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 56
... angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the ...
... angle BAC equal to the angle EDF . The third side BC shall be equal to the third side EF , and the triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the ...
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
... 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 , the sides opposite to the two equal angles are equal to one another . Let BAC be a ...
... 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 , the sides opposite to the two equal angles are equal to one another . Let BAC be a ...
Σελίδα 61
... triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the angle ABC to DEF , and ACB to DFE . For , let the triangle BAC be applied to the triangle EDF , so ...
... triangle BAC to the triangle EDF ; and the other angles , to which the equal sides are opposite , shall be equal respectively , viz . the angle ABC to DEF , and ACB to DFE . For , let the triangle BAC be applied to the triangle EDF , so ...
Σελίδα 68
... angle . [ That is , to divide it into two equal angles . ] • 1.3 . † I. 1 . + Constr . • Constr . + I . 8 . I. 13 . Let BAC be the given angle . It is required to bisect it . First Case ; if BAC is less than the sum of two right angles ...
... angle . [ That is , to divide it into two equal angles . ] • 1.3 . † I. 1 . + Constr . • Constr . + I . 8 . I. 13 . Let BAC be the given angle . It is required to bisect it . First Case ; if BAC is less than the sum of two right angles ...
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