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
... kind is called a plane . From these , all the relations of straight lines and planes may be inferred . If in this there is any novelty and truth , it is surprising that a property which was the foundation of the Platonic notion of the ...
... kind is called a plane . From these , all the relations of straight lines and planes may be inferred . If in this there is any novelty and truth , it is surprising that a property which was the foundation of the Platonic notion of the ...
Σελίδα viii
... kind should be supposed to be founded on axioms ; and it is no answer to say , that in a particular case they were true . The Second Book of Euclid would be true , if the First existed only in the shape of the heads of the Propo ...
... kind should be supposed to be founded on axioms ; and it is no answer to say , that in a particular case they were true . The Second Book of Euclid would be true , if the First existed only in the shape of the heads of the Propo ...
Σελίδα xii
... kind . For the line itself has neither thickness nor breadth ; wherefore its extremity can have neither . And if the so - called extremity had length , it would not be the extremity , but part of the line . Thus the extremity of a line ...
... kind . For the line itself has neither thickness nor breadth ; wherefore its extremity can have neither . And if the so - called extremity had length , it would not be the extremity , but part of the line . Thus the extremity of a line ...
Σελίδα 1
... kind , [ that is to say , solids with solids , surfaces with surfaces , & c . ] , are called magnitudes . XIV . Magnitudes which if their boundaries were applied to one another , would coincide ; or might be made capable of doing so ...
... kind , [ that is to say , solids with solids , surfaces with surfaces , & c . ] , are called magnitudes . XIV . Magnitudes which if their boundaries were applied to one another , would coincide ; or might be made capable of doing so ...
Σελίδα 5
... kind . For example , if the original proposition is as in the last article ; the contrary of this proposition is , that if of equals one be less than some thing else , the rest are severally less than the same . SCHOLIUM . Neither the ...
... kind . For example , if the original proposition is as in the last article ; the contrary of this proposition is , that if of equals one be less than some thing else , the rest are severally less than the same . SCHOLIUM . Neither the ...
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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