On the History of certain Formulae in Spherical Trigonometry. 99 



these theorems in the Connoisance des Terns, 1808, before the 

 publication of the work of Gauss. . . .'* T. S. Davies says, on 

 p. 37 of the second volume of the twelfth edition of Hutton's 

 ( Course of Mathematics/ " The four formulae ... are usually 

 known as Gauss's Analogies, their demonstration having been 

 first given by that illustrious geometer in his Theoria Motus 

 Corporum Ccelestium (1809): but they had been published by 

 Delambre some years previously in the Connaissance des Temps 

 (for 1808) . . " Here, besides the expansion of an exact two 

 years into an indefinite some years, we have the statement that 

 Gauss gave a demonstration of the formula? in 1809; but as we 

 have already stated, Gauss omitted the demonstration. In a 

 note Mr. Davies adds : " Gauss did not deliver his theorems, or 

 their investigations, in precisely the forms given in the text . . ." 

 But Gauss did deliver his theorems in those forms. Then what 

 Mr. Davies goes on to say respecting the forms and investiga- 

 tions may perhaps apply to some other work, but does not apply 

 to the Theoria Motus, where Gauss delivered the theorems. 



It must be observed that Gauss had been anticipated even in 

 Germany in the publication of the formulae. They were given by 

 Mollweide in Zactr's Monatliche Correspondenz for November 

 1808, with a demonstration. 



The subject is noticed in an article in KlugePs Mathematisches 

 Worterbuch, vol. v. p. 211 ; the passage has been reproduced in 

 the ( Proceedings of the London Mathematical Society/ vol. iii. 

 p. 320. The writer states correctly the positions of Gauss and 

 Mollweide ; and then he adds that Delambre published the for- 

 mulae in the Connaissance des Terns for 1808, and so French 

 writers usually call them after him. But these few words rela- 

 ting to Delambre seem to me to fall below the usual high standard 

 of German accuracy. For in the first place the erroneous date 

 (1808) must have been borrowed without verification, although 

 there is nothing to warn us of this. And in the next place the 

 writer apparently puts the claims of Mollweide and Delambre 

 as equal, by ascribing to both the date 1808, overlooking the 

 fact that the Connaissance des Terns for an assigned year is 

 published in advance of that year. 



Thus, finally, although Mollweide has priority over Gauss, 

 yet he comes about a year and a half after Delambre ; and there- 

 fore until any other person can be shown to have published the 

 formulae before April 1807, they must be justly ascribed to 

 Delambre. 



Demonstrations of the formulae in two ways were published 

 by Delambre in his Astronomie (see pp. 164 and 196 of his first 

 volume). It would appear from his page 164 that he consi- 

 dered this to be the first publication of a demonstration ; but, 



H2 



