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 sider |
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Side vi
... whole being turned about the two centres , shall be without change of place ; and if this be extended to imagining one sphere to increase continuously in magnitude and the other to decrease , the line described by their point of contact ...
... whole being turned about the two centres , shall be without change of place ; and if this be extended to imagining one sphere to increase continuously in magnitude and the other to decrease , the line described by their point of contact ...
Side vii
... whole with the easiest parts always foremost and the Planes in the Eleventh Book . But if she has not , or till somebody can establish that she has , there seems to be no cause why bad reasoning should be admitted for the sake of a ...
... whole with the easiest parts always foremost and the Planes in the Eleventh Book . But if she has not , or till somebody can establish that she has , there seems to be no cause why bad reasoning should be admitted for the sake of a ...
Side viii
... whole therefore it may be an interesting question in what place a geometer would be warranted in saying , ' I could have proved these preliminaries , but it would have been necessary to disturb the order which directs that lines be ...
... whole therefore it may be an interesting question in what place a geometer would be warranted in saying , ' I could have proved these preliminaries , but it would have been necessary to disturb the order which directs that lines be ...
Side ix
... whole to be greater than its part , has been omitted as amounting , after the explanation of the terms greater ' and ' less ' introduced from Euclid's Book of Data , to no more than the proposition that the greatest is greatest . ' In ...
... whole to be greater than its part , has been omitted as amounting , after the explanation of the terms greater ' and ' less ' introduced from Euclid's Book of Data , to no more than the proposition that the greatest is greatest . ' In ...
Side 2
... to be equal to the other by the hypothesis . For that they are equal , is the original supposition or groundwork on which the whole question proceeds . See Note . XXIII . When a thing is said 3 bis EUCLID'S Elements .
... to be equal to the other by the hypothesis . For that they are equal , is the original supposition or groundwork on which the whole question proceeds . See Note . XXIII . When a thing is said 3 bis EUCLID'S Elements .
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... Thomas Perronet Thompson Uten tilgangsbegrensning - 1833 |
Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Side 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 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.
Side 72 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 70 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.