The Connexion of Number and Magnitude: An Attempt to Explain the Fifth Book of Euclid

A₁ abstract number algebra alternative angles are equal arithmetic arithmetic means assumed assumption AUGUSTUS DE MORGAN axiom AXIOMS OF EUCLID Book of Euclid called commensurable common logarithm Consequently contradiction curve descending assertion exceed existence falls short Fifth Book follows fourth proportional geometry give given greater ratio greater than Q greatest common measure Hence idea incommensurable quantities infinite number infinite subdivision infinitum insert length less ratio less than 4B Let us suppose lies mathematical mean proportionals metic metre namely never notion number of points number or fraction P₁ P₂ parallels Pm+1 Pn Pn+1 postulates preceding Prop proposition proved rectangles reductio ad absurdum relative magnitude relative multiple scale result right angles shew shewn side square square root straight line student supposition symbols theorem thing tiple Trigonometry true V₁ V₂ whence whole numbers yard