On Conoids and Spheroids

Work by Archimedes

On Conoids and Spheroids (Ancient Greek: Περὶ κωνοειδέων καὶ σφαιροειδέων) is a surviving work by the Greek mathematician and engineer Archimedes (c. 287 BC – c. 212 BC). Consisting of 32 propositions, the work explores properties of and theorems related to the solids generated by revolution of conic sections about their axes, including paraboloids, hyperboloids, and spheroids.^[1] The principal result of the work is comparing the volume of any segment cut off by a plane with the volume of a cone with equal base and axis.^[2]

The work is addressed to Dositheus of Pelusium.

Footnotes

^ Coolidge 1945:7
^ Heath, Thomas Little (1911). "Archimedes" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 02 (11th ed.). Cambridge University Press. pp. 368–369, see page 369. (3) On Conoids and Spheroids.....

References

Coolidge, J.L. (1945). A history of the conic sections and quadric surfaces. Dover Publications. ISBN 9780486619125. Retrieved 2018-12-16.

External links

ON CONOIDS AND SPHEROIDS - The Works of Archimedes
Chisholm, Hugh, ed. (1911). "Conoid" . Encyclopædia Britannica. Vol. 06 (11th ed.). Cambridge University Press. p. 964.
Chisholm, Hugh, ed. (1911). "Spheroid" . Encyclopædia Britannica. Vol. 25 (11th ed.). Cambridge University Press. p. 661.

Archimedes

Written works

Discoveries and inventions

Miscellaneous

Related people

Category

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
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