( C 33* ) 
the Nautical Meridian is a Scale of Logarithms of the Diffe- 
rences wbtrtb'j the Secants of Latitude exceed their.refpetfhe 
Tangents , Radius being Unity, So here R M is the Loga- 
rithm of ML, the Difference of theSedant and Tangent 
of the Latitude whofe Meridional part is R M. 
19. Suppofing the precedent Conftrudion, if through 
any point C of the Curve ACB be drawn a right Line 
GC W parallel to M R, terminated with the Logarithmic 
Curve in W and the Radius A R in G^fiay that the fame 
right Line fVG is equal to the intercepted part of theCurve 
Line^C. • f 1 i * -r, 
20. Lcftvg be a Line infinitely near and parallel to 
JVG, and terminated by the fame Lines ; and CS, IV ur f 
perpendicular to the Meridian ; C S interfering vg in z, 
and TV a in Let CM be a Tangent to A C in. C; 
TV* a Tangent to A TV in TV ; fo is C M = <r v. Becaufe of 
tike Triangles Czc, C SM; and TVyw, TV a ry CS : 
CM : : C z : C c : alfo TV a a e r :t TV f * ym. Buifc 
TVtr — CS; 0 t =± C M; Cz—Wy\ therefore is yw 
the Fluxion of G W t equal to C c the Fluxion of the 
Curve A C. Conlequently G W~ AC, q» e.d~ 
ft may be noted that this Equitangential Curve gives 
the Quadrature of a Figure of Tangents (landing perpen- 
dicular on their Radius. In Fig. let AyT be a Curve 
whole Ordinates as g y, G F, are equal to the Tangents 
of their refpedive intercept Arcs A k, A k» Let FG be 
produced to touch the Curve A C in C : then is the Area 
AFG equal to the Redangle contained by Radius A R 
and GC the produced part of the Ordinate; or AFG — . 
A R* G C. The Demonfl ration of which, and of the fol- 
lowing Section, ! for Brevity omit. 
12. If we fuppole the Figure A CB &c. KR (Fig. 3.) 
infinitely continued, to be turned about its Afymptote 
A iT as an Axe, the Solid fd generated will be equal to 
