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FORMULAE TO DETERMINE THE RADIUS OE CURVATURE-

At any point.

Ellipse Ordinate = y

Transverse axis= tConjugate = cParameter = p

Hyperbola Ordinate = y iTransverse axis— t

(c* + 4:.t 3 —c^1/*y2\cc*

(I’p 3 -f 4 t.t—p]y*)i

2t 3 p*

2tc*

Conjugate

Parameter

Parabola Ordinate

ege-v

= c= p J

= A

Parameter — p !>Absciss := x]

Cycloid Diameter of the ge-'nerating circleAbsciss at anypoint = x.

Catenary Constant quan-tity = c

Absciss = x

Ordinate = y J.

Angle the curvemakes with itsordinate =

Catenary 1 Constant quan-of equal | tity = c

strength 'f Angle the curve vat every j makes with its l <ppoint, j ordinate J

Tract 3, page 169.

(t-p*+4 t.t+plp » )$

21 3 J) 2

2 _p2 a/ x

2 a/ d 2 —dx

: sec . $ 1 *

c see <{>

At the vertex.C 32t

L2

c**2t

jP_

2

r

2.x

2d

1 )

* In the equations •— and exhibiting the radii of curvature

at the vertex in the three conic sections, putting radius of curva-ture equal r , then in the ellipse hyperbola r is a third proportional

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