Euclid defines the angle as an inclination of lines...he meant halflines, because otherwise he would not be able to distinguish adjacent angles from each other... Euclid does not know zero angles, nor straight and bigger than straight angles...Euclid takes the liberty of adding angles beyond two and even four right angles; the result cannot be angles according to the original definitions...Nevertheless one feels that Euclid's angle concept is consistent.
Hans FreudenthalRelated topics
able angle beyond concept euclid four liberty mean nor result right straight zero feelsRelated quotes
The history of medicine proves that in so far as man seeks to know himself and face his whole nature, he has become free from bewildered fear, despondent shame, or arrant hypocrisy. As long as sex is dealt with in the current confusion of ignorance and sophistication, denial and indulgence, suppression and stimulation, punishment and exploitation, secrecy and display, it will be associated with a duplicity and indecency that lead neither to intellectual honesty nor human dignity.
Alfred Kinsey
Unbelievers, those who believe with difficulty, or believe in part, are those who do not show their faith through works. Apart from works the demons also believe (cf. Jms. 2:19) and confess Christ to be God and Master. 'We know Who You are' (Mk. 1:24), they say, 'You are the Son of God' (Mt. 8:29), and elsewhere, 'These men are the servants of the Most High God' (Acts 16:17). Yet such faith will not benefit the demons, nor even humans. This faith is of no use, for it is dead.
Symeon the New Theologian
Let no one out of laziness or continuous worldly occupations miss these holy Sunday gatherings, which God Himself handed down to us, lest he be justly abandoned by God... If you are detained and do not attend on one occasion, make up for it the next time, bringing yourself to Christ's Church. Otherwise you may remain uncured, suffering from unbelief in your soul because of deeds or words, and failing to approach Christ's surgery to receive... holy healing.
Gregory Palamas
The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. ...Simplicius.
Morris Kline
The inhabitants of the ceded territory shall be incorporated in the Union of the United States, and admitted as soon as possible, according to the principles of the Federal constitution, to the enjoyment of all the rights, advantages, and immunities, of citizens of the United States; and, in the mean time, they shall be maintained and protected in the free enjoyment of their liberty, property, and the religion which they profess.
Thomas Jefferson