EQU 



EQU 



its corresponding ordinate, or else the re- 

 lation of their fluxions, &c. Thus, the 

 equation to the circle is a x x 1 = T/ Z , 

 where a is its diameter, x any absciss or 

 part of that diameter, and y the ordinate 

 at that point of the diameter; the mean- 

 ing being, that whatever absciss is de- 

 noted by x, then the square of its cor- 

 responding ordinate will be a x x*. In 

 like manner the equation 



of the ellipse is a x x 1 = y\ 

 a 



of the hyperbola is -=. a x+x* = y 1 , 



of the parobola is .p x = y* 



Where a is an axis, and// the parameter. 

 And in like manner for any other curves. 

 This method of expressing the nature 

 of curves by algebraical equations was 

 first introduced by Des Cartes, who, by 

 thus connecting together the two sciences 

 of algebra and geometry, made them mu- 

 tually assisting to each other, and so laid 

 the foundation of the greatest improve- 

 ments that have been made in every 

 branch of them since that time. 



EQ.TJATION of time, in astronomy and 

 chronology, the reduction of the appa- 

 rent time or motion of the sun to equa- 

 ble, mean, or true time. The difference 

 between true and apparent time arises 

 from two causes, the excentricity 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 complement of the lati- 

 tude 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 living on this cir- 

 cle, called by geographers and navigators 

 the line, have their days and nights con- 

 stantly 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 3 - 6 J> = 15 

 degrees: hence one degree of the equator 

 will contain four minutes of time ; 15 mi- 

 nutes of a degree will make a minute of 

 an hour ; and, consequently, four seconds 

 answer 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 pur- 

 pose they give their attendance monthly, 

 one at a time, and are allowed 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 

 are natives of most parts of Europe, in 

 woods and shady places. 



EQUIANGULAR, in geometry, an epi- 

 thet given to figures, whose angles are 

 all equal ; such are, a square, an equilate- 

 ral triangle, &c. 



EQUICRURAL, in geometry, the same 

 with isosceles. See ISOSCELES TRIAN- 

 GLE. 



EQUID1FFERENT numbers, in arith- 

 metic, are of two kinds. 1. Continually 

 equidiflferent, is when, in a series of three 

 numbers, there is the same difference be- 

 tween the first and second, as there is 

 between the second and third ; as 3, 6, 9. 

 And 2. Discretely equidiflferent, 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, some- 

 thing that hath equal sides, as an equila- 

 teral angle. 



EQ.UILATERAL hyperbola, one whose 

 transverse diameter is equal to its para- 

 meter ; and so all the other diameters 

 equal to their parameters: in such an hy- 

 perbola, the asymptotes always cut one 

 another at right angles in the centre. Its 

 most simple equation, with regard to the 

 transverse axis, is y 1 = x a 1 -, and with 

 regard to the conjugate, y 1 = x 1 -f- a 1 , 

 when a is the semitransverse, or semicon- 

 jugate. The length of the curve cannot 

 be found by means of the quadrature of 

 any space, of which a conic 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 

 multiplied by one and the same number 

 or quantity. Hence, equimultiples are 



