The author in question is
Carl Christian Bruhns (1830-1881)
The first edition referred to above was published in 1870:
[1] (in German)
"Neues logarithmisch-trigonometrisches Handbuch auf sieben Decimalen",
bearbeitet von Dr. C. Bruhns, Leipzig: B. Tauchnitz, 1870.
[2] (in English)
"A new manual of logarithms to seven places of decimals", edited by
Dr. Bruhns, Sterotype edition, Leipzig: B. Tauchnitz, 1870.
[3] (in Italian)
"Nuovo manuale logaritmico-trigonometrico con sette decimali", opera
del Dre. C. Bruhns, Ed. stereotipa, Lipsia: B. Tauchnitz, 1870.
Julio Gonzalez Cabillon