The length 
of tiie curve cannot be found by means of 
the quadrature of any space, of which a co- 
nic section is any part of the perimeter. 
EQUILIBRIUM, in mechanics, is when 
the two ends of a lever or balance hang so 
exactly even and level, that neither doth 
ascend or descend, but keep in a position 
parallel to the horizon, which is occasioned 
by their being both charged with an equal 
weight. 
EQUIMULTIPLES, in arithmetic and 
geometry, are numbers and quantities mul- 
tiplied by one and the same number or 
quantity. Hence, equimultiples are always 
in the same ratio to each other, as the sim- 
ple quantities before multiplication : thus, 
if 6 and 8 are multiplied by 4, the equimul- 
tiples 24 and 32 will be to each other, as 6 
to 8. 
EQUINOCTIAL, in astronomy, a great 
circle of the celestial globe, whose poles 
are the poles of the world. It is so called, 
because whenever the sun comes to this 
circle, the days and nights are equal all 
over the globe ; being the same with that 
which the sun seems to describe, at the 
time of the two equinoxes of spring and 
autumn. All stars directly under this cir- 
cle, have no declination, and always rise 
due east, and set full west. The hour cif- 
cles are drawn at right angles to it, passing 
through every fifteenth degree ; and the 
parallels to it are called parallels of decli- 
nation. \ 
