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 11
Side 52
... triangles , such as have two sides equal , 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 , 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 straight line . * INTERC.13 . Cor . 3 . 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 straight line . * INTERC.13 . Cor . 3 . 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 K H E 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 circle ...
... equilateral triangle K H E 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 circle ...
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 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 half the angle 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
Populære avsnitt
Side 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Side 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Side 72 - Any two sides of a triangle are together greater than the third side.
Side 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Side 70 - Any two angles of a triangle are together less than two right angles.
Side 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Side 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.