This illustration is the first page of Peter Apian's Instrument Book published in 1533 in Ingolstadt, which is a town in Germany. Germany was the leading place for making mathematical instruments in the 16th century.
The illustration is very well drawn. It shows several different types of mathematical instruments which all work by measuring angles. The drawing is supposed to show how useful a mathematical principle like measuring angles is to solving many different problems.
On the right a man is using a 'nocturnal' (the round instrument with a pointer that he is holding up) to determine the time at night. This is done by measuring the angle of rotation around the pole star of the constellation Ursa Major or The Plough. The two in the middle are using different types of quadrant to tell the time from the angle of the sun above the horizon. The man in the middle in the background is using a simple instrument called a 'Jacob's staff' to measure the width of a building, from the angle between its corners (using the principle of similar triangles). Finally, the person on the left is measuring the angle between two stars using the oldest mathematical instrument ever invented: the fingers on our own hands!
The mathematical theme of the picture is emphasised by two huge imaginary mathematical shapes in the front. One is made out of sides with pentagons and is called a regular Dodecahedron. The other has sides made out of equilateral triangles and is called a regular Icosahedron.
Peter Apian's Instrument Book was the first printed book ever to be sold about different types of mathematical instruments. It came out only about fifty years after printing had been invented. Apian was born in 1496 in Saxony, which is in Germany. He died in 1552. He studied mathematics and astronomy in Leipzig in Germany. From 1527 to 1552 he was Professor of Mathematics in Ingolstadt, where his Instrument Book was published.
Apian printed many important maths books on his own printing presses. Printing books was very expensive in the 16th century so Apian raised money from rich patrons to pay for them. Many of his maths books are dedicated to important people, such as archbishops, who wanted to show how intelligent they were by having their names put in books about maths.
Apian's most famous mathematical book is a book about astronomy called the Astronomicum Caesareum which means 'astronomy fit for a king'. This was published in 1540 and was dedicated to the Holy Roman Emperor, Charles V, who was the most important person in Europe in the 16th century. The book cost an enormous amount of money and is completely amazing to see. It contains lots of paper models of mathematical instruments made out of cut-out pieces of paper tied together with string. These paper instruments can actually be made to work by rotating their dials. Copies of the Astronomicum Caesareum are very rare so recently a modern copy was made. Unfortunately, whoever was in charge of making the paper instruments for the modern copy put the pieces for the instruments together in the wrong order so they didn't work. Separate instructions had to be printed to tell people how to take the book apart and put it together again so that the instruments worked properly!
Charles V was so impressed with the maths books that Apian published that he rewarded him by making him the official Royal Mathematician.