1915-16.] The “ Geometria Organica” of Colin Maclaurin. 149 
Prop. XXVII 
shows how to draw a C 2n through 2?i + 4 given points, of which three 
are 'ft-ple points, while a fourth is an (n — l)-ple point. 
APPENDIX. 
In the light of the account just given, the student will find it interesting 
to examine the following references to Loria’s Ebene Kurven. The pages 
refer to the first edition of Loria’s treatise. 
Page 39. 
The locus of the image of the vertex of a parabola in the tangent is a 
cissoid of Diodes. 
Loria refers to Mirman : “ Sur la Cissoide de Diokles,” Nouvelles 
Annales, 1885. 
When a parabola rolls externally on a congruent parabola its vertex 
describes a cissoid. 
Reference toHendrick’s “Demonstration of a Proposition” (A nalyst, 1877). 
Page 48. 
The Opliiuride. 
Given a right angle OBC on whose sides O and C are fixed points. 
Through C is drawn CD cutting OB in D ; DM is J_ r CD, and OM l r DM 
The locus of M as CD varies is the ophiuride. 
Reference to Uhlhorn: Entwickelungen in derhoheren Geometrie, 1809. 
Page 49. 
The pedal of a parabola for a pole on the tangent at the vertex is an 
ophiuride, and a cissoid for the vertex. 
Page 60. 
The Strophoid. 
This name was given by Montucci ( Nouvelles Annales , 1846). 
It is the logocyclic curve of Booth (1877). 
Page 69. 
The generalised strophoidal curve, given by Maclaurin, is ascribed to 
Lagrange (Xouv. Ann., 1900). 
Page 86. 
The trisectrix of Catalan is the first negative pedal of the parabola 
when the pole is at the focus. 
(.'. a sine spiral admitting of rectification.) 
