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 sider |
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Side 16
... . For if this be disputed , First Case ; let it be assumed that they coincide in the surface CEGDHF in Fig . 1 below , and not elsewhere . But if so , Fig . 1 . 4 . E F · B H D * INTERC . 4 . + INTERC . 2 . 16 INTERCALARY BOOK ,
... . For if this be disputed , First Case ; let it be assumed that they coincide in the surface CEGDHF in Fig . 1 below , and not elsewhere . But if so , Fig . 1 . 4 . E F · B H D * INTERC . 4 . + INTERC . 2 . 16 INTERCALARY BOOK ,
Side 17
... CEGDHF , is brought into the situation IESF ; and because the spheres will still coincide in CEGDHF and not elsewhere , the portion CESF of IESF will coincide with the sphere whose centre is B , and the portion IECF will not . Let now ...
... CEGDHF , is brought into the situation IESF ; and because the spheres will still coincide in CEGDHF and not elsewhere , the portion CESF of IESF will coincide with the sphere whose centre is B , and the portion IECF will not . Let now ...
Side 18
... CEGDHF in Fig . 2. below ; and not elsewhere . But if so , it may be shown as before , that they must continue to coincide in the same line in fixed space CEGDHF and not elsewhere , in whatsoever manner they may be turned about their ...
... CEGDHF in Fig . 2. below ; and not elsewhere . But if so , it may be shown as before , that they must continue to coincide in the same line in fixed space CEGDHF and not elsewhere , in whatsoever manner they may be turned about their ...
Side 19
... CEGDHF , the two portions EKF and ETF of KETF can in no way be turned about the points E and F so as to be both of them above or both below the line IESF or its portions , other than by their particles , or some of them , being moved ...
... CEGDHF , the two portions EKF and ETF of KETF can in no way be turned about the points E and F so as to be both of them above or both below the line IESF or its portions , other than by their particles , or some of them , being moved ...
Andre utgaver - Vis alle
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson Uten tilgangsbegrensning - 1833 |
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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