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 viii
... true . The Second Book of Euclid would be true , if the First existed only in the shape of the heads of the Propo- sitions under the title of Axioms ; but this would make a most lame and imperfect specimen of reasoning . The ways in ...
... true . The Second Book of Euclid would be true , if the First existed only in the shape of the heads of the Propo- sitions under the title of Axioms ; but this would make a most lame and imperfect specimen of reasoning . The ways in ...
Side 2
... true , is called a Theorem . An operation which it is proposed to show how to perform , is called a Problem . And both are called by the title of Propositions . XIX . A Proposition dependent on some other that has been previously ...
... true , is called a Theorem . An operation which it is proposed to show how to perform , is called a Problem . And both are called by the title of Propositions . XIX . A Proposition dependent on some other that has been previously ...
Side 3
... true , without the other being true also ; is called a consequence . XXVI . When such preceding position is not known to be true , but is only assumed to be true for the purpose of trying its truth or falsehood by examination of the ...
... true , without the other being true also ; is called a consequence . XXVI . When such preceding position is not known to be true , but is only assumed to be true for the purpose of trying its truth or falsehood by examination of the ...
Side 4
... true in the instances in which experiment has actually been made . For example , a cooper knows that in every instance where he has tried it , the distance that went exactly round the rim of his cask at six times , was the distance to ...
... true in the instances in which experiment has actually been made . For example , a cooper knows that in every instance where he has tried it , the distance that went exactly round the rim of his cask at six times , was the distance to ...
Side 5
... true , till it has been demonstrated as a distinct proposition . For till this be done , it is impossible to know whether it is true or not . For example , it is shown in the sequel , that if one angle of a triangle is greater than a ...
... true , till it has been demonstrated as a distinct proposition . For till this be done , it is impossible to know whether it is true or not . For example , it is shown in the sequel , that if one angle of a triangle is greater than a ...
Andre utgaver - Vis alle
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.