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 16
Side 34
... aret equal but do not coincide , and the point B INTERC.11 . is in the surface of both ; they will cut one another ... same time made from it in the parts which lie in some other direction from B as for instance on the side of K ...
... aret equal but do not coincide , and the point B INTERC.11 . is in the surface of both ; they will cut one another ... same time made from it in the parts which lie in some other direction from B as for instance on the side of K ...
Side 54
... equal to BC . From the point A to B draw * the straight line AB , and upon it describet the equilateral triangle ... aret equal ; INTERC . 1. therefore the remainder AL is equal to the remainder BG . But it has been shown that BC is ...
... equal to BC . From the point A to B draw * the straight line AB , and upon it describet the equilateral triangle ... aret equal ; INTERC . 1. therefore the remainder AL is equal to the remainder BG . But it has been shown that BC is ...
Side 56
... equal to two sides of the other respectively ; and have also the angles between those sides , equal to one another ... aret equal . And because the straight line AC is ‡ equal to DF , the point C would coincide with the point F. But the ...
... equal to two sides of the other respectively ; and have also the angles between those sides , equal to one another ... aret equal . And because the straight line AC is ‡ equal to DF , the point C would coincide with the point F. But the ...
Side 58
... equal ; it follows that the remainders * INTERC . 1. are * equal , viz . the angle ACB equal to the angle ABC . Cor ... aret equal to one another . And since the angles A and C are also equal to B , the angles A , B , C are all equal to ...
... equal ; it follows that the remainders * INTERC . 1. are * equal , viz . the angle ACB equal to the angle ABC . Cor ... aret equal to one another . And since the angles A and C are also equal to B , the angles A , B , C are all equal to ...
Side 64
... equal to it . And by parity of reasoning , the like may be proved in every other instance , Wherefore , universally ... aret two right angles ; therefore the sum of the angles ABC and INTERC . 1. ABD ist also equal to two right angles ...
... equal to it . And by parity of reasoning , the like may be proved in every other instance , Wherefore , universally ... aret two right angles ; therefore the sum of the angles ABC and INTERC . 1. ABD ist also equal to 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