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 iii
... half . TO WHICH IS ADDED AN APPENDIX Containing Notices of Methods at different times proposed for getting over the difficulty in the Twelfth Axiom of Euclid . 205 By a Member of the University of Cambridge . LIPERTE FOURTH EDITION ...
... half . TO WHICH IS ADDED AN APPENDIX Containing Notices of Methods at different times proposed for getting over the difficulty in the Twelfth Axiom of Euclid . 205 By a Member of the University of Cambridge . LIPERTE FOURTH EDITION ...
Σελίδα ix
... half , and in substance to the following . If a tessera [ or quadrilateral recti- linear plane figure of which two of the opposite sides are equal to one another and make equal interior angles with a side between them which shall be ...
... half , and in substance to the following . If a tessera [ or quadrilateral recti- linear plane figure of which two of the opposite sides are equal to one another and make equal interior angles with a side between them which shall be ...
Σελίδα 9
... half of a greater magnitude is greater than the half of a less . And so of any other equipartites . For , if it be not greater , it must either be equal or less . It cannot be equal , for then ( by Cor . 10 ) its double would be equal ...
... half of a greater magnitude is greater than the half of a less . And so of any other equipartites . For , if it be not greater , it must either be equal or less . It cannot be equal , for then ( by Cor . 10 ) its double would be equal ...
Σελίδα 11
... half , and from the remainder not less than its half , and so on ; there shall at length remain a magni- tude less than the least of the proposed magnitudes . A C D E H F For if AB and C be the two proposed magnitudes , of which AB is ...
... half , and from the remainder not less than its half , and so on ; there shall at length remain a magni- tude less than the least of the proposed magnitudes . A C D E H F For if AB and C be the two proposed magnitudes , of which AB is ...
Σελίδα 12
To which is Added an Appendix ... Thomas Perronet Thompson. taken its half HI , and so on till the half be taken successively as many times as C was doubled successively to make DG ; the last remainder AI will be less than C. For as many ...
To which is Added an Appendix ... Thomas Perronet Thompson. taken its half HI , and so on till the half be taken successively as many times as C was doubled successively to make DG ; the last remainder AI will be less than C. For as many ...
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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