Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ...Robert Heward, 1833 - 150 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 33.
Σελίδα viii
... true . The Second Book of Euclid would be true , if the First existed only in the shape of the heads of the Propo- sitions under the title of Axioms ; but this would make a most lame and imperfect specimen of reasoning . The ways in ...
... true . The Second Book of Euclid would be true , if the First existed only in the shape of the heads of the Propo- sitions under the title of Axioms ; but this would make a most lame and imperfect specimen of reasoning . The ways in ...
Σελίδα 2
... true , is called a Theorem . An operation which it is proposed to show how to perform , is called a Problem . And both are called by the title of Propositions . XIX . A Proposition dependent on some other that has been previously ...
... true , is called a Theorem . An operation which it is proposed to show how to perform , is called a Problem . And both are called by the title of Propositions . XIX . A Proposition dependent on some other that has been previously ...
Σελίδα 3
... true , without the other being true also ; is called a consequence . XXVI . When such preceding position is not known to be true , but is only assumed to be true for the purpose of trying its truth or falsehood by examination of the ...
... true , without the other being true also ; is called a consequence . XXVI . When such preceding position is not known to be true , but is only assumed to be true for the purpose of trying its truth or falsehood by examination of the ...
Σελίδα 4
... true in the instances in which experiment has actually been made . For example , a cooper knows that in every instance where he has tried it , the distance that went exactly round the rim of his cask at six times , was the distance to ...
... true in the instances in which experiment has actually been made . For example , a cooper knows that in every instance where he has tried it , the distance that went exactly round the rim of his cask at six times , was the distance to ...
Σελίδα 5
... true , till it has been demonstrated as a distinct proposition . For till this be done , it is impossible to know whether it is true or not . For example , it is shown in the sequel , that if one angle of a triangle is greater than a ...
... true , till it has been demonstrated as a distinct proposition . For till this be done , it is impossible to know whether it is true or not . For example , it is shown in the sequel , that if one angle of a triangle is greater than a ...
Άλλες εκδόσεις - Προβολή όλων
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points aret assigned point Axiom axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal angles equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively SCHOLIUM self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.-If third side triangle ABC turned unlimited length Wherefore