This
is rather a rare book, with copies surviving in the Herzog August Bibliothek at
Wolfenbüttel and in the Würtembergische
Landesbibliothek at Stuttgart, and an (incomplete?) copy at the University of
Uppsala. It consists of 110 small
copper plates engraved by Andreae and a brief accompanying text.
The plates illustrate the material covered in a mathematical seminar,
divided into 11 sections as follows:
Geometry:
plates 1-10. "The
authority of geometry among the sciences is so great that Plato would scarcely
allow anyone who was ignorant of it into his Academy. It measures everything and it examines everything..."
Andreae's sources are cited as Euclid, Christoph Clavius and Adrian
Metius. Pl. 9 includes a diagram of 'squaring the circle' which tries to show
that a square whose side is 75 units is equal in area to a circle whose diameter
is the square root of the sum of the squares of 75, 39 and 4.
Arithmetic:
plates 11-20. "Arithmetic
is the sister of Geometry, no less admirable ... and doing with numbers what
Geometry does with lines." Andreae suggests that Arithmetic may be more
profound than Geometry since "our Creator placed many of his secrets in
it." His sources are Michael
Stifelius, Simon Jacob, Georg Reinhold and (for music) Jo. Lippius. Includes
some algebra ('the cossic art') and music; Pascal's triangle; series of
triangular, square etc numbers; the diameter, circumference and volume of the
earth. Pl. 19 shows a 'player piano' sheet of parchment to operate a
mechanical organ, and Pl.20 the relative lengths of organ pipes.
Statics: plates 21-30. The third sister (Number, Measure and Weight), of whom
"Archimedes said he could move the earth itself if he were given a fixed
place." Sources include Jerome
Cardan, Walter Rivius and Giovanni Battista della Porta..
Includes wheels, cogs, screws and pulleys;
inclined planes; a
treadmill-powered crane; syphons,
vacuum experiments; methods of
raising water, including chain of buckets and a pump;
principle of leverage in horse bits, presumably to illustrate the
proposition that 'statics' enables us to make use of the forces of nature and
control animals.
Astronomy:
plates 31-40. 'Evidently the
Queen of the sciences, which opens up the heavens to us'.
Andreae cites Maestlin (under whom he studied, as did his friend Kepler),
Röslin, Copernicus, Johann Bayer, and Haffenreffer (a family friend and
tutor at Tübingen) as his sources for diagrams to illustrate ancient and modern
views on the solar system, including the models of Copernicus, Röslin,
Brahe and Baer; stars of 1st and
2nd magnitude in Northern and Southern hemispheres;
equipment such as astrolabes and armillary spheres.
Pl.36 shows astrological correspondences with parts of the human body,
areas of the face and palm, and times of the day/week, and includes a horoscope
for the birth of Andreae himself, who states that he does not vouch for the
validity of this material - it is up to the reader to make his own judgement.
Sundials: plates 41-50. 'Gnomics' for which his authorities are Sebastian Munster and
Barth. Scultetus, and 'that most honourable and learned gentleman David Magirus'
(another of Andreae's professors, for whom he later wrote a funeral tribute)
Illustrates the construction and orientation of sundials, including
horizontal models 'which present no difficulty'.
Pl.50 represents the circle of the winds.
Automata:
plates 51-60. These follow
on here since they almost imitate the heavens. They are mainly clock/watch
mechanisms, to be described in German because Latin is unsuitable, provided by
Mattias Lösch. Pl.59 depicts the
mechanism for a pedometer, 'a useful instrument which counts ones steps
automatically' and the next plate depicts a perpetual calendar. 
'Optics':
plates 61-70. The heading is misleading to modern readers, for this is
mainly a treatment of perspective drawing, particularly in its application to
architectural subjects such as archways, staircases, roofs, colonades etc.
mainly taken from Sebastiano Serlio. The
final plate is a plan and perspective elevation of an abbey or monastery.
Architecture:
plates 71-80. Depicts the
classical columns (Tuscan, Doric, Ionic, Corinthian, Composite) singly and in
series. Pl.76 copies the plan of Tycho Brahe's observatory at Uraniborg, and the
succeeding plates depict a variety of forms of domestic accommodation, from
a fairly grand house to modest dwellings. Pl.80 illustrates the seven
canonical rectangles, Serlio's method of constructing rafters with wood too
short to bridge the gap, and Serlio's way of making a table 7x4 from one which
is 10x3.
Fortification: plates 81-90. Illustrates a variety of fortifications (triangular, square, etc), fortified houses, bastions, a fortified town with citadel, and (pl.89) a trace of Speckle's 'ideal fortification'. Pl.90 shows arrangements of an army on the march.
Misc.
I (no heading): plates 91-100. pls.91-2
deal with distances between locations in Germany, and 93-5 concern the
conversions of local measures of length and mass. Pls. 96-97 reproduce Cesariano's 'Vitruvian man' with the
addition of a loincloth (Cesariano's original appears to depict the ideal man
with an erection!), and link the human measurements with those of Noah's
ark. Pl. 100 is a chart of
historical correspondences on the assumption that there are six milleniary
cycles.
Misc.
II (no heading): plates 101-110. The
first regular solids and their dissection;
various ovals and ovoids, spirals and projections of columns;
pl.110 is a maze to illustrate the errors of human life.
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