page_title: Q.E.D.
section_title: Modern philosophy
hierarchical_section_title: Q.E.D. / Modern philosophy
caption_attribution_description: English: A 1604 use of "quod erat demonstrandum". Latin text: 8. Sinus rectus peripheriae, et complementi sui aequepossunt radio. Complementum peripheriae dicimus reliquam datae ad circuli quadrantem. Sit igitur in / praemissa figura, recta EF, sinus rectus peripheriae GE vel BCE: et complementi sui CE sinus rectus / ED, vel aequalis illi AF per trigesimam quartam primi elementorum. Dico AF et EF, aequeposse / radio AE. Nam per penultimam primi Euclidis, in Triangulis rectangulis, quadrata laterum rectum / angulum continentium, aequalia sunt lateri rectum angulum subtendenti. Sed AFE est Triangulum / rectangulum ad F per septimam hujus, crura verò rectum ambientia sunt AF et EF: aequepossunt / ergo radio AE rectum angulum subtendenti; quod erat demonstrandum.
context_page_description: Q.E.D. or QED is an initialism of the Latin phrase "quod erat demonstrandum", literally meaning "what was to be shown". Traditionally, the abbreviation is placed at the end of a mathematical proof or philosophical argument in print publications to indicate that the proof or the argument is complete, and hence is used with the meaning "thus it has been demonstrated".
context_section_description: During the European Renaissance, scholars often wrote in Latin, and phrases such as Q.E.D. were often used to conclude proofs.
  Perhaps the most famous use of Q.E.D. in a philosophical argument is found in the Ethics of Baruch Spinoza, published posthumously in 1677. Written in Latin, it is considered by many to be Spinoza's magnum opus. The style and system of the book are, as Spinoza says, "demonstrated in geometrical order", with axioms and definitions followed by propositions. For Spinoza, this is a considerable improvement over René Descartes's writing style in the Meditations, which follows the form of a diary.
caption: Philippe van Lansberge's 1604 Triangulorum Geometriæ used quod erat demonstrandum to conclude some proofs; others ended with phrases such as sigillatim deinceps demonstrabitur, magnitudo demonstranda est, and other variants.[7]
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