The Contents of the Fifth and Sixth Books of Euclid (with a Note on Irrational Numbers) Arranged and Explained |
Contents
SECTION II | 12 |
To divide a finite segment of a straight line into any number of equal parts | 19 |
If all values of r s which make rAsB also make rCsD and if all values | 29 |
If from any vertex of a triangle a perpendicular be drawn to the opposite side | 103 |
SECTION X | 110 |
BX | 117 |
If three magnitudes be in proportion the first has to the third the duplicate ratio | 141 |
Common terms and phrases
ABCD angles reciprocally proportional Archimedes Axiom Axiom of Archimedes B₁ bisected BLNO Cantor-Dedekind Axiom centre commensurable common measure Commutative Law compounded construction corresponding sides cross-ratio diagonal divided duplicate ratio EFGH ENUNCIATION Euclid's EXAMPLE Fifth Book Fifth Definition follows four harmonic points four straight lines given 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 proof PROPOSITION rA rB radical axis ratio of equality rational fraction rational numbers rect rectangle contained required to prove respectively equal right angle segments Seventh Definition similar figures similar triangles similarly described Sixth Book squares described system of rational three magnitudes triangle ABC triangle are respectively triangles are similar upper class vertex