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 21
To which is Added an Appendix ... Thomas Perronet Thompson. * I. Nom.26 . PROP . VI . 21 the turning be in the new situation E. But if the spheres ... sphere cannot have more than one centre . Let there be a sphere de- scribed about the ...
To which is Added an Appendix ... Thomas Perronet Thompson. * I. Nom.26 . PROP . VI . 21 the turning be in the new situation E. But if the spheres ... sphere cannot have more than one centre . Let there be a sphere de- scribed about the ...
Σελίδα 22
... sphere whose centre INTERC . 2. is C , let the sphere whose centre is A be turned * about A till the + INTERC.3 . point B is in that surface . About any centre as D , describe † another sphere with a central distance equal to AC ; and apply ...
... sphere whose centre INTERC . 2. is C , let the sphere whose centre is A be turned * about A till the + INTERC.3 . point B is in that surface . About any centre as D , describe † another sphere with a central distance equal to AC ; and apply ...
Σελίδα 23
... sphere whose centre is C ; and let the line then described by the point A from A to C , be afterwards turned about B in various * INTERC.3 . directions as called for , till a sphere is described * with a central distance equal to BA ...
... sphere whose centre is C ; and let the line then described by the point A from A to C , be afterwards turned about B in various * INTERC.3 . directions as called for , till a sphere is described * with a central distance equal to BA ...
Σελίδα 24
... which remain at rest . Their point of contact C shall remain unmoved . Because the centre of each sphere remains at rest , each sphere + INTERC . 4. is turned about its own centre ; wherefore each sphere will be without change of place ...
... which remain at rest . Their point of contact C shall remain unmoved . Because the centre of each sphere remains at rest , each sphere + INTERC . 4. is turned about its own centre ; wherefore each sphere will be without change of place ...
Σελίδα 25
... which is within the sphere last described , describe another sphere AC ; and about the centre B , + INTERC.7 . describe † a sphere touching the sphere AC externally , and let the ‡ INTERC . 5. single point ‡ in which it touches it , be ...
... which is within the sphere last described , describe another sphere AC ; and about the centre B , + INTERC.7 . describe † a sphere touching the sphere AC externally , and let the ‡ INTERC . 5. single point ‡ in which it touches it , be ...
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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