## A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |

### Dentro del libro

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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

... 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

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

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**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

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**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

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**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

ABCD AC is equal alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal apply axioms base BC bisect BOOK called centre circle coincide common Const construction definitions demonstration describe diagonals diameter difference divided double draw equal sides equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater Hence isosceles triangle join length less Let ABC meet method namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained rectilineal figure remainder result right angles side BC sides square on AC Take THEOREM things triangle ABC true truths twice the rectangle unequal units whole