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 30
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1. Ax . ) to one another ; therefore the angles CBE , EBD are equal to the an- gles DBA , ABC ; but CBE , EBD , are two right angles ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1. Ax . ) to one another ; therefore the angles CBE , EBD are equal to the an- gles DBA , ABC ; but CBE , EBD , are two right angles ...
Página 31
... demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the point of their ...
... demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the point of their ...
Página 32
... demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles ...
... demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles ...
Página 33
... than BC . In the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. E PROP . XXI . THEOR . If from the ends OF GEOMETRY . BOOK I. 333.
... than BC . In the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. E PROP . XXI . THEOR . If from the ends OF GEOMETRY . BOOK I. 333.
Página 34
... demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from the ends of , & c . Q. E. D. PROP . XXII . PROB . To construct a triangle of which the ...
... demonstrated that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle BAC . Therefore , if from the ends of , & c . Q. E. D. PROP . XXII . PROB . To construct a triangle of which the ...
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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