ON MATHEMATICAL TABLES. 43 



Rheticus, 1596 (' Opus Palatinum '). Complete ten-deeimal trigonome- 

 trical canon for every ten seconds of the quadrant, semiquadrantally arranged, 

 with differences for all the tabular results throughout. Sines, cosines, and 

 secants are given on the versos of the pages in columns headed respectively 

 Perjpendiculum, Basis, Hypotenusa ; and on the rectos appear tangents, cose- 

 cants, and cotangents, in columns headed respectively Perpendiculum, Hypo- 

 tenusa, Basis*. This is the celebrated canon of George Joachim llheticus, 

 the greatest of the table-computers, to whom also is due the canon of sines 

 described below under Pitiscus, 1613. At the time of his death (1576) 

 Rheticus left the canon all but complete ; and the trigonometry was finished 

 and the whole edited by Valentine Otho under the title ' Opus Palatinum,' 

 so- called in honour of the Elector Palatine Frederick IV., who bore the ex- 

 pense of publication. The edition before us is in two volumes, the second 

 containing the ten-decimal canon and occupying 540 pp. (2-541) folio ; then 

 follow 13 pp. of errata numbered 142-153 and 554. At the end of the 

 first volume is a canon of cosecants and cotangents (in columns headed 

 Hypotenusa and Basis respectively) to 7 places for every 10 seconds, in a 

 semiquadrantal arrangement. It occupies 180 pp. (separate pagination, 

 2-181) ; and there seems no reason why it should have been printed at all, as 

 the great ten-decimal canon completely supersedes it. Besides, it is exceed- 

 ingly incorrect, as comparison with the latter shows at once. On this point 

 De Morgan says that its insertion "was merely the editor's want of judg- 

 ment ; it is clearly nothing but a previous attempt made before the larger 

 plan was resolved on ;" while Hutton writes, " But I cannot discover the 

 reason for adding this less table, even if it were correct, which is far from 

 being the case, the numbers being uniformly erroneous and- different from the 

 former through the greatest part of the table." Mention of it is introduced 

 by Hutton with the words, " After the large canon is printed another smaller 

 table," &c., while in the copy before us it ends the first volume, the second 

 containing the great canon. It is also to be inferred from De Morgan's ac- 

 count that the whole work generally is bound in one (very thick) volume. 

 The tangents and secants in the early part of the great canon were found to 

 be •inaccurate ; and the emendation of them was intrusted to Pitiscus, who 

 "corrected the first eighty-six pages, in which the tangents and secants were 

 sensibly erroneous " (De Morgan) ; and copies of this corrected portion alone 

 were issued separately in 1607, as well as of the whole table with the correc- 

 tions. We have not seen one of these corrected copies ; but vide De Morgan's 

 fuU account, ' English Cyclopaedia,' Article " Tables," and ' Notices of the 

 Roy. Astron. Soc.,' t. vi. p. 213, and ' Phil. Mag.' June, 1845, The pagina- 

 tion of the other parts of the work is ' De Triangulis globi cum angulo recto,' 

 pp. 3-140 ; ' De Fabi'ica Canonis,' pp. 3-85 ; ' De Triquetris rectarum line- 

 arum in planitie,' pp. 86-104 ; ' De Trianguhs globi sine angulo recto,' pp. 

 1-341 ; ' Meteoroscopium,' pp. 3-121 (the first three by Rheticus and the 

 rest by Otho). 



In 1551 Rheticus had published a ten-minute seven-place canon in his 

 ' Canon Doctrinae Triangulorum,' Leipzig, with which the present work must 

 not be confounded. And in 1579 Vieta published his ' Canon Mathematicus, 

 seu ad triangula cum Adpendicibus,' for every minute of the quadrant. This 



* The explanation of these terms is evident. The sines and cosines arc perpendiculars 

 and bases to a hypotenuse 10,000,000,000 ; the secants and tangents are hypotenuses 

 and perpendiculars to a base 10,000,000,000, and the cosecants and cotangents are hypo- 

 tenuses and bases to a perpendicular 10,009,000,000. The object Eheticus had in view 

 was to calculate the ratios of each pair of the sides of a right-angled triangle. 



