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 Seiten |
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Seite iii
... Parallel Lines without recourse to any principle not grounded on previous demonstration . In the present Edition the part relating to Parallel Lines is reduced in bulk one half . TO WHICH IS ADDED AN APPENDIX Containing Notices of ...
... Parallel Lines without recourse to any principle not grounded on previous demonstration . In the present Edition the part relating to Parallel Lines is reduced in bulk one half . TO WHICH IS ADDED AN APPENDIX Containing Notices of ...
Seite v
... Parallel Lines without recourse to any principle not grounded on previous demonstration . On showing the results to some of the leading mathematicians at Cambridge , they replied by the remark , that they had always felt something to be ...
... Parallel Lines without recourse to any principle not grounded on previous demonstration . On showing the results to some of the leading mathematicians at Cambridge , they replied by the remark , that they had always felt something to be ...
Seite vii
... the reasoning depends altogether on the supposition of a continuity of motion ; as , notably , in the very pinch and nip of the argument on Parallel Lines in Prop . XXVIII D in the First Book , where the conclusion PREFACE . vii.
... the reasoning depends altogether on the supposition of a continuity of motion ; as , notably , in the very pinch and nip of the argument on Parallel Lines in Prop . XXVIII D in the First Book , where the conclusion PREFACE . vii.
Seite ix
... Parallel 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 to one another and make equal interior ...
... Parallel 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 to one another and make equal interior ...
Seite 82
... parallel . COR . 1. If a straight line falling upon two other straight lines which are both in the same plane , makes the alternate angles equal to one another , those two straight lines shall be parallel . For it has been shown in the ...
... parallel . COR . 1. If a straight line falling upon two other straight lines which are both in the same plane , makes the alternate angles equal to one another , those two straight lines shall be parallel . For it has been shown in the ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points 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 half the angle 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
Beliebte Passagen
Seite 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Seite 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Seite 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Seite 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Seite 72 - Any two sides of a triangle are together greater than the third side.
Seite 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Seite 103 - ... twice as many right angles as the figure has sides.
Seite 70 - Any two angles of a triangle are together less than two right angles.
Seite 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Seite 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.