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
... universally . And a proposition so established is called a universal proposition . XXV . A conclusion the truth of which is shown to be so con- nected with the truth of some preceding position or statement , that the preceding cannot be ...
... universally . And a proposition so established is called a universal proposition . XXV . A conclusion the truth of which is shown to be so con- nected with the truth of some preceding position or statement , that the preceding cannot be ...
Σελίδα 6
... 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 same . Let A and B be ...
... 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 same . Let A and B be ...
Σελίδα 13
... universally , a hard body may be turned & c . Which was to be demonstrated . COR . Any solid , surface , line , or figure , may be turned about any one point , or about any two points , in it ; such point or points remaining unmoved ...
... universally , a hard body may be turned & c . Which was to be demonstrated . COR . Any solid , surface , line , or figure , may be turned about any one point , or about any two points , in it ; such point or points remaining unmoved ...
Σελίδα 16
... universally , if a sphere be turned & c . Which was to be demonstrated . PROPOSITION V. THEOREM . - If two spheres touch one another externally , they touch only in a point . Let there be two spheres whose centres are A and B , touching ...
... universally , if a sphere be turned & c . Which was to be demonstrated . PROPOSITION V. THEOREM . - If two spheres touch one another externally , they touch only in a point . Let there be two spheres whose centres are A and B , touching ...
Σελίδα 21
... universally , if two spheres touch one another externally , they touch only in a point . Which was to be demonstrated . COR . Two spheres may be applied to one another externally , so that they shall touch in a point assigned on the ...
... universally , if two spheres touch one another externally , they touch only in a point . Which was to be demonstrated . COR . Two spheres may be applied to one another externally , so that they shall touch in a point assigned on the ...
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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