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 viii
... 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 which 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 which the ...
Σελίδα 2
... second . And a magnitude is said to be less than another by a certain mag- nitude , when this last - mentioned magnitude being added to the first , the sum is equal to the second . XVI . Magnitudes are said to be given , when equals to ...
... second . And a magnitude is said to be less than another by a certain mag- nitude , when this last - mentioned magnitude being added to the first , the sum is equal to the second . XVI . Magnitudes are said to be given , when equals to ...
Σελίδα 4
... second presents to the eye , or to the imagination , a particular instance , in respect of which the truth of the proposition is to be established ; with an understanding always , that nothing shall be done in respect of this par ...
... second presents to the eye , or to the imagination , a particular instance , in respect of which the truth of the proposition is to be established ; with an understanding always , that nothing shall be done in respect of this par ...
Σελίδα 7
... Second Case ; If either C be added in some other manner than as above ; or if A and B would not coincide with one another , but are only such as by a different arrangement of parts might be made to do so ; the magnitudes which are the ...
... Second Case ; If either C be added in some other manner than as above ; or if A and B would not coincide with one another , but are only such as by a different arrangement of parts might be made to do so ; the magnitudes which are the ...
Σελίδα 12
... Second Case ; the body A may be turned about any two points in it , as B and C , both these points remaining unmoved . For because the body is * By the a hardt Hypothesis . body , the distance from the point B in + I. Nom . 3 . it to ...
... Second Case ; the body A may be turned about any two points in it , as B and C , both these points remaining unmoved . For because the body is * By the a hardt Hypothesis . body , the distance from the point B in + I. Nom . 3 . it to ...
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