Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página viii
... books of EUCLID . There are , however , a few others , which , though less considerable , it is hoped may in some degree facilitate the study of the elements . Such are those made on the definitions in the first Book , and viii PREFACE .
... books of EUCLID . There are , however , a few others , which , though less considerable , it is hoped may in some degree facilitate the study of the elements . Such are those made on the definitions in the first Book , and viii PREFACE .
Página ix
... definitions in the first Book , and particularly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third ...
... definitions in the first Book , and particularly on that of a straight line . A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily some of the properties of parallel lines . In the third ...
Página xvi
... ; and that , as he has not been careful in laying the foundation , he will never be success- ful in raising the superstructure . COLLEGE OF EDINBURGH , Dec. 1 , 1813 . ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . I. " xvi PREFACE .
... ; and that , as he has not been careful in laying the foundation , he will never be success- ful in raising the superstructure . COLLEGE OF EDINBURGH , Dec. 1 , 1813 . ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . I. " xvi PREFACE .
Página 17
... DEFINITIONS . I. " A Point is that which has position , but not magnitude . " ( See Notes . ) II . A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the inter- " sections of one line with ...
... DEFINITIONS . I. " A Point is that which has position , but not magnitude . " ( See Notes . ) II . A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the inter- " sections of one line with ...
Página 22
... Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
... Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore