382 Prof. De Morgan on thejirst introduction 



field's storm-paths are confined to the westward of the fiftieth 

 meridian, and he is only able to give one-half of the ellipse in 

 any case. Nearly the whole breadth of the Atlantic is a per- 

 fect blank in any storm-map. Surely several captains may be 

 found who will be happy to make observations on their pas- 

 sages out and homeward, and transmit them to head quar- 

 ters, either in London or some principal city in America ; the 

 only additional information required to that furnished by their 

 logs, will be the altitudes of the barometer at given hours of the 

 day and night, with its attached thermometer. The American 

 steamers might furnish important and valuable information. 



I have the honour to be, 

 Gentlemen, 

 Your very obedient Servant, 

 Cambridge Heath, April 22, 1846. W. R. BlRT. 



LXII. On the Jirst introduction of the words Tangent and 

 Secant. By Prof. De Morgan*. 



A BOUT the meaning and origin of the word sine, there is 

 -*-*- now no discussion. The words tangent and secant, 

 though clear as to their meaning, have an origin which is not 

 mentioned by historians. Nobody, in fact, knows where they 

 came from ; very few people care. 



As it may appear surprising, and perhaps even doubtful, 

 that the first inventor of names now so universally recognised 

 should be unknown, I will begin by stating, that neither 

 Weidler, Heilbronner, Montucla, nor Delambre, mentions the 

 work in which the words first appear. Montucla does not 

 allude to the question of the invention of these terms. De- 

 lambre does it, as follows, in a manner which shows that his 

 impression on the subject was not founded on anything precise. 

 In speaking (Astr. Moy., p. 437) of Vieta's mode of desig- 

 nating the trigonometrical functions, he informs us that Vieta, 

 after stating that no elegant name had been given to what we 

 now call the table of tangents, proposed to continue the use of 

 the term tabula fcecunda, which had been given by Regiomon- 

 tanus. " Ce qui," continues Delambre, "n'est pourtant pas 

 plus elegant que le mot tangente qu'il reprouve; quant aux 

 secantes, il veut qu'on les appelle hypotSnuses des feconds. Ces 

 denominations n'etaient pas faites pour etre accueillies ; on 

 s'est decide pour ce qui etait plus naturel, plus commode, et 

 meme plus elegant, quoiqu'en dise Viete." Here it is plain 

 that he thinks the word tangent to have been one of those 

 which Vieta spoke ofj when he threw his imputation of want 

 * Communicated by the Author. 



