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 |
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Σελίδα 3
... impossible consequence , the as- sumption cannot be true . This is the rationale [ or reasonable principle ] of the mode of proof im- properly called reductio ad absurdum , reduction to an absurdity . ' XXVII . The establishment of some ...
... impossible consequence , the as- sumption cannot be true . This is the rationale [ or reasonable principle ] of the mode of proof im- properly called reductio ad absurdum , reduction to an absurdity . ' XXVII . The establishment of some ...
Σελίδα 5
... 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 right angle , the other two are necessarily less than right angles . The converse of which 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 right angle , the other two are necessarily less than right angles . The converse of which is ...
Σελίδα 8
... impossible ; for the things by the hypothesis were equal to begin with . The assumption * , therefore , which involves this impossible consequence , cannot be true ; or one remainder cannot be greater than the other . And because one is ...
... impossible ; for the things by the hypothesis were equal to begin with . The assumption * , therefore , which involves this impossible consequence , cannot be true ; or one remainder cannot be greater than the other . And because one is ...
Σελίδα 9
... impossible , for it is equal . The assumption " , therefore , cannot be true ; or the one magnitude , that was doubled , is not greater than the other ; and because one is not greater than the other , they are equal . And in like manner ...
... impossible , for it is equal . The assumption " , therefore , cannot be true ; or the one magnitude , that was doubled , is not greater than the other ; and because one is not greater than the other , they are equal . And in like manner ...
Σελίδα 15
... impossible , for they are equal . The central distances , therefore , cannot be unequal ; that is , they are equal . PROPOSITION IV . THEOREM . - If a sphere be turned in any manner whatsoever about the centre which remains at rest ...
... impossible , for they are equal . The central distances , therefore , cannot be unequal ; that is , they are equal . PROPOSITION IV . THEOREM . - If a sphere be turned in any manner whatsoever about the centre which remains at rest ...
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