Geometric Proof (QED)
Every Greek proof followed one fixed script — state it, draw it, build it, argue it — and sealed it with 'which was to be proved.'
Greek geometry turned the proof into a fixed literary form: state the proposition, set out the figure, make the needed construction, advance the argument, and close with 'that which was to be demonstrated' (in Latin, quod erat demonstrandum, or QED) — or, for a construction, 'that which was to be done.' Euclid of Alexandria (c. 300 BCE) is the great exemplar, but the formula and structure were shared across Greek mathematicians such as Archimedes and Apollonius. This template set the public standard of mathematical rigor for two thousand years.
How it traveled
- FragmentaAlexandria · -300explains
- DataAlexandria · -265explains
- OpticaAlexandria · -265explains
- Data (demonstrationes alterae)Alexandria · -265explains
- Catoptrica (recensio Theonis?)Alexandria · -265explains
- PhaenomenaAlexandria · -265explains
- Liber assumptorumSyracuse (Sicily) · -240explains
- De sphaera et cylindroSyracuse (Sicily) · -212explains
- De lineis spiralibusSyracuse (Sicily) · -212explains
- De conoidibus et sphaeroidibusSyracuse (Sicily) · -212explains
- Quadratura parabolaeSyracuse (Sicily) · -212explains
- Ad Eratosthenem methodusSyracuse (Sicily) · -212explains
- De planorum aequilibriisSyracuse (Sicily) · -212explains
- De corporibus fluitantibusSyracuse (Sicily) · -212explains
- Dimensio circuliSyracuse (Sicily) · -212applies
- Opticorum recensio TheonisAlexandria · 370explains
- SynagogeAlexandriaexplains
- Syntaxis mathematicaAlexandriaexplains
- MetricaAlexandriaexplains
- Scholia in Euclidis Data—explains
- Commentarii in libros de sphaera et cylindroAlexandriaexplains
- ConicaPergaexplains
- Scholia in opticorum recensionem Theonis (scholia vetera)—explains
- De magnitudinibus et distantiis solis et lunaeSamosexplains
- Scholia in Euclidis optica (scholia vetera)—explains
- Scholia in Euclidis catoptrica (scholia vetera)—explains
- Scholia in Euclidis phaenomena—explains
- De utilitate mathematicaeSmyrnaapplies
- Commentarius in libros de planorum aequilibriisAlexandriaexplains
Key passages(20)
De conoidibus et sphaeroidibus · Archimedes
Syntaxis mathematica · Claudius Ptolemaeus
Opticorum recensio Theonis · Theon of Alexandria
Scholia in opticorum recensionem Theonis (scholia vetera) · Scholia in Euclidem
De conoidibus et sphaeroidibus · Archimedes
De conoidibus et sphaeroidibus · Archimedes
De corporibus fluitantibus · Archimedes