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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Resultat 6-10 av 11
Side 60
... triangle ACB . Join CD ; + INTERC.12 . and prolong † AC and AD , to E and F. Cor . 6 . E F D A B Because AD is equal ... equilateral triangle was required to be described ; and consequently no more equilateral triangles than one could ...
... triangle ACB . Join CD ; + INTERC.12 . and prolong † AC and AD , to E and F. Cor . 6 . E F D A B Because AD is equal ... equilateral triangle was required to be described ; and consequently no more equilateral triangles than one could ...
Side 62
... equilateral triangle ACB , + INTERC.12 . and prolong † CA , CB , to D and E. Upon AB and on the other side of it , describe another equilateral triangle AFB . Because the angles 1.5 . Cor.1 . BAD and ABE are equal to one another , and ...
... equilateral triangle ACB , + INTERC.12 . and prolong † CA , CB , to D and E. Upon AB and on the other side of it , describe another equilateral triangle AFB . Because the angles 1.5 . Cor.1 . BAD and ABE are equal to one another , and ...
Side 68
... equilateral triangle DFE on the side remote from A ; whereupon may be shown ( as in Prop . IX ) that the point F ... triangles DAF , EAF , the two sides AD , AF are equal to the two sides AE , AF respectively . Also the third side DF is ...
... equilateral triangle DFE on the side remote from A ; whereupon may be shown ( as in Prop . IX ) that the point F ... triangles DAF , EAF , the two sides AD , AF are equal to the two sides AE , AF respectively . Also the third side DF is ...
Side 130
... triangle ABC to the triangle ACB as proposed above . The readiest way of seeing the truth of this , is to imagine BF ... equilateral and equiangular hexagon in a given circle . PROP . VII . — BOOK I. The sides terminated in the first ...
... triangle ABC to the triangle ACB as proposed above . The readiest way of seeing the truth of this , is to imagine BF ... equilateral and equiangular hexagon in a given circle . PROP . VII . — BOOK I. The sides terminated in the first ...
Side 141
... triangle are greater than a right angle and a half ; for if they were equal to this , the angles of an equilateral and equiangular oktagon would be right angles , and the fifth straight line in the series proposed would never meet the ...
... triangle are greater than a right angle and a half ; for if they were equal to this , the angles of an equilateral and equiangular oktagon would be right angles , and the fifth straight line in the series proposed would never meet the ...
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.