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
... change of place . And on receipt of the remark mentioned above , this track was pursued with renewed vigour , and the results are presented in the sequel . For the use of those who are not disposed to go into details , the substance may ...
... change of place . And on receipt of the remark mentioned above , this track was pursued with renewed vigour , and the results are presented in the sequel . For the use of those who are not disposed to go into details , the substance may ...
Σελίδα 15
... change of place . Let the substantial sphere whose INTERC . 2. centre is B , bet turned in any man- ner whatsoever about the centre B which remains at rest . The sphere shall be without change of place . • INTERC . 3 . Cor . 3 . + ...
... change of place . Let the substantial sphere whose INTERC . 2. centre is B , bet turned in any man- ner whatsoever about the centre B which remains at rest . The sphere shall be without change of place . • INTERC . 3 . Cor . 3 . + ...
Σελίδα 16
... change of place ; the substantial sphere is without change of place . So also of the hollow sphere , if it be turned while the substantial one which is its reciprocal remains unmoved . And by parity of reasoning , the like may be proved ...
... change of place ; the substantial sphere is without change of place . So also of the hollow sphere , if it be turned while the substantial one which is its reciprocal remains unmoved . And by parity of reasoning , the like may be proved ...
Σελίδα 17
... space CEGDHF and not else- where . For each of them will be * without change of place ; wherefore they must at all times coincide in that surface and not elsewhere ; for if they do not , one or both must have suffered change of place ...
... space CEGDHF and not else- where . For each of them will be * without change of place ; wherefore they must at all times coincide in that surface and not elsewhere ; for if they do not , one or both must have suffered change of place ...
Σελίδα 20
... change its place ; for it cannot have its face turned to all sides in succession and be without change of place . Let it therefore , at some period during the turning , be in the situation EF . But if the spheres do at first coincide in ...
... change its place ; for it cannot have its face turned to all sides in succession and be without change of place . Let it therefore , at some period during the turning , be in the situation EF . But if the spheres do at first coincide in ...
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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