File:4Fold Root Figure 6m.gif
4Fold_Root_Figure_6m.gif (745 × 422 pixels, file size: 38 KB, MIME type: image/gif)
Captions
Captions
Summary
editDescription4Fold Root Figure 6m.gif |
English: screenshot from p.196 of the pdf file download from archive.org, using maximal resolution, 0% saturation, maximal b/w contrast
The diagram is intended as Schopenhauer's proof "by intuition"[1] of (a special case of) the Pythargorean theorem.[2] Using the names from the image annotations, and taking for granted that abd, adf, dfg, bdg, acf, and beg are all congruent triangles which therefore all have the same area,[3] we have ab2 = A(abd)+A(adf)+A(dfg)+A(bdg) = 4*A(abd), while ad2 = A(adf)+A(acf) = 2*A(abd) and bd2 = A(bdg)+A(bge) = 2*A(abd). Notes:
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Source | Djvu file of Arthur Schopenhauer's essay On the Fourfold Root of the Principle of Sufficient Reason at archive.org | |||||||||||||||||
Author |
creator QS:P170,Q38193 |
Licensing
editPublic domainPublic domainfalsefalse |
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This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author's life plus 100 years or fewer. ![]() |
This file has been identified as being free of known restrictions under copyright law, including all related and neighboring rights. |
https://creativecommons.org/publicdomain/mark/1.0/PDMCreative Commons Public Domain Mark 1.0falsefalse
Annotations InfoField | This image is annotated: View the annotations at Commons |
a
b
c
d
e
f
g
Triangle abd
Triangle bdg
Triangle dfg
Triangle adf
Triangle acf
Triangle beg
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current | 14:21, 30 May 2015 | ![]() | 745 × 422 (38 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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