# Abstract

The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus that was noted and named by G.W. Leibniz.

## Introduction

The **praeclarum theorema**, or *splendid theorem*, is a theorem of propositional calculus that was noted and named by G.W. Leibniz, who stated and proved it in the following manner:

If

aisbanddisc, thenadwill bebc.This is a fine theorem, which is proved in this way:

aisb, thereforeadisbd(by what precedes),

disc, thereforebdisbc(again by what precedes),

adisbd, andbdisbc, thereforeadisbc. Q.E.D.(Leibniz,

Logical Papers, p. 41).

Expressed in contemporary logical notation, the praeclarum theorema (PT) may be written as follows:

Representing propositions in the language of logical graphs, and operating under the existential interpretation, the praeclarum theorema is expressed by means of the following formal equivalence or logical equation:

(1) |

And here’s a neat proof of that nice theorem:

(2) |

## References

- Leibniz, Gottfried W. (1679–1686 ?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966),
*Leibniz : Logical Papers*, Oxford University Press, London, UK.

## Readings

- Awbrey, Jon — Propositional Equation Reasoning Systems
- Sowa, John F. — Peirce’s Rules of Inference

## Resources

- Logical Graph @ MyWikiBiz
- Praeclarum Theorema @ PlanetMath
- Dau, Frithjof — Computer Animated Proof of Leibniz’s Praeclarum Theorema
- Megill, Norman — Praeclarum Theorema @ Metamath Proof Explorer