Exhibit Guide Navigation

Philip van Lansbergen, In astrolabium introductorio (Middelburg, 1635)

Introduction to the Astrolabe

Astronomers use astrolabes for dozens of astronomical operations including telling time by the Sun or stars and determining the positions of planets.

This introduction to the astrolabe contains a striking, full-size, detailed design for an astrolabe, representing both the climate and the rete in fold-out plates.

Lansbergen, a Dutch Calvinist theologian, pastor, mathematician and astronomer, is perhaps best known for his astronomical tables published in 1632, the year of his death. He also published in 1620 (Dutch) and in 1630 (Latin) a popular work promoting the heliocentric system and refuting objections based on biblical interpretations. The frontispiece of his collected works (1663) displays a diagram of the Earth revolving around the Sun alongside portraits of celebrated astronomers including Copernicus and Tycho Brahe. 

Lansbergen responded to Tycho’s argument about star sizes (explained in the gallery on the Controversy over the Comets). Tycho argued that if the Copernican system were true, one must accept the implication that stars are unlike the Sun, for even an ordinary star would be the size of the Earth’s orbit, and bright stars would be as large as the dimensions for Tycho’s entire universe. Lansbergen agreed, pointing to the vast sizes of stars as an expression of divine omnipotence and wisdom.

Galileo's World Exhibition Location

Source: History of Science Collections

Section: Observational Astronomy

Section Number: 6

Object Number: 28

Subject Area(s): Astronomy, Mathematics, Scientific Instruments

Time Period: 17th Century

Region(s): Europe, Netherlands

Click any Image for a larger version

Exhibit Gallery OERs

Coma Berenices Learning Leaflet

Coma Berenices Learning Leaflet

Coma Berenices is the only one of the modern 88 official constellations named after a historical figure. It represents the hair of Berenice, Queen of Egypt (267 221 BCE), who reigned with Ptolemy III Euergetes. Learn more about this in this learning leaflet.


Discorso particolare intorno all'unisono

Vincenzo Musical Score

Vincenzo Galilei was among the first music theorists to advocate for a new system of tuning based on performance, instead of the mathematical principles of music set fourth by Pythagoras. Pythagorean music theory bases pitch on the mathematical proportions of dividing a string. Vincenzo's primary problem with this system is that, although it is great for the mathematician and the music theorist, it is impractical for the performer. All music based on this particular system of tuning would inevitably sound out of tune and unpleasant. In this learning leaflet learn about the tuning systems in the late-Renaissance period.


Pythagorean Solids: Five Regular Solids

Pythagorean Solids Learning Leaflet

Can you identify the five regular solids? 

Throughout history the regular solids were studied with keen interest by astronomers, mathematicians, artists, architects and philosophers. The Pythagoreans proved that there are only five regular solids: the cube, triangle, octahedron, dodecahedron, and icosahedron. 


Johann Kepler: Blueprints of the Universe

Kepler-Blueprints Learning Leaflet

Is there a mathematical basis of the universe? 

Johann Kepler's "Mystery of the Universe" is one of the brilliant illustrations in the history of astronomy. Kepler used the five regular Pythagorean solids to refute the major objections to Copernicanism. In this work he demonstrated that vast empty regions lying between the planetary spheres, which were required by Copernicus, were not wasted space. Rather, these gaps perfectly matched, within the limits of observational error, the geometry of the 5 regular Pythagorean solids. 


Astronomy & Music: Introduction to the Duochord

Duochord Learning Leaflet

Can you identify simple musical intervals? 

The ancient Pythagoreans envisioned the heavens as a musical scale, comprised of celestial spheres rotating according to harmonious music. For Robert Fludd, a seventeenth-century physician, the universe was a monochord, its physical structure unintelligible without an understanding of music. In this activity, explore the relationship between mathematics, astronomy, and music.