Johann Zahn, in his Oculus Artificialis Teledioptricus (1685-1686), described and figured two forms of portable box cameras with lenses.
In the same year Vlacq published at Gouda his Trigonometria artificialis, giving log sines and tangents to every ro seconds of the quadrant to ro places.
The calculation of the logarithms not only of numbers but also of the trigonometrical functions is therefore due to Briggs and Vlacq; and the results contained in their four fundamental works - A rithmetica logarithmica (Briggs), 1624; Arithmetica logarithmica (Vlacq), 1628; Trigonometria Britannica (Briggs), 1633; Trigonometria artificialis (Vlacq), 1633 - have not been superseded by any subsequent calculations.
In 1794 Vega published his Thesaurus logarithmorum completus, a folio volume containing a reprint of the logarithms of numbers from Vlacq's Arithmetica logarithmica of 1628, and Trigonometria artificialis of 1633.
The next great advance on the Trigonometria artificialis took place more than a century and a half afterwards, when Michael Taylor published in 1792 his seven-decimal table of log sines and tangents to every second of the quadrant; it was calculated by interpolation from the Trigonometria to 10 places and then contracted to 7.
- In law, a day may be either a dies naturalis or natural day, or a dies artificialis or artificial day.