272 



NOTES AND QUERIES. 



[2°'i S. X. Oct. 6. '60. 



which has been published in Ethiopic and also in 

 English, Nor is there any ancient Christian 

 author of the name of Thadrus. 



2. The Book of Jehu, 2 Chron. xx. 34. No 

 such book is named in the Hebrew, which is, 

 " Behold, they are written in the words of Jehu, 

 son of Hanani, who is mentioned in the book of 

 the Kings of Israel." 



3. The book of the battles of the Lord (Num. 

 xxi. 14.) Of this nothing is known ; it may not 

 have been inspired. 



4. The book of Nathan. Probably part of the 

 books ascribed to Samuel and of the Kings. 2 

 Chron. ix. 29. 



5. The book of Iddo ; unknown. 2 Cliron. ix. 

 29. ; xii. 15. 



6. The prophecy of Ahijah, 2 Chron. xiv. 29. 

 (Reference wrong ; see ix. 29.) 



7. The book of Shemaiah, 2 Chron. xii. 15. 

 Some of these were probably portions of the 

 existing historical books, others are lost. But we 

 must remember that the Jews wrote other books 

 besides such as were inspired, and that the mere 

 mention of a lost book in the Bible does not prove 

 such book to have been inspired. 



8. The book of Jashar. The Hebrews have 

 several books with this title ; one of them has 

 been published in English. Some suppose the 

 book was the Pentateuch, or a part of the Pen- 

 tateuch ; others, that it was a collection of re- 

 ligious odes, which received successive additions. 

 The most recent theory is that of Dr. Donaldson, 

 who has published a book with this title, full of 

 learning and unsound criticism. 



9. The Book of Gad. Unknown. 



10. Epistle to Corinthians, 1 Cor. v. 9. Very 

 doubtful ; the same argument would prove lost 

 epistles by John. See 1 John iii. 14. 



11. The First Epistle to Ephesians, iii. 3. 

 Extremely doubtful. 



12. Epistle to Laodiceans, Col. iv. 16. There 

 is no proof that Paul wrote one to them. He 

 mentions the epistle from Laodicea, not to it. 

 However, Abracadabea sees what is debited as 

 such. 



13. Book of Henoch. Same as No. 1. 



14. Book of Solomon's 3000 Proverbs, and 1000 

 Songs, &c. Solomon is not said to have written 

 these things, and no such hook is mentioned. 



15. Epistle of Barnabas. Printed over and 

 over again. 



16. Revelation of Peter. With reference to 

 this my memory fails me, but we have sundry 

 Apocryphal books about him. 



17. Doctrine of the Apostles. Often printed, 

 but spurious. B. H. C. 



LEONARD EULER. 

 (2"^ S. iii. 388.) 



There is a Query now rather more than three 

 years old, of the following purport : — Who first 

 denoted the sine, cosine, &c. of an angle A by the 

 abbreviations sin A, cos A, &c. ? Dr. Olinthus 

 Gregory affirms that it was Thomas Simpson : 

 Dr. Peacock affirms that it was Euler. 



Dr. Gregory (Hints to Teachers, p. 114.') states 

 that Simpson made the improvement eighty years 

 before the date of his writing (1837 — 1840), and 

 he refers to the Miscellaneous Tracts, 1757. On 

 this he says that Simpson has a priority of " many 

 years " : at what time he imagined the second to 

 Simpson to have come into the field I cannot con- 

 jecture. 



Dr. Peacock states that it was Euler who made 

 the step : for which he quotes the preface of the 

 Analysis Infinitorum, first published in 1748. In 

 this preface Euler announces, in indefinite terms,, 

 an addition to the notation of trigonometry. It 

 would have been 'better to have quoted the 8th 

 chapter, in which Euler says, " Sinum autem Arcus 

 z in posterum hoc modo indicabo fm. A. z, seu 

 tantum Jin. z." This looks very much like the 

 first announcement of a notation : and the more 

 so as it shows successive steps of abridgment. 

 But it is rather to be wondered at that no one has 

 produced earlier instances : for Euler himself, in 

 spite of the formality which he throws into his 

 elementary work, had been using and printing a 

 still more abridged notation for more than four- 

 teen years ; during which time some had probably 

 adopted the method. This is Euler all over : 

 hundreds of times, if not thousands, he lays down 

 with the precision of a first announcement — that 

 is, with much more precision than is found in the 

 first announcements of many — matters with which 

 the readers of his works must have been perfectly 

 familiar. 



Before I ascertained, as presently described^ 

 that Euler had forestalled himself, I felt satisfied 

 that, if he dated in this matter from 1748, Clairaut 

 must have preceded him. For Clairaut presented 

 his theory of the Moon to the Academy in 1750 ; 

 and any one who looks at that production will feel 

 satisfied that no one could have written it who 

 had not been conversant with the notation in 

 question much more than two years. 



I cannot undertake to say where Euler jftrst 

 used this notation. In 1744, the y£ar in which 

 he scattered it thickly through all the pages of 

 a long work, he had published five separate 

 works, and upwards of forty memoirs. Gunter 

 fell into the word cosine (as the abbrevia- 

 tion of complemental sine) in the act of writing a 

 sentence introductory to the tables he had just 

 printed, in the headings of which it does not ap- 

 pear. And Gunter himself, and Wingate in re- 



