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 vi
... whose surface shall be equidistant from a given point within ; such a solid is called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of place . Consequences deducible from this are , that if two ...
... whose surface shall be equidistant from a given point within ; such a solid is called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of place . Consequences deducible from this are , that if two ...
Σελίδα 14
... Spheres are said to touch one another , which meet but do not cut one another . Spheres described about the same centre , are called concentric . COR . 2. A sphere may be described about any centre , and with a central distance equal to ...
... Spheres are said to touch one another , which meet but do not cut one another . Spheres described about the same centre , are called concentric . COR . 2. A sphere may be described about any centre , and with a central distance equal to ...
Σελίδα 15
... sphere will be greater + than the other ; which is impossible , for they are equal . The central distances ... centre which remains at rest , the sphere will be without change of place . Let the substantial sphere whose INTERC . 2. centre ...
... sphere will be greater + than the other ; which is impossible , for they are equal . The central distances ... centre which remains at rest , the sphere will be without change of place . Let the substantial sphere whose INTERC . 2. centre ...
Σελίδα 17
... sphere whose centre is A , be turned about A , till the portion of its surface which was originally in the situation CEGDHF , is brought into the situation IESF ; and because the spheres will still coincide in CEGDHF and not elsewhere ...
... sphere whose centre is A , be turned about A , till the portion of its surface which was originally in the situation CEGDHF , is brought into the situation IESF ; and because the spheres will still coincide in CEGDHF and not elsewhere ...
Σελίδα 18
... whose centre is A , be turned about A , till the line on its surface which ori- ginally coincided with CEGDHF , is brought into the situation IESF ; and on the sphere ... sphere be turned round its centre again , till the points on its ...
... whose centre is A , be turned about A , till the line on its surface which ori- ginally coincided with CEGDHF , is brought into the situation IESF ; and on the sphere ... sphere be turned round its centre again , till the points on its ...
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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