Class 2/1/12 - Reading 3.3

Salut mes amants des maths!

Autre jour, autre blog! (Another day, another blog)

Today we went over the several of the propositions from Book II of Euclid's Elements. He gave us a handout with explanations of some of these to serve as an additional resource to the book. His comments during lecture as well as the handout helped us to understand the modern interpretation of each of the propositions as well as their geometric representations.

Proposition II-1: If there are two straight lines, and one of the them is cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the sum of the rectangles contained by the uncut straight line and each of the segments.

Proposition II-5: If a straight line is cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the striaght line btween the points of secftion is equal to the square on the half.

Modern Interpretation:
(b-x)x + (b/2 - x)^2 = (b/2)^2




Proposition II-6: If a straight line is bisected and a straight line is added to it, the rectangle contained by the whole with the added straight line and the added straight line together with the square on the half is equal to the square on the straight line made up of the half and the added straight line. 

Modern Interpretation:
(b+x)x + (b/2)^2 = (b/2 + x)^2

Proposition II-11: To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment.

Modern Interpretation: a (a-x) = x^2  OR x^2+ax = a^2  => x = sqrt((a/2)^2 + a^2 - (a/2))





Dr. Daddel ended class by giving us more information about the material that would be covered on the first exam such as certain propositions in Book 2 in addition to those shown above. I'm so nervous about this test!

Until next time, mes amis!

Bisous!
-MB