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 σελίδες |
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Σελίδα 34
... aret equal but do not coincide , and the point B INTERC.11 . is in the surface of both ; they will cut one another in a self - rejoining line passing through B , or else touch in B only . But whichever of these they do , ( inasmuch as ...
... aret equal but do not coincide , and the point B INTERC.11 . is in the surface of both ; they will cut one another in a self - rejoining line passing through B , or else touch in B only . But whichever of these they do , ( inasmuch as ...
Σελίδα 54
... aret equal ; INTERC . 1. therefore the remainder AL is equal to the remainder BG . But it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG . And things which are * INTERC . 1. equal to the same ...
... aret equal ; INTERC . 1. therefore the remainder AL is equal to the remainder BG . But it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG . And things which are * INTERC . 1. equal to the same ...
Σελίδα 56
... aret equal . And because the straight line AC is ‡ equal to DF , the point C would coincide with the point F. But the point B coincides with the point E ; wherefore ( the point B coin- * INTERC , 12 . ciding with E , and C with F ...
... aret equal . And because the straight line AC is ‡ equal to DF , the point C would coincide with the point F. But the point B coincides with the point E ; wherefore ( the point B coin- * INTERC , 12 . ciding with E , and C with F ...
Σελίδα 58
... 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 one another . ‡ I. 3 . Hyp . + I. 4 . PROPOSITION VI . THEOREM . - If two angles of a triangle are equal to one another ...
... 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 one another . ‡ I. 3 . Hyp . + I. 4 . PROPOSITION VI . THEOREM . - If two angles of a triangle are equal to one another ...
Σελίδα 64
... aret two right angles ; therefore the sum of the angles ABC and INTERC . 1. ABD ist also equal to two right angles . Cor . 1 . And by parity of reasoning , the like may be proved in every INTERC.12 . Cor . 6 . other instance . Wherefore ...
... aret two right angles ; therefore the sum of the angles ABC and INTERC . 1. ABD ist also equal to two right angles . Cor . 1 . And by parity of reasoning , the like may be proved in every INTERC.12 . Cor . 6 . other instance . Wherefore ...
Άλλες εκδόσεις - Προβολή όλων
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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