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# Notes on Euclid

a Give three specific examples that the work does not meet modern standards of rigorEuclid made many tacit assumptions in this work that by todays standards would not e sufficient to prove the things he proved 3 of those assumptions areThe existence of points lines etcThe uniqueness of a line between two pointsIf a circle has one point inside and one point outside of another circle it intersects the circle at two different pointsb What are three substantial positive aspects of the work that helped it be a very important book of mathematics for 2000 yearsIt gathered a lot of important information into one collectionIt was well organizedThe postulates were chosen wisely so that other axioms could easily be formed using the postulates3 The ancient Greeks were particularly interested in three straight edge and compass constructions problemsa Describe the trisection of an angle problemThey looked for a way to split an angle into 3 equal parts using only a straight edge and a compass because since bisecting an angle in this way is so easy they assumed trisecting it would be too They were able to trisect a right angle however they were not able to successfully trisect other angles b indicated a solution to the trisection problem that involves more than a straight edge and compass no proof is requiredThis proof said that if you measured the radius of the semi-circle and drew it from point A so that it hits the circle at point B and then continued it to hit the line extended from the diameter at point C the angle alpha would be one third theta This used a straight edge however it broke Platos rule because it required marking off the straight edge which Plato said is not allowed c Indicated a part of your answer to part that means that the solution fails to be a straight edge and compass constructionOne uses a straight edge and compass

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