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 52
... triangles , such as have two sides equal , A are called isoskeles . XLVII . A triangle which has all its three sides equal , is called equilateral . Hence all equilateral triangles are at the same time isoskeles ; but isoskeles triangles ...
... triangles , such as have two sides equal , A are called isoskeles . XLVII . A triangle which has all its three sides equal , is called equilateral . Hence all equilateral triangles are at the same time isoskeles ; but isoskeles triangles ...
Side 53
... equilateral triangle upon a given * INTERC . 13 . Cor . 3 . straight line . Let AB be the given straight line . It is required to describe an equilateral triangle upon it . About the centre A , with the radius AB , de- scribe the circle ...
... equilateral triangle upon a given * INTERC . 13 . Cor . 3 . straight line . Let AB be the given straight line . It is required to describe an equilateral triangle upon it . About the centre A , with the radius AB , de- scribe the circle ...
Side 54
... equilateral triangle B G K H LE INTERC . 12. DAB , and prolong ‡ the straight lines DA and DB , to E and F ; which will be in the same plane with the rest . About the centre * INTERC.13 . Cor . 2. B , with the radius BC , describe + the ...
... equilateral triangle B G K H LE INTERC . 12. DAB , and prolong ‡ the straight lines DA and DB , to E and F ; which will be in the same plane with the rest . About the centre * INTERC.13 . Cor . 2. B , with the radius BC , describe + the ...
Side 58
... equilateral triangle is also equiangular . For if ABC be an equilateral triangle , then because the sides CB and CA are equal , the angle A ( by Prop . V above ) is equal to the angle B. Again , because the sides AB and AC are equal ...
... equilateral triangle is also equiangular . For if ABC be an equilateral triangle , then because the sides CB and CA are equal , the angle A ( by Prop . V above ) is equal to the angle B. Again , because the sides AB and AC are 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