The Contents of the Fifth and Sixth Books of EuclidFirst published in 1908 as the second edition of a 1900 original, this book explains the content of the fifth and sixth books of Euclid's Elements, which are primarily concerned with ratio and magnitudes. Hill furnishes the text with copious diagrams to illustrate key points of Euclidian reasoning. This book will be of value to anyone with an interest in the history of education. |
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ABCD angles reciprocally proportional Archimedes Axiom Axiom of Archimedes B=rQ B₁ B₁C₁ B₂C₂ bisected BLNO BÔA CÂD Cantor-Dedekind Axiom centre commensurable common measure Commutative Law compounded corresponding sides cross-ratio diagonal duplicate ratio EFGH ENUNCIATION Euclid's EXAMPLE Fifth Book four harmonic points four straight lines greater greatest number hypotenuse incommensurable magnitudes integer irrational number kind least number lower class mean proportional middle point P₁ P₂ parallel to BC parallelogram points of division possible PQRST PROPOSITION rA rB radical axis ratio of equality rational fraction rational numbers rect rectangle contained rectilineal figure required to prove respectively equal right angle segments similar figures similar triangles similarly described squares described system of rational THEORY OF RATIO three magnitudes triangle ABC triangle are respectively triangles are similar upper class vertex