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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 60
... meet , if produced towards , B , D ; let them meet in G , and join AG : Then , because AC is equal to CE , the angle CEA is equal ( 5. 1. ) to the angle EAC ; and the angle ACE is a right angle ; therefore each of the angles CEA , EAC ...
... meet , if produced towards , B , D ; let them meet in G , and join AG : Then , because AC is equal to CE , the angle CEA is equal ( 5. 1. ) to the angle EAC ; and the angle ACE is a right angle ; therefore each of the angles CEA , EAC ...
Página 66
... meets the circle , and being produced does not cut it . II . Circles are said to touch one another , which meet , but do not cut one another . III . Straight lines are said to be equally dis- tant from the centre of a circle , when the ...
... meets the circle , and being produced does not cut it . II . Circles are said to touch one another , which meet , but do not cut one another . III . Straight lines are said to be equally dis- tant from the centre of a circle , when the ...
Página 68
... meet the circumference in F. Then , because DA is equal to DB , the an- gle DAB is equal ( 5. 1. ) to the angle DBA ; and because AE , a side of the triangle DAE , is produced to B , the angle DEB is greater ( 16. 1. ) than the angle ...
... meet the circumference in F. Then , because DA is equal to DB , the an- gle DAB is equal ( 5. 1. ) to the angle DBA ; and because AE , a side of the triangle DAE , is produced to B , the angle DEB is greater ( 16. 1. ) than the angle ...
Página 77
... meet the circle in C. Because DAF is a right angle , it is greater than the angle AFD ) ( 32. 1. ) ; but the greater angle of any triangle is subtended by the greater side ( 19 . 1. ) , therefore DF is greater than DA ; now DA is equal ...
... meet the circle in C. Because DAF is a right angle , it is greater than the angle AFD ) ( 32. 1. ) ; but the greater angle of any triangle is subtended by the greater side ( 19 . 1. ) , therefore DF is greater than DA ; now DA is equal ...
Página 78
... meet the circle in two , it would fall within it ( 2. 3. ) . Also it is evident that there can be but one straight line which touches the circle in the same point . PROP . XVII . PROB . To draw a straight line from a given point ...
... meet the circle in two , it would fall within it ( 2. 3. ) . Also it is evident that there can be but one straight line which touches the circle in the same point . PROP . XVII . PROB . To draw a straight line from a given point ...
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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 multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals 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 parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore