#axioms

The Elements of Euclid - Part 1 As we have seen, Book 1 of Euclid’s Elements lists five Common Notions: axioms that are shared by geometry and several other branches of logic and mathematics. Over the

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the fifth of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish εʹ. Καὶ τὸ ὅλον τοῦ μέρους μεῖζόν [ἐστιν].5. And the whole [is]

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the fourth of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish δʹ. Καὶ τὰ ἐφαρμόζοντα ἐπ ̓ ἀλλήλα ἴσα ἀλλήλοις ἐστίν.4. And things

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the third of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish γʹ. Καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ, τὰ καταλειπόμενά ἐστιν ἴσα.3.

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the second of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish βʹ. Καὶ ἐὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα.2. And if equal

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the first of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish αʹ. Τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα.1. Things equal to the

The Elements of Euclid - Part 1 In Book 1 of the Elements, following the Five Postulates, Euclid states five Common Notions, or Κοιναὶ ἔννοιαι [Koinai ennoiai] (Fitzpatrick 7): GreekEnglish αʹ. Τὰ τῷ αὐτῷ

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 5 reads (Fitzpatrick 7): GreekEnglish εʹ. Καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 4 reads (Fitzpatrick 7): GreekEnglish δʹ. Καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι.4. And that all right-angles are equal

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 3 reads (Fitzpatrick 7): GreekEnglish γʹ. Καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι.3. And to draw a circle with any center

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 2 reads (Fitzpatrick 7): GreekEnglish βʹ. Καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ εὐθείας ἐκβαλεῖν.2. And to produce a finite

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 1 reads (Fitzpatrick 7): GreekEnglish αʹ. ̓Ηιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν.1. Let it have been

[Image 1] Introduction Hey it's a me again @drifter1! Today we continue with Mathematics, and more specifically the branch of "Discrete Mathematics", in order to get into Fields. So, without

[Image 1] Introduction Hey it's a me again @drifter1! Today we continue with Mathematics, and more specifically the branch of "Discrete Mathematics", in order to get into Rings. So, without further

The road to hell is paved with good intentions. This is one of my favourite axioms. Some of the most damaging things have been done with the best of intentions. Many people expect reward for their intention

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William Glasser's Theory of Choice: The only people whose behavior we can control are ourselves. The only thing we can give or receive from others is information. How this information will be used is a

When inquiring into aspects of truth and reality, there are limits to the degree of verification we can employ to trace something back to its roots in the grounding of reality. We can only regress back

While reading @dwinblood's post about the fallacy communism this little fragment got my attention: I am not religious, so when I say "this is evil" it has nothing to do with religion. It has

While editing some of my new videos recently such as my new tutorial on OpenLedger (which you can check out here ... I came across a video I made a few months ago that I never published. This wouldn't