the first book of euclid's elements with a commentary

ABC is equal ABCD adjacent angles alternate angles Anaritius angle ACD angle BAC angles ABC angles equal Axioms base BC bisected centre circle constructed definition demonstration distance drawn Elementist elliptic hypothesis enunciation equal angles equal in area equal straight lines equal to BC equilateral Euclid Euclid's Theorem Euclidean Geometry Eudemus fifth Postulate Geminus given rectilinear angle given straight line gram homogeneous space hyperbolic geometry hyperbolic hypothesis infinite inner and opposite inner angles intersect joined Lemma length less Let ABC magnitude method non-secant obtuse opposite angles outer angle parabolic geometry parabolic hypothesis parallel parallelogram plane polygon present Theorem Proclus produced proof PROP Proposition proved Ptolemy rectilinear figure remaining angles right angles right gram side equal square straight angle straight line BC straight line falling surface triangle ABC triangle DEF καὶ Οπερ ἔδει δεῖξαι