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 vi
... follows . A solid may be described , all the points in whose surface shall be equidistant from a given point within ; such a solid is called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of ...
... follows . A solid may be described , all the points in whose surface shall be equidistant from a given point within ; such a solid is called a sphere . A sphere may be turned in any manner whatsoever about its centre , without change of ...
Σελίδα vii
... follows , but to take advantage of the habits of rea- soning that may be thus acquired , before attempting what must be characterized as , in some parts , at least equal in complexity to anything in the succeeding Books . If this ...
... follows , but to take advantage of the habits of rea- soning that may be thus acquired , before attempting what must be characterized as , in some parts , at least equal in complexity to anything in the succeeding Books . If this ...
Σελίδα 2
... follow , as , for instance , that the sum of them shall be equal to some third magnitude ; one of these magnitudes may at any period of the operations in hand be avouched to be equal to the other by the hypothesis . For that they are ...
... follow , as , for instance , that the sum of them shall be equal to some third magnitude ; one of these magnitudes may at any period of the operations in hand be avouched to be equal to the other by the hypothesis . For that they are ...
Σελίδα 4
... follows : - : - The first conveys a statement of the universal proposition to be finally established . Which is called the enunciation . The second presents to the eye , or to the imagination , a particular instance , in respect of ...
... follows : - : - The first conveys a statement of the universal proposition to be finally established . Which is called the enunciation . The second presents to the eye , or to the imagination , a particular instance , in respect of ...
Σελίδα 57
... the angle BCF to CBG . And since it has been demonstrated that the whole angle ACF is equal to the whole angle ABG , parts of which , the angles Cor . 7 . ⚫ I. 4 . BCF and CBG , are also equal ; it follows BOOK I. - PROP . V. 57.
... the angle BCF to CBG . And since it has been demonstrated that the whole angle ACF is equal to the whole angle ABG , parts of which , the angles Cor . 7 . ⚫ I. 4 . BCF and CBG , are also equal ; it follows BOOK I. - PROP . V. 57.
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