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 53
... triangle ABC is equilateral ; and it is described upon the given straight line AB . Which was to be done . And by parity of reasoning , the like may be done in every other instance . SCHOLIUM . It has not yet been proved that the place ...
... triangle ABC is equilateral ; and it is described upon the given straight line AB . Which was to be done . And by parity of reasoning , the like may be done in every other instance . SCHOLIUM . It has not yet been proved that the place ...
Σελίδα 56
... triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal ... ABC to the angle DEF , and the angle ACB to the angle Dfe . INTERC.12 . Cor . 6 . t I. 3 . 56 EUCLID'S ELEMENTS .
... triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal ... ABC to the angle DEF , and the angle ACB to the angle Dfe . INTERC.12 . Cor . 6 . t I. 3 . 56 EUCLID'S ELEMENTS .
Σελίδα 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 ...
Σελίδα 58
... triangle be pro- longed , the two angles exterior to the third side shall be equal . For the angle FBC was shown to be equal to GCB . A B COR . 2. Every equilateral triangle is also equiangular . For if ABC be an equilateral triangle ...
... triangle be pro- longed , the two angles exterior to the third side shall be equal . For the angle FBC was shown to be equal to GCB . A B COR . 2. Every equilateral triangle is also equiangular . For if ABC be an equilateral triangle ...
Σελίδα 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 ...
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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