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

admit affirmative algebra alternative appears applied arithmetic assertion assumed assumption axiom called circle cloth commensurable common measure Consequently consider consideration contained continued curve define definition demonstration difficulty divided Edition equal Euclid evident exceed exists falls Fifth follows four fourth fraction geometry give given granted greater half Hence idea incommensurable infinite number insert instance kind latter length less lies limit magnitude manner mathematical mean proportionals method multiple scale multiples namely nearly never notion parallels points possible postulates preceding present Prop proposition proved quantities question ratio reason relation relative remain represent result right angles scale sense shew shewn side square straight line student subdivision sufficiently suppose symbols taken theorem thing third true V₁ values whence whole numbers yard