A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página xii
... true as those from which it has been deduced , and becomes in its turn a sure stepping - stone to still further results . So we are conducted steadily and surely , step by step , to the most remote and important consequences . From this ...
... true as those from which it has been deduced , and becomes in its turn a sure stepping - stone to still further results . So we are conducted steadily and surely , step by step , to the most remote and important consequences . From this ...
Página 26
... true and the other false . This principle justifies the 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 ...
... true and the other false . This principle justifies the 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 ...
Página 43
... true . Similarly it may be shown that if two quadrilaterals stand on the same base , and one is enclosed by the other , the perimeter of the inner figure is less than that of the outer figure . Ex . If O be a point within the triangle ...
... true . Similarly it may be shown that if two quadrilaterals stand on the same base , and one is enclosed by the other , the perimeter of the inner figure is less than that of the outer figure . Ex . If O be a point within the triangle ...
Página 59
... true of all rectilineal figures . The first is only true of convex figures which have no re - entrant angle , ie ,, no angle which is greater than two right angles . Let ABCDE be a concave figure having the re - entrant angle EDC ...
... true of all rectilineal figures . The first is only true of convex figures which have no re - entrant angle , ie ,, no angle which is greater than two right angles . Let ABCDE be a concave figure having the re - entrant angle EDC ...
Página 81
... true for all divisions of the lines , whether commensurable or not . 2. Because in Arithmetic and Algebra we proceed by general rules and processes without stopping to interpret each step of the operation . But one of the principal ...
... true for all divisions of the lines , whether commensurable or not . 2. Because in Arithmetic and Algebra we proceed by general rules and processes without stopping to interpret each step of the operation . But one of the principal ...
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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