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 23
Side 30
... EF ; and not elsewhere . In EF take any point as G ; and on the other side of CD take any point as H , in the ... equal spheres are equal ) ; whereupon the surfaces of the two spheres will + coincide throughout . And because the lines ...
... EF ; and not elsewhere . In EF take any point as G ; and on the other side of CD take any point as H , in the ... equal spheres are equal ) ; whereupon the surfaces of the two spheres will + coincide throughout . And because the lines ...
Side 56
... equal to two sides of the other respectively ; and have also the angles between those sides , equal to one another ... EF , and the triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall ...
... equal to two sides of the other respectively ; and have also the angles between those sides , equal to one another ... EF , and the triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall ...
Side 61
... equal to two sides of the other respectively , and have also their third sides equal ; the angle which is between ... EF . The angle BAC shall be equal to the angle EDF ; and the triangle BAC to the triangle EDF ; and the other angles ...
... equal to two sides of the other respectively , and have also their third sides equal ; the angle which is between ... EF . The angle BAC shall be equal to the angle EDF ; and the triangle BAC to the triangle EDF ; and the other angles ...
Side 63
... equal to the two EC , CF respectively . Also the third side DF is equal to the third side EF ; therefore the angle DCF is * equal to ECF ; and they are adjacent angles . But when the adjacent angles which one straight line makes with ...
... equal to the two EC , CF respectively . Also the third side DF is equal to the third side EF ; therefore the angle DCF is * equal to ECF ; and they are adjacent angles . But when the adjacent angles which one straight line makes with ...
Side 68
... equal angles . ] • 1.3 . † I. 1 . + Constr . • Constr . + I . 8 . I. 13 . Let BAC be the given angle . It is ... EF ; therefore the angle DAF ist equal to the angle EAF . Wherefore the given angle BAC is bisected by the straight line AF ...
... equal angles . ] • 1.3 . † I. 1 . + Constr . • Constr . + I . 8 . I. 13 . Let BAC be the given angle . It is ... EF ; therefore the angle DAF ist equal to the angle EAF . Wherefore the given angle BAC is bisected by the straight line AF ...
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