108 Mr WALLACE, ON GEOMETRICAL THEOREMS, AND FORMULAE, 



2. In comparatively modern times an interesting application of the 

 problem was made to geodetical measurements. In the year 1620 

 Snellius, when ascertaining the distance between Bergen-op-zoom and 

 Alcmaer, with a view to the determination of the magnitude of the 

 Earth, employed it in finding the position of his Observatory. He 

 assumed as given points three stations whose positions had been deter- 

 mined, and taking the angle which each two of them made at the Obser- 

 vatory, he was able to determine, by a ti'igonometrical computation, 

 the distances of the stations, and thence its position*. The same 

 problem was proposed by Richard Towneley as a chorographical problem f, 

 and resolved trigonometrically in the Philosophical Transactions about the 

 year 1670, by John Collins. 



3. We are informed by Delambre^ that Lalande wishing to com- 

 pute some observations of the Moon which had been made at the 

 Military School, Paris, proposed to find the longitude of the station 

 where the observations had been made, by observing there the angles 

 subtended by three steeples whose positions were known. He was 

 thus led to the same application as had been made long before by 

 Snellius, without knowing or without thinking of his solution. La- 

 lande's patience was exhausted by the length of the calculations, and 

 the slips he made in performing them : he therefore referred the 

 problem to Delambre, who gave a solution which was printed in Cag- 

 noli's Trigonometry (First Edition), and again, but with more detail, 

 in his own treatise Methodes Analytiques pour la Determination d'un 

 Arc du 3Ieridien. 



Delambre's solution, which is analytical, is good, his formulas have 

 however but little of that symmetry and simplicity wiiich constitute 

 elegance in a geometrical speculation, and make it easy to be compre- 

 hended and remembered. 



4. In considering the problem I have found two Theorems ; from 

 one of them a particularly simple and elegant geometrical construction 



* Snellius, Erastosthenes Bataviis, p. 203. 



+ Lowthorpe's Abridgement of Phil. Trans. Vol. I. p. 120. 



J Histoire de I'Aetronomie Moderne, T. II. p. 109. 



