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 ... |
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Page v
... Lines without recourse to any principle not grounded on previous ... straight line and plane . - 6 It had been stated , about the time when the circumstances were ... equal parts by means of circles only . ' But this sufficed to indicate ...
... Lines without recourse to any principle not grounded on previous ... straight line and plane . - 6 It had been stated , about the time when the circumstances were ... equal parts by means of circles only . ' But this sufficed to indicate ...
Page vi
... the other to decrease , the line described by their point of contact will be without change of place throughout ; such a line is called a straight line . If two equal spheres be placed touching one another externally , and about the ...
... the other to decrease , the line described by their point of contact will be without change of place throughout ; such a line is called a straight line . If two equal spheres be placed touching one another externally , and about the ...
Page vii
... equal in complexity to anything in the succeeding Books . If this process is objected to as irregular , it may be a ... straight line from turning them about certain points . But there are others where the reasoning depends altogether on the ...
... equal in complexity to anything in the succeeding Books . If this process is objected to as irregular , it may be a ... straight line from turning them about certain points . But there are others where the reasoning depends altogether on the ...
Page ix
... Lines has been reduced in bulk to one 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 ... straight line of unlimited length which shall travel ...
... Lines has been reduced in bulk to one 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 ... straight line of unlimited length which shall travel ...
Page 1
... the same place , are said to coincide . The only way in which coincidence can ... lines or points may actually touch one another and coincide . But besides ... equal to the distance of C and D ; when if A and C were applied to one ...
... the same place , are said to coincide . The only way in which coincidence can ... lines or points may actually touch one another and coincide . But besides ... equal to the distance of C and D ; when if A and C were applied to one ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson No preview available - 2015 |
Common terms and phrases
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