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 ix
... opposite to the bases ; which is inconsistent with those sides forming one straight line as must be the case if the angles opposite to the bases in the tesseras were right angles . Whence may be inferred that the three angles of every ...
... opposite to the bases ; which is inconsistent with those sides forming one straight line as must be the case if the angles opposite to the bases in the tesseras were right angles . Whence may be inferred that the three angles of every ...
Σελίδα 52
... opposite angular points is called a diagonal . For brevity , quadrilateral figures may be named by the letters at two of their opposite angles , when no obscurity arises therefrom . LIV . Of polygons , such as have five , six , seven ...
... opposite angular points is called a diagonal . For brevity , quadrilateral figures may be named by the letters at two of their opposite angles , when no obscurity arises therefrom . LIV . Of polygons , such as have five , six , seven ...
Σελίδα 56
... opposite . D AÅ B CE F Let BAC , EDF be two triangles , which have the two sides AB , AC of the one , equal to the two sides DE , DF of the other re- spectively , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF ...
... opposite . D AÅ B CE F Let BAC , EDF be two triangles , which have the two sides AB , AC of the one , equal to the two sides DE , DF of the other re- spectively , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF ...
Σελίδα 57
... 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 lengths , as for instance ...
... 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 lengths , as for instance ...
Σελίδα 58
... opposite to two equal sides are equal to one another . Which was to be demonstrated . COR . 1. If two equal sides of any isoskeles triangle be pro- longed , the two angles exterior to the third side shall be equal . For the angle FBC ...
... opposite to two equal sides are equal to one another . Which was to be demonstrated . COR . 1. If two equal sides of any isoskeles triangle be pro- longed , the two angles exterior to the third side shall be equal . For the angle FBC ...
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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