Planisphaerium

The Planisphaerium is a work by Ptolemy. The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties of circles.

Publication

Originally written in Ancient Greek, Planisphaerium was one of many scientific works which survived from antiquity in Arabic translation. One reason why Planisphaerium attracted interest was that stereographic projection was the mathematical basis of the plane astrolabe, an instrument which was widely used in the medieval Islamic world. In the 12th century the work was translated from Arabic into Latin by Herman of Carinthia, who also translated commentaries by Maslamah Ibn Ahmad al-Majriti. The oldest known translation is in Arabic done by an unknown scholar as part of the Translation Movement in Baghdad.^[1]

Planisphere

The word planisphere (Latin planisphaerium) was originally used in the second century by Ptolemy to describe the representation of a spherical Earth by a map drawn in the plane. ^[2]

Planisphere

Editions and translations

Commandino, Federico, ed. (1558). Ptolemaei Planisphaerium. Iordani Planisphaerium. Federici Commandini Vrbinatis in Ptolemaei Planisphaerium commentarius (in Latin). Venice: Paulus Manutius.

References

^ Sidoli, Nathan; J. L. Berggren (2007). "The Arabic version of Ptolemy's Planisphere or Flattening the Surface of the Sphere: Text, Translation, Commentary" (PDF). Sciamvs. 37. 8 (139).
^ Journal of the British Astronomical Association yr:1995 pg:35

External links

"Ptolemy on Astrolabes"

Ancient Greek mathematics

Mathematicians
(timeline)

Treatises

Almagest
Archimedes Palimpsest
Arithmetica
Conics (Apollonius)
Catoptrics
Data (Euclid)
Elements (Euclid)
Measurement of a Circle
On Conoids and Spheroids
On the Sizes and Distances (Aristarchus)
On Sizes and Distances (Hipparchus)
On the Moving Sphere (Autolycus)
Optics (Euclid)
On Spirals
On the Sphere and Cylinder
Ostomachion
Planisphaerium
Spherics (Theodosius)
Spherics (Menelaus)
The Quadrature of the Parabola
The Sand Reckoner

Problems

Concepts
and definitions

Angle
- Central
- Inscribed
Axiomatic system
- Axiom
Chord
Circles of Apollonius
- Apollonian circles
- Apollonian gasket
Circumscribed circle
Commensurability
Diophantine equation
Doctrine of proportionality
Euclidean geometry
Golden ratio
Greek numerals
Incircle and excircles of a triangle
Method of exhaustion
Parallel postulate
Platonic solid
Lune of Hippocrates
Quadratrix of Hippias
Regular polygon
Straightedge and compass construction
Triangle center

Results

In Elements	Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem of the gnomon
Apollonius	Apollonius's theorem
Other	Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Law of sines Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Ancient Greek astronomy Attic numerals Greek numerals Latin translations of the 12th century Non-Euclidean geometry Philosophy of mathematics Neusis construction
History of	A History of Greek Mathematics by Thomas Heath algebra timeline arithmetic timeline calculus timeline geometry timeline logic timeline mathematics timeline numbers prehistoric counting numeral systems list
Other cultures	Arabian/Islamic Babylonian Chinese Egyptian Incan Indian Japanese