26 REPOiiT — 1873. 



little known." This is true ; but Kulik, 1848, is of the same extent, and 

 also gives cubes vp to that of 100,000, thus giving the largest table of squares, 

 and by far the largest table of cubes in the same work, and in a compact and 

 convenient form : of this work also it may be said that it is very little known. 



Httttois-, 1781 (§ 4), gives squares to that of 25,400, and cubes to that of 

 10,000 ; but for most purposes Baelow (stereo. 1840), which gives squares, 

 cubes, and square roots and cube roots (and reciprocals) of numbers to 1000, 

 and is very accurate, is the best. We have not seen any square-root or cube- 

 root table of greater extent. 



Extensive tables of quarter squares have been published, which are de- 

 scribed in § 3, art. 3 ; and some tables of squares, as Eaa de Bruno, were 

 constructed with the view of being used in applying the method of least 

 squares. 



It is scarcely necessary to remark that logarithms find one of tlie most 

 valuable applications in the extraction of roots. Multiplications &c. can bo 

 performed generally without their aid with a little more trouble ; for finding 

 square and cube roots they are extremely useful ; but for the extraction of 

 higher roots there exists no other method admitting of convenient application. 



Maginus, 1592. The ' Tabula Tetragonica ' is introduced by the words 

 " sequitur tabula numerorum quadratorum cum suis radicibus nunc primum 

 ab auctore supputata, ac in lucem aBdita," and occupies leaves 41-04. It 

 gives the squares of all numbers from 1 to 100,100. We have seen the 

 ' Tabula Tetragonica ' quoted as an independent work ; and De Morgan says 

 that it was published separately, with headings and explanations in Italian 

 instead of Latin. In the copy before us Tavola is misprinted for Tahvla on 

 pp. 41 and 43 back (only the leaves are numbered). 



The work contains sines, tangents, and secants also. 



Magini was, we suppose, the vernacular name of the author, and Maginus 

 the same Latinized. We have somewhere seen Magini and Maginus spoken 

 of as if they were different persons. 



Alstedius, 1649. In part 3. pp. 254-260, Alsted gives a tabic of squares 

 and cubes of numbers from 1 to 1000. Alsted's is the first Cyclopaedia, in 

 the sense that we now understand the word. 



[Moore, Sir Jonas, 1650?] Squares and cubes of numbers from 1 to 

 1000, fourth powers from 1 to 300, fifth and sixth powers from 1 to 200. 



In the book before us (Brit. Mus.) this tract (which has a separate pagina- 

 tion) is bound up at the end, after Moore's 'Arithmetick (and Algebra), 

 Contemplationes Geometricoe, and Conical Sections.' De Morgan says that 

 power tables, exactly the same as these, were given in Jonas Moore's ' Arith- 

 metic ' of 1650, and reprinted in the edition of 1660 ; so that probably the 

 tract noticed here usually formed part of the 'Arithmetick.' 



[Pell], 1672. Squares of numbers from 1 to 10,000 (pp. 29). This is 

 followed by the 6 one-figure endings, the 22 two-figure endings, the 159 

 three-figure endings, and the 1044 four-figure endings, which square numbefs 

 admit of. They are given at length, and also in a synoptical form. The last 

 page in the Eoy. Soc. copy is signed John Pell. (In the Itoyal Society's Li- 

 brary Catalogue this table is entered under Fell, the signature at the end in 

 the Society's copy having been struck out so as to render the first letter 

 uncertain.) 



In the Brit. Mus. is a copy without any name (so that perhaps Pell's name 

 was supplied in the Eoy. Soc. copy only in manuscript). ' Dr. Poll's Tables,' 

 however, is written in it, and no doubt can exist about its authorship. 



