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 22
... one continuous hard body , let the * INTERC . 2. whole be turned * about B , in such קוווד E -B sort that the sphere A shall be moved to a new situation having no 23 PROP . VII . part in common with the 22 INTERCALARY BOOK .
... one continuous hard body , let the * INTERC . 2. whole be turned * about B , in such קוווד E -B sort that the sphere A shall be moved to a new situation having no 23 PROP . VII . part in common with the 22 INTERCALARY BOOK .
Σελίδα 23
... common with the old , as for instance to the situation of the sphere whose centre is C ; and let the line then described by the point A from A to C , be afterwards turned about B in various * INTERC.3 . directions as called for , till a ...
... common with the old , as for instance to the situation of the sphere whose centre is C ; and let the line then described by the point A from A to C , be afterwards turned about B in various * INTERC.3 . directions as called for , till a ...
Σελίδα 30
... common surface by a common point N , these lines will coincide with one another , and the surfaces inclosed by them will coincide throughout . Also if on the one sphere the points M , N , O , P , do not coincide with the same points on ...
... common surface by a common point N , these lines will coincide with one another , and the surfaces inclosed by them will coincide throughout . Also if on the one sphere the points M , N , O , P , do not coincide with the same points on ...
Σελίδα 31
... common centre A , and the whole surfaces HOPLNM and IOPKNM will continue to coincide throughout . Which having been done , let the spheres be returned to their original situation . Wherefore the two surfaces HOPLNM and IOPKNM which ...
... common centre A , and the whole surfaces HOPLNM and IOPKNM will continue to coincide throughout . Which having been done , let the spheres be returned to their original situation . Wherefore the two surfaces HOPLNM and IOPKNM which ...
Σελίδα 32
... common , must be in that line . And if they do not cut , but still have a + INTERC.5 . point in common ; they touch in that point , and † that only . PROPOSITION XII . See Note . THEOREM . - Two straight lines , which are not in one and ...
... common , must be in that line . And if they do not cut , but still have a + INTERC.5 . point in common ; they touch in that point , and † that only . PROPOSITION XII . See Note . THEOREM . - Two straight lines , which are not in one and ...
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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