389 
without success to find something beyond what is quoted above 
about the table; but the hope is there expressed that, consider- » 
ing the attention so large a work must have received from 
contemporary mathematicians, some information might still be 
gained with regard to the calculator of the table, his objects, 
&e. . 
I recently found a correspondence of six letters between 
Herwart and Kepler, which took place at the end of 1608, with 
regard to the table, and which throws light upon these points. 
The letters are printed in Dr Frisch’s ‘Joannis Kepleri As- 
tronomi opera omnia’ (t. iv. pt. II. pp. 527—530, 1863). 
In the first letter, dated September 13, 1608, Herwart 
writes, “Ich hab bisher in Multiplicatione et Divisione sonder- 
bare geschriebene praxin gebraucht, dadureh ich den numerum 
ex quavis multiplicatione productum, per solam additionem, 
und den Quotienten ex divisione resultantem per solam sub- 
tractionem (absque tediosa multiplicationnm et divisionum 
operatione) gefunden.” He states that J. Preetorius and others 
who have seen it recommend him to have it printed, and he 
adds that if he had not had this method, on account of his 
continual occupations and because he is not a good calculator, 
he should long ago have had to give up all mathematics that 
required calculation. He sends a specimen page of the table, 
the use of which he explains, and he prays Kepler to give him 
his opinion on the matter without delay. 
Kepler replies on October 18, 1608, and remarks that 1000 
pages will make a large volume, which the computer will often 
not have at hand. He suggests that short precepts on the 
solution of triangles should be added, as Herwart’s table would 
often be preferable to the ‘tpooOadaipeors Vitichiana, which is 
too elaborate to be retained in the memory, confuses sines and 
their complements, &c. Besides, the reasons for the operations 
are hidden in work, “At si multiplicemus et dividamus simpli- 
citer, tunc videmus quid agamus; et possunt varietates trian- 
