Introduction and books 1,2The University Press, 1908  Mathematics, Greek 
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Review: The Thirteen Books of the Elements, Vol. 1 (The Elements #1)
User Review  Kellie  GoodreadsI read this, "proved" most of the propositions, and understood about 1/3 of it. Read full review
Review: The Thirteen Books of the Elements, Vol. 1 (The Elements #1)
User Review  GoodreadsI read this, "proved" most of the propositions, and understood about 1/3 of it. Read full review
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anNairizi angle ABC angle BAC angles equal Apollonius Arabic Archimedes Aristotle assumed axiom base BC bisects Book Campanus centre circle circumference coincide commentary Common Notion congruent construction curve definition diameter distance drawn edition Elements enunciation equilateral triangle Eucl Euclid Euclid's Elements Eudemus Eutocius figure Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interior angles interpolated intersection joined lemma length less Let ABC magnitude means meet method observes Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proof proposition proved Pythagoras Pythagorean quadrilateral quoted rectangle contained reductio ad absurdum reference remaining angle respectively Riemann hypothesis right angles rightangled triangle says Schol scholia segment Simplicius solid square suppose surface Suter Theon theorem things three angles translation triangle ABC words
Popular passages
Page 402  AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 218  After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 307  If two triangles have two sides of the one equal to two sides of the...
Page 202  That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 218  In any triangle, the sum of the three angles is equal to two right angles, or 180°.
Page 176  A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
Page 181  When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Page 315  Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 190  Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
Page 259  Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.