The Thirteen Books of Euclid's Elements, Tr. from the Text of Heiberg, Volume 1The University Press, 1926 - Mathematics, Greek |
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Page 121
... common notion are the same thing1 . Aristotle discusses the indemonstrable character of the axioms in the Metaphysics . Since " all the demonstrative sciences use the axioms , " the question arises , to what science does their ...
... common notion are the same thing1 . Aristotle discusses the indemonstrable character of the axioms in the Metaphysics . Since " all the demonstrative sciences use the axioms , " the question arises , to what science does their ...
Page 122
... common notion , and without being taught , that the circle is such and such a figure , but , when we are told so , we assent without demonstration . When again what is asserted is both unknown and assumed even without the assent of the ...
... common notion , and without being taught , that the circle is such and such a figure , but , when we are told so , we assent without demonstration . When again what is asserted is both unknown and assumed even without the assent of the ...
Page 123
... common to all investigation which is concerned with quantity and magnitude . Thus it is the geometer who knows that all right angles are equal and how to produce in a straight line any limited straight line , whereas it is a common notion ...
... common to all investigation which is concerned with quantity and magnitude . Thus it is the geometer who knows that all right angles are equal and how to produce in a straight line any limited straight line , whereas it is a common notion ...
Page 124
... common notion . Thus Aristotle's account of an axiom as a principle common to all sciences , which is self - evident , though incapable of proof , agrees sufficiently with the contents of Euclid's common notions as reduced to five in ...
... common notion . Thus Aristotle's account of an axiom as a principle common to all sciences , which is self - evident , though incapable of proof , agrees sufficiently with the contents of Euclid's common notions as reduced to five in ...
Page 148
... common to two solids which are contiguous or the boundary which divides one solid into two contiguous parts ; this ... notion of either the other must be comprised as well . The second kind of definition which is based on what is not prior is ...
... common to two solids which are contiguous or the boundary which divides one solid into two contiguous parts ; this ... notion of either the other must be comprised as well . The second kind of definition which is based on what is not prior is ...
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Common terms and phrases
angle ABC angle ACB angle BAC angles equal Apollonius Arabic Archimedes Aristotle assumed axiom bisected Book Campanus centre circle circumference commentary Common Notion congruent construction definition diameter drawn edition Elements enunciation equilateral triangle Eucl Euclid Euclid's Elements Eudemus Eutocius Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interior angles interpolated isosceles joined lemma less Let ABC magnitude means meet namely Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proposition proved Ptolemy Pythagoras Pythagorean quoted rectangle rectangle contained reductio ad absurdum reference remaining angle respectively right angles right-angled triangle says Schol scholia scholium segment sides Simplicius solid square on AC suppose surface Suter Theon Theonine MSS theorem things three angles translation triangle ABC twice the rectangle words καὶ τὸ τῶν