1 66 JMijceUanea Curio fa. 



The Quadrature of the Logarithm 

 mical Curve. 



.By J. Craig. 



(Fig. 26.) 



LET ONF be the Logarith mical Curve, 

 vvhofe Afymptote is AR, in which let 

 fuch a point A be taken, as that the firft 

 Ordinate AO may be equal to the Subtan- 

 gent or Unity. 'Tis required to find the 

 Area of the Curvilinea! Space AONM com- 

 prehended under the two Ordinates AO, 

 MN, the AbicilTe AM, and the Curve ON. 

 From O draw OE parallel to AM and cut- 

 ting MN in E ; 1 fay, that the Re&angle 

 under the Segments ME, EN, is equal to 

 the Space fought. Demonstration.' Let the 

 Ordinate MN pZ, Subtangent AO or ME 

 £ss \ and to the Axis AR let another Curve 

 HGE be conftructed, whofe Equation fhall 

 be 2$z,t=zx*, its Ordinate GM being t=ix. I 

 fay, that this Curve is the Quadratix of the 

 Logarithmical Curve (according to the Prin- 

 ciples of my Method) viz.. its Subnormal is 

 relpedively equal to the Ordinate of this, 

 as is plain from the Calculus of that Me-> 

 tbod. Therefore (according to what I have 

 fhewn in another place) if to the point G 

 we draw GC perpendicular and equal to GM, 

 as alio HD parallel to GC, and meeting 

 tlie Lines GM ? CM, in B and D j then will 



