A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página vii
... been very much simplified . But his object seems to have been to reduce his assumptions to the narrowest possible limits , and to demand nothing which he was able to prove . The result of this self - INTRODUCTION . vii.
... been very much simplified . But his object seems to have been to reduce his assumptions to the narrowest possible limits , and to demand nothing which he was able to prove . The result of this self - INTRODUCTION . vii.
Página viii
Euclides Charles MANSFORD. able to prove . The result of this self - imposed limitation is , that many of the constructions are very complicated even where the object to be attained is very simple ; as for example in prop . 3 , where ...
Euclides Charles MANSFORD. able to prove . The result of this self - imposed limitation is , that many of the constructions are very complicated even where the object to be attained is very simple ; as for example in prop . 3 , where ...
Página x
... results are then used to establish further and more complex truths , and so the process is continued until all the truths which constitute the science of geometry are demonstrated , and their relation to each other exhibited . In order ...
... results are then used to establish further and more complex truths , and so the process is continued until all the truths which constitute the science of geometry are demonstrated , and their relation to each other exhibited . In order ...
Página xi
... results arrived at by this method are true so long as the premisses are true . But in Euclid the assertions contained in the premisses are either , 1 : truths contained in the definitions and axioms , or 2 : truths which are given in ...
... results arrived at by this method are true so long as the premisses are true . But in Euclid the assertions contained in the premisses are either , 1 : truths contained in the definitions and axioms , or 2 : truths which are given in ...
Página xii
... result thus established is felt to be as 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 ...
... result thus established is felt to be as 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 ...
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
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 CBA axioms base BC BC is equal 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 Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop PROPOSITION 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