Euclid's Phaenomena

Phaenomena is a work by Euclid on spherical astronomy. The book is divided into 18 propositions, each dealing with "the important arcs on the celestial sphere". The book was fully translated into English in 1996, authors used two surviving copies for translation.^[1]^[2]

Translations

Latin

Euclidis Phaenomena, published in Romæ, 1591

English

Berggren, J. L.; Thomas, R. S. D. (2006). Euclid's phaenomena: a translation and study of a hellenistic treatise in spherical astronomy (PDF). Providence, RI: American Mathematical Society [u.a.] ISBN 0-8218-4072-X. Retrieved 13 March 2024.

References

^ "Euclid's Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy . Euclid, J. L. Berggren, R. S. D. Thomas". Isis. 88 (3): 528–529. September 1997. doi:10.1086/383789.
^ Gouvêa, Fernando Q. "Euclid's Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy | Mathematical Association of America". maa.org. Retrieved 13 March 2024.

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
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