The Axiomatic-Deductive Method
Start from a tiny list of agreed-upon truths, smuggle in nothing else, and prove an entire science from there.
The axiomatic-deductive method starts with a handful of building blocks: explicit definitions, a few unproved postulates, and self-evident 'common notions.' From these alone, every later theorem follows by strict logical proof, with nothing slipped in along the way. Euclid of Alexandria (c. 300 BCE) gave the method its classic form in the Elements, drawing on earlier Greek geometry and on Aristotle's account of demonstrative science. It went on to become the template for rigorous reasoning far beyond mathematics: Spinoza, Newton, and modern logic all echo its 'from first principles' design.
How it traveled
- FragmentaAlexandria · -300explains
- DataAlexandria · -265explains
- OpticaAlexandria · -265explains
- Data (demonstrationes alterae)Alexandria · -265explains
- Catoptrica (recensio Theonis?)Alexandria · -265explains
- PhaenomenaAlexandria · -265explains
- Sectio canonis [Sp.]Alexandria · -265explains
- Phaenomena (demonstrationes alterae recensionis b)Alexandria · -265explains
- Liber assumptorumSyracuse (Sicily) · -240explains
- De sphaera et cylindroSyracuse (Sicily) · -212explains
- De conoidibus et sphaeroidibusSyracuse (Sicily) · -212explains
- De lineis spiralibusSyracuse (Sicily) · -212explains
- Quadratura parabolaeSyracuse (Sicily) · -212explains
- De planorum aequilibriisSyracuse (Sicily) · -212explains
- Ad Eratosthenem methodusSyracuse (Sicily) · -212explains
- De corporibus fluitantibusSyracuse (Sicily) · -212explains
- Dimensio circuliSyracuse (Sicily) · -212explains
- Opticorum recensio TheonisAlexandria · 370explains
- SynagogeAlexandriaexplains
- MetricaAlexandriaexplains
- Scholia in Euclidis Data—explains
- Syntaxis mathematicaAlexandriaexplains
- Commentarii in libros de sphaera et cylindroAlexandriaexplains
- ConicaPergaexplains
- Scholia in opticorum recensionem Theonis (scholia vetera)—explains
- DioptraAlexandriaexplains
- De magnitudinibus et distantiis solis et lunaeSamosexplains
- Scholia in Euclidis phaenomena—explains
- Scholia in Euclidis optica (scholia vetera)—explains
- Commentarius in dimensionem circuliAlexandriaexplains
Key passages(20)
De conoidibus et sphaeroidibus · Archimedes
De sphaera et cylindro · Archimedes
De sphaera et cylindro · Archimedes
De sphaera et cylindro · Archimedes
De sphaera et cylindro · Archimedes
De magnitudinibus et distantiis solis et lunae · Aristarchus of Samos
Catoptrica (recensio Theonis?) · Pseudo-Euclid
Data (demonstrationes alterae) · Euclid
Data (demonstrationes alterae) · Euclid
Data (demonstrationes alterae) · Euclid
Data (demonstrationes alterae) · Euclid
Data (demonstrationes alterae) · Euclid
Data (demonstrationes alterae) · Euclid