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 |
Im Buch
Ergebnisse 1-5 von 34
Seite 3
... impossible consequence , the as- sumption cannot be true . This is the rationale [ or reasonable principle ] of the mode of proof im- properly called reductio ad absurdum , ' reduction to an absurdity . ' XXVII . The establishment of ...
... impossible consequence , the as- sumption cannot be true . This is the rationale [ or reasonable principle ] of the mode of proof im- properly called reductio ad absurdum , ' reduction to an absurdity . ' XXVII . The establishment of ...
Seite 5
... 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 right angle , the other two are necessarily less than right angles . The converse of which 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 right angle , the other two are necessarily less than right angles . The converse of which is ...
Seite 8
... impossible ; for the things by the hypothesis were equal to begin with . The assumption " , therefore , which involves this impossible consequence , cannot be true ; or one remainder cannot be greater than the other . And because one is ...
... impossible ; for the things by the hypothesis were equal to begin with . The assumption " , therefore , which involves this impossible consequence , cannot be true ; or one remainder cannot be greater than the other . And because one is ...
Seite 9
... impossible , for it is equal . The assumption " , therefore , cannot be true ; or the one magnitude , that was doubled , is not greater than the other ; and because one is not greater than the other , they are equal . And in like manner ...
... impossible , for it is equal . The assumption " , therefore , cannot be true ; or the one magnitude , that was doubled , is not greater than the other ; and because one is not greater than the other , they are equal . And in like manner ...
Seite 15
... impossible , for they are equal . The central distances , therefore , cannot be unequal ; that is , they are equal . PROPOSITION IV . THEOREM . - If a sphere be turned in any manner whatsoever about the centre which remains at rest ...
... impossible , for they are equal . The central distances , therefore , cannot be unequal ; that is , they are equal . PROPOSITION IV . THEOREM . - If a sphere be turned in any manner whatsoever about the centre which remains at rest ...
Andere Ausgaben - Alle anzeigen
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.