From following 13 books of the Elements, which do you regard as the most importa

Question

From following 13 books of the Elements, which do you regard as the most important? Which are the least? Please justify your answers.

Book1: Euclid's 10 axioms, basic propositions of geometry: the pons asinorum, the Pythagorean theorem, equality of angles and areas, parallelism, the sum of the angles in a triangle and the three cases in which triangles are equal.

Book2 is commonly called the "book of geometric algebra"

Book3 deals with circles and their properties: inscribed angles, tangents, the power of a point, Thales' theorem

Book4: constructs the incircle and circumcircle of a triangle and constructs regular polygons with 4,5,6, and 15 sides

Book5 is a treatise on proportions of magnitudes.

Book6 applies proportions to geometry: similar figures

Book7 deals strictly with elementary number theory: divisibility, prime number, the greatest common divisor, least common multiple

Book8 deals with proportions in number theory and geometric sequences

Book9 applies the results of the preceding two books and gives the infinitude of prime numbers, the sum of a geometirc series, and the construction of even perfect numbers

Book10 attempts to classify incommensurable magnitudes by using the method of exhaustion, a precursor to integration

Book11 Generalizes the results of Books 1-6 to space: perpendicularity, parallelism, volumes of parallelepipeds

Book12 studies volumes of cones, pyramids and sylinders in detail and shows for example that the volume of a cone is a third of the colume of the corresponding cylinder.

Book13 constructs the five regular Platonic solids inscribed in a sphere, calculates the ratio of their edges to the radius of the sphere and proves that there are no further regular solids.

Explanation / Answer

According to me book numbers r 8 as it contains most important part numbers system& geometry

Second highest regards is book number 11 as it is contained almost all basic elements including geometry & very fundamental laws for playing with geometry

& least is book number 5 as it contains treaties of magnitude which was I think basic

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