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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Resultat 1-5 av 37
Side vi
... passing through the centre of the other , and a straight line of unlimited length be drawn from the point of contact of the two smaller spheres to any point in the inter- section of the others ; this straight line , on the whole being ...
... passing through the centre of the other , and a straight line of unlimited length be drawn from the point of contact of the two smaller spheres to any point in the inter- section of the others ; this straight line , on the whole being ...
Side 1
... pass , is when the things touch one another or are in contact . Thus there is coincidence between the surface of a cast and the surface of the mould which contains it . And in like manner two lines or points may actually touch one ...
... pass , is when the things touch one another or are in contact . Thus there is coincidence between the surface of a cast and the surface of the mould which contains it . And in like manner two lines or points may actually touch one ...
Side 10
... pass . Wherefore there will be some remainder MO such , that it is a limit which they cannot pass , but if any smaller magnitude be substituted they shall pass it ; for if they would not pass such smaller magnitude , the difference ...
... pass . Wherefore there will be some remainder MO such , that it is a limit which they cannot pass , but if any smaller magnitude be substituted they shall pass it ; for if they would not pass such smaller magnitude , the difference ...
Side 11
... pass ; and consequently ( by Cor . 16 ) the magnitudes would not be all equal to one another . Which cannot be , for they are equal . The assumptiont therefore cannot be true ; or there is not a magnitude which they cannot pass . That ...
... pass ; and consequently ( by Cor . 16 ) the magnitudes would not be all equal to one another . Which cannot be , for they are equal . The assumptiont therefore cannot be true ; or there is not a magnitude which they cannot pass . That ...
Side 24
... pass through it , and at another instant they would not ; which cannot be with- out one or both of the spheres having suffered change of place . And because the point of contact always coincides with one and the same point in fixed ...
... pass through it , and at another instant they would not ; which cannot be with- out one or both of the spheres having suffered change of place . And because the point of contact always coincides with one and the same point in fixed ...
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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