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 26
... radius of the sphere . A straight line drawn through the centre and terminated both ways by the surface , is called a diameter of the sphere . COR . A straight line may be described or made to pass from any one point to any other point ...
... radius of the sphere . A straight line drawn through the centre and terminated both ways by the surface , is called a diameter of the sphere . COR . A straight line may be described or made to pass from any one point to any other point ...
Σελίδα 27
... radius , is the greater . For if ( See the Figure to Prop . IX ) a straight line be described from the point B in the surface of a sphere , to the centre A , no point in that straight line , between B and A , as I , can also be in the ...
... radius , is the greater . For if ( See the Figure to Prop . IX ) a straight line be described from the point B in the surface of a sphere , to the centre A , no point in that straight line , between B and A , as I , can also be in the ...
Σελίδα 28
... radius is AB ; or the sphere whose radius is AB , is the greater . COR . 6. A sphere may be described about any centre , and with a radius of any length that shall have been assigned . For it has been shown * how it may be described ...
... radius is AB ; or the sphere whose radius is AB , is the greater . COR . 6. A sphere may be described about any centre , and with a radius of any length that shall have been assigned . For it has been shown * how it may be described ...
Σελίδα 33
... radius EB , describe a sphere ; and about A as a centre , with the radius AB , describe another sphere . Cor . 9 . Cor . 4 . • Constr . Because the surfaces of these two spheres pass through the point B , which is a point in the ...
... radius EB , describe a sphere ; and about A as a centre , with the radius AB , describe another sphere . Cor . 9 . Cor . 4 . • Constr . Because the surfaces of these two spheres pass through the point B , which is a point in the ...
Σελίδα 37
... radius as AD , describet a sphere ; and about any other centre , and with a radius equal to AD , de- scribe another sphere , which + INTERC.10 . will be equal to the first ; Cor . 4. and let these two equal spheres be placed touching ...
... radius as AD , describet a sphere ; and about any other centre , and with a radius equal to AD , de- scribe another sphere , which + INTERC.10 . will be equal to the first ; Cor . 4. and let these two equal spheres be placed touching ...
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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