Character Catalog

A treatise in 13 books covering plane geometry, the theory of proportions, arithmetic, and solid geometry. It is the most influential mathematical work in history, serving as the foundation of geometry education for over 2,000 years.

A companion to the Elements dealing with what can be deduced as 'given' from hypotheses. This work is essential for solving geometric problems.

The earliest known treatise on perspective and geometric optics. Euclid studies vision by modeling light rays as straight lines emanating from the eye.

An astronomy treatise applying spherical geometry to the study of the celestial vault. It addresses the rising and setting of stars.

A work on dividing geometric figures into equal parts or according to given ratios. The original Greek text is lost, but a partial Arabic translation survives.

A treatise on conic sections (ellipse, parabola, hyperbola), now lost. It was superseded by the more comprehensive treatise on the same subject by Apollonius of Perga.

Let it be required to draw a straight line from any point to any point. That a point is that of which there is no part. That a line is a length without breadth.

This scholar lived under the first Ptolemy, for Archimedes, who came immediately after the first Ptolemy, mentions Euclid. It is also reported that Ptolemy asked him whether there was not a shorter way than the Elements, and that he replied that there is no royal road to geometry.

If given magnitudes are added to given magnitudes, the wholes are also given in magnitude.

Someone who had begun to study geometry with Euclid, after learning the first proposition, asked: 'What profit shall I gain from these things?' Euclid called his slave and said: 'Give him three obols, since he must profit from what he learns.'

City where Euclid lived and taught, intellectual capital of the Hellenistic world. He wrote the Elements there, most likely within the Mouseion founded by Ptolemy I.

Major cultural and scientific institution where Euclid most likely taught. It housed hundreds of thousands of papyrus scrolls.

Euclid is said to have studied at Plato's Academy in Athens before settling in Alexandria. The Elements belong to the Platonic mathematical tradition.

Greek city in Sicily where Archimedes lived, the most celebrated heir of the Euclidean tradition. Syracuse maintained close intellectual ties with Alexandria.

A everyday writing instrument used by Euclid and his students to draw geometric figures and take notes during lessons.

The two fundamental instruments of Euclidean geometry, the only tools permitted for the constructions described in the Elements.

The writing medium on which the Elements were composed and disseminated. Papyrus, manufactured in Egypt, was the primary carrier of knowledge in Alexandria.

A vertical rod whose cast shadow allowed the height of the sun to be measured. Euclid refers to it in his treatise on optics.

An astronomical model representing the celestial circles. Euclid took an interest in astronomy in his Phaenomena, where he studies the geometry of the celestial sphere.

A counting board used in the Greek world to perform arithmetic operations, as a complement to geometric reasoning.