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 3
... parity of reasoning any other two magnitudes which are equal to a third , are equal to one another . For it is open to be demonstrated by the same steps . When the parity of reasoning is extended to all instances to which the ...
... parity of reasoning any other two magnitudes which are equal to a third , are equal to one another . For it is open to be demonstrated by the same steps . When the parity of reasoning is extended to all instances to which the ...
Side 6
... parity of reasoning , the like may be proved in every other instance . Wherefore , universally , magnitudes which are equal to the same , are equal to one another . Which was to be demonstrated . COROLLARY 1. If of equals , one be equal ...
... parity of reasoning , the like may be proved in every other instance . Wherefore , universally , magnitudes which are equal to the same , are equal to one another . Which was to be demonstrated . COROLLARY 1. If of equals , one be equal ...
Side 13
... reason , between the situations A and M the body may be placed in other situations as N and O , in all of which the ... parity of reasoning , the like may be proved of every other hard body . Wherefore , universally , a hard body may be ...
... reason , between the situations A and M the body may be placed in other situations as N and O , in all of which the ... parity of reasoning , the like may be proved of every other hard body . Wherefore , universally , a hard body may be ...
Side 14
... parity of reasoning , the like may be done in every other instance . COR . 1. Instead of being described about B , the solid , if required , may be described about any other assigned point as D. For the hard body in which are the points ...
... parity of reasoning , the like may be done in every other instance . COR . 1. Instead of being described about B , the solid , if required , may be described about any other assigned point as D. For the hard body in which are the points ...
Side 16
... parity of reasoning , the like may be proved of every other sphere . Wherefore , universally , if a sphere be turned & c . Which was to be demonstrated . PROPOSITION V. THEOREM . - If two spheres touch one another externally , they ...
... parity of reasoning , the like may be proved of every other sphere . Wherefore , universally , if a sphere be turned & c . Which was to be demonstrated . PROPOSITION V. THEOREM . - If two spheres touch one another externally , they ...
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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