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 21
Side 56
... angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the ...
... angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the ...
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 ... BAC be a triangle having the angle ACB equal to the angle ABC ; the side BA is equal to the side CA. C For if BA be ...
... angle ACB equal to the angle ABC . Cor . 7 . See Note . + INTERC . 1 . And by parity of reasoning , the like may be ... BAC be a triangle having the angle ACB equal to the angle ABC ; the side BA is equal to the side CA. C For if BA be ...
Side 61
... BAC , EDF be two triangles , having the two sides BA , AC , equal to the two sides DE , DF respectively , viz . AB to DE , and AC to DF ; and also the third side BC equal to the third side EF . The angle BAC shall be equal to the angle ...
... BAC , EDF be two triangles , having the two sides BA , AC , equal to the two sides DE , DF respectively , viz . AB to DE , and AC to DF ; and also the third side BC equal to the third side EF . The angle BAC shall be equal to the angle ...
Side 68
... angle . [ That is , to divide it into two equal angles . ] • 1.3 . † I. 1 . + Constr . • Constr . + I . 8 . I. 13 . Let BAC be the given angle . It is required to bisect it . First Case ; if BAC is less than the sum of two right angles ...
... angle . [ That is , to divide it into two equal angles . ] • 1.3 . † I. 1 . + Constr . • Constr . + I . 8 . I. 13 . Let BAC be the given angle . It is required to bisect it . First Case ; if BAC is less than the sum of two right 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