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 vii
... instance in the conclusions drawn with respect to the sphere and straight line from turning them about certain points . But there are others where the reasoning depends altogether on the supposition of a continuity of motion ; as ...
... instance in the conclusions drawn with respect to the sphere and straight line from turning them about certain points . But there are others where the reasoning depends altogether on the supposition of a continuity of motion ; as ...
Side 2
... instance , that the sum of them shall be equal to some third magnitude ; one of these magnitudes may at any period of the operations in hand be avouched to be equal to the other by the hypothesis . For that they are equal , is the ...
... instance , that the sum of them shall be equal to some third magnitude ; one of these magnitudes may at any period of the operations in hand be avouched to be equal to the other by the hypothesis . For that they are equal , is the ...
Side 3
... instance , may by taking the same steps be shown to be true in this . Thus , if it has been shown that because two particular magnitudes are each equal to a third magnitude they are equal to one another ; and if the same steps can be ...
... instance , may by taking the same steps be shown to be true in this . Thus , if it has been shown that because two particular magnitudes are each equal to a third magnitude they are equal to one another ; and if the same steps can be ...
Side 4
... 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 be taken in ...
... 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 be taken in ...
Side 6
... instance . Wherefore , universally , magnitudes which are equal to the same , are equal to one another . Which was to be demonstrated . COROLLARY 1. If of equals , one be equal to some thing else , the rest are severally equal to the ...
... instance . Wherefore , universally , magnitudes which are equal to the same , are equal to one another . Which was to be demonstrated . COROLLARY 1. If of equals , one be equal to some thing else , the rest are severally equal to the ...
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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 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