A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 26
... method of proof called the ' Indirect Demonstration , ' in which we estab- lish the truth of a proposition by showing that we cannot con- tradict it without being led to an absurd conclusion . Thus in this prop . 6 it is asserted that ...
... method of proof called the ' Indirect Demonstration , ' in which we estab- lish the truth of a proposition by showing that we cannot con- tradict it without being led to an absurd conclusion . Thus in this prop . 6 it is asserted that ...
Página 28
... methods , prop . 7 might have been ommitted . It follows from this proposition that the triangle is a rigid figure ; ie . , its sides cannot be forced into any other relative position . In first figure to the prop . , for example , the ...
... methods , prop . 7 might have been ommitted . It follows from this proposition that the triangle is a rigid figure ; ie . , its sides cannot be forced into any other relative position . In first figure to the prop . , for example , the ...
Página 32
... method of drawing a line at right angles to a given line from its extremity and without producing the line will be pointed out in the note to prop . 32 . Ex . Show how to find a point in a given line which shall be equi- distant from ...
... method of drawing a line at right angles to a given line from its extremity and without producing the line will be pointed out in the note to prop . 32 . Ex . Show how to find a point in a given line which shall be equi- distant from ...
Página 54
... method of supplying the defect is probably as simple as any other when the axiom is thus stated . " Two straight lines which cut one another cannot be both parallel to a third straight line . " With the help of this axiom we can now ...
... method of supplying the defect is probably as simple as any other when the axiom is thus stated . " Two straight lines which cut one another cannot be both parallel to a third straight line . " With the help of this axiom we can now ...
Página 81
... methods of proof can only apply when the lines are commensurable , whereas the propositions are true for all ... methods of the former were substituted for the latter , one of the principal advantages to be derived from a study of ...
... methods of proof can only apply when the lines are commensurable , whereas the propositions are true for all ... methods of the former were substituted for the latter , one of the principal advantages to be derived from a study of ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join less Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal