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
... rest , the point of contact remains unmoved . Hence if about two assigned points be described a succession of spheres touching one another , any number of intermediate points may be determined that shall be desired , which , on the ...
... rest , the point of contact remains unmoved . Hence if about two assigned points be described a succession of spheres touching one another , any number of intermediate points may be determined that shall be desired , which , on the ...
Σελίδα viii
... rests entirely on the impossibility of a certain line ceasing to cut a series of other lines during a continuous motion , in a way incapable of being supplied by any ... rest . The Axiom which declared the whole to be viii PREFACE .
... rests entirely on the impossibility of a certain line ceasing to cut a series of other lines during a continuous motion , in a way incapable of being supplied by any ... rest . The Axiom which declared the whole to be viii PREFACE .
Σελίδα ix
To which is Added an Appendix ... Thomas Perronet Thompson. rest . The Axiom which declared the whole to be greater than its part , has been omitted as amounting , after the explanation of the terms ' greater ' and ' less ' introduced ...
To which is Added an Appendix ... Thomas Perronet Thompson. rest . The Axiom which declared the whole to be greater than its part , has been omitted as amounting , after the explanation of the terms ' greater ' and ' less ' introduced ...
Σελίδα 5
... rest are severally greater than the same ; the negative of this proposition is , that if of equals one be not greater than some thing else , the rest are severally not greater than the same . XXXII . What is called the contrary of a ...
... rest are severally greater than the same ; the negative of this proposition is , that if of equals one be not greater than some thing else , the rest are severally not greater than the same . XXXII . What is called the contrary of a ...
Σελίδα 6
... rest are severally equal to the same . Let A and B be equal , and let B be equal to C. A shall also be equal to C. For A is equal to B , and C is equal to B ; therefore ( by Prop . I. above ) A and C are equal . COR . 2. If of equals ...
... rest are severally equal to the same . Let A and B be equal , and let B be equal to C. A shall also be equal to C. For A is equal to B , and C is equal to B ; therefore ( by Prop . I. above ) A and C are equal . COR . 2. If of equals ...
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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