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 sider |
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Side vi
... was the foundation of the Platonic notion of the perfection of the sphere ( Vide Plat . De Anim . Mund . ) should not have been sooner carried into its consequences . These results , together with the proofs offered of what vi PREFACE .
... was the foundation of the Platonic notion of the perfection of the sphere ( Vide Plat . De Anim . Mund . ) should not have been sooner carried into its consequences . These results , together with the proofs offered of what vi PREFACE .
Side vii
... proofs offered of what have usually been termed the Axioms and Postulates , have been formed into an Intercalary Book , with a view to facilitate their postponement in the case of students beginning geometry for the first time . And for ...
... proofs offered of what have usually been termed the Axioms and Postulates , have been formed into an Intercalary Book , with a view to facilitate their postponement in the case of students beginning geometry for the first time . And for ...
Side viii
... proof . ' In labouring to get rid of Axioms , the object has been to assail the belief in the existence of such things as self - evident truths . Nothing is self - evident , except perhaps an identical proposition . There may be things ...
... proof . ' In labouring to get rid of Axioms , the object has been to assail the belief in the existence of such things as self - evident truths . Nothing is self - evident , except perhaps an identical proposition . There may be things ...
Side 3
... proof im- properly called reductio ad absurdum , ' reduction to an absurdity . ' XXVII . The establishment of some universal proposition , is called a demonstration . The peculiar object of a demonstration , is to display the reasons ...
... proof im- properly called reductio ad absurdum , ' reduction to an absurdity . ' XXVII . The establishment of some universal proposition , is called a demonstration . The peculiar object of a demonstration , is to display the reasons ...
Side 4
... proof . The fifth extends the conclusion to all instances that come under the terms conveyed in the enunciation . Which is called the generalization . XXIX . When all the instances to which a proposition may be applied , cannot be ...
... proof . The fifth extends the conclusion to all instances that come under the terms conveyed in the enunciation . Which is called the generalization . XXIX . When all the instances to which a proposition may be applied , cannot be ...
Andre utgaver - Vis alle
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson Uten tilgangsbegrensning - 1833 |
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points 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 half the angle 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
Populære avsnitt
Side 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Side 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Side 72 - Any two sides of a triangle are together greater than the third side.
Side 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Side 70 - Any two angles of a triangle are together less than two right angles.
Side 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Side 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.