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 34
... common as aforesaid , can be a straight line ; two straight lines , which are not in one and the same line , cannot have the common segment AB . And by parity of reasoning , the like may be proved in every other instance . Wherefore ...
... common as aforesaid , can be a straight line ; two straight lines , which are not in one and the same line , cannot have the common segment AB . And by parity of reasoning , the like may be proved in every other instance . Wherefore ...
Σελίδα 35
... common segment CB ; which is impos- sible . And in like manner , because BCA is a straight line , no point in CA will change its place . Wherefore no point in all the line AD will change its place ; and because no point in it changes ...
... common segment CB ; which is impos- sible . And in like manner , because BCA is a straight line , no point in CA will change its place . Wherefore no point in all the line AD will change its place ; and because no point in it changes ...
Σελίδα 39
... common to both , which is * impossible . And in the same Cor . 1. manner may be shown that there is no other point in the one surface , either within or without the line FJHK , which does not after transposition of the united spheres ...
... common to both , which is * impossible . And in the same Cor . 1. manner may be shown that there is no other point in the one surface , either within or without the line FJHK , which does not after transposition of the united spheres ...
Σελίδα 45
... common segment [ in the part wherein the two planes coincide ] . Each of which is impossible . END OF THE INTERCALARY BOOK . RECAPITULATION of matters and propositions which have been usually received PROP . XIV . 45.
... common segment [ in the part wherein the two planes coincide ] . Each of which is impossible . END OF THE INTERCALARY BOOK . RECAPITULATION of matters and propositions which have been usually received PROP . XIV . 45.
Σελίδα 48
... common segment . If any two points in one straight line coincide with two points in another , the two straight lines shall coincide with one another to the extent of the length that is common to both , and be one and the same straight ...
... common segment . If any two points in one straight line coincide with two points in another , the two straight lines shall coincide with one another to the extent of the length that is common to both , and be one and the same straight ...
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