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 |
Inni boken
Resultat 1-5 av 38
Side 50
... angle between them . B A D C E Hence angles are compared together by their extension sideways only ; without reference to the greater or smaller length of the straight lines between which they lie . Thus the angle ... ABC , or CBA ; that ...
... angle between them . B A D C E Hence angles are compared together by their extension sideways only ; without reference to the greater or smaller length of the straight lines between which they lie . Thus the angle ... ABC , or CBA ; that ...
Side 56
... triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . * For , if the triangle BAC was ...
... triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . * For , if the triangle BAC was ...
Side 57
... triangle , the angles opposite to two equal sides are equal to one another . Let BAC be an isoskeles triangle , of which the side AB is equal to AC . The angles ACB and ABC shall be equal to one another . Prolong * AB and AC to any ...
... triangle , the angles opposite to two equal sides are equal to one another . Let BAC be an isoskeles triangle , of which the side AB is equal to AC . The angles ACB and ABC shall be equal to one another . Prolong * AB and AC to any ...
Side 58
... angle ACB equal to the angle ABC . Cor . 7 . See Note . + INTERC . 1 . And by parity of reasoning , the like may be proved in every other instance . Wherefore , universally , in an isoskeles triangle the angles opposite to two equal ...
... angle ACB equal to the angle ABC . Cor . 7 . See Note . + INTERC . 1 . And by parity of reasoning , the like may be proved in every other instance . Wherefore , universally , in an isoskeles triangle the angles opposite to two equal ...
Side 59
... triangle whereof two angles are equal to one another . Wherefore , universally , if two angles & c . Which was to be demonstrated . COR . Every equiangular triangle is also equilateral . For if ABC be a triangle of which all the angles ...
... triangle whereof two angles are equal to one another . Wherefore , universally , if two angles & c . Which was to be demonstrated . COR . Every equiangular triangle is also equilateral . For if ABC be a triangle of which all the angles ...
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