188 



The parallelogram which formed the subject of this commuuica- 

 tion is the rectangle whose sides are to each other in the ratio of 

 the diagonal of a square to its side, — a figure well known to archi- 

 tects, sculptors, and painters, from its beauty, and frequently adopt- 

 ed in the practical arts. 



The author shewed that if the given rectangle be bisected by a 

 line parallel to its shortest side, each segment will be a figure simi- 

 lar in all respects to the original rectangle ; and if either of these 

 halves be itself bisected in the same manner, their halves will be 

 rectangles similar to the original rectangle; and so on adinjinitutn. 

 The sides of the primary figure and its halves are continual propor- 

 tionals, represented by the series 



The author endeavours to trace an analogy between the properties 

 of this parallelogram and the logarithmic spiral. 



A class of figures may be obtained by trisection and by di- 

 vision into four, five, or any number of figures, all of them similar 

 to the primary figure, and capable of division ad infinitum in the 

 same manner. 



Mmiday, 19th February. 

 De hope, V. P., in the Chair. 

 The following Donations were presented : 



Comptes Rendus Hebdomadaires des Seances de I'Academie des 

 Sciences, (18b8, 1" Semestre), Nos. 3, 4, 5.— By the Aca- 

 demy. 



Bulletin des Seances de I'Academie Royale de Bruxelles, (1837). 

 Nos. 1, 2, 3, 4, 5, 6, 7, 8. 



Nouveaux Memoires de I'Academie Royale des Sciences et Belles 

 Lettres de Bruxelles. Tome x. 



Memoires Couronnes par I'Academie Royale des Sciences et Belles 

 Lettres de Bruxelles. Tome xi By the Academy. 



Annales de I'Observatoire de Bruxelles, publies, aux frais de I'etat, 

 par le Directeur A. Quetelet. Tome i. partie 2. — By the 

 Author. 



Memoires sur Trois Integrales Definies, par M. J. Plana, Directeur 

 de I'Observatoire de Turin. — By tlie Author. 



