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
... less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the ...
... less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the ...
Página 32
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . A Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the ...
... less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . A Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the ...
Página 33
... less than it ; it is not equal , because then the an- gle ABC would be equal ( 5. 1. ) to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the angle ABC would be less ( 18. 1. ) than ...
... less than it ; it is not equal , because then the an- gle ABC would be equal ( 5. 1. ) to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it less ; because then the angle ABC would be less ( 18. 1. ) than ...
Página 34
... less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
... less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC , to the point D within it ; BD and DC are less ...
Página 37
... less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; there- fore the angle BAC is not less than the angle EDF ; and it was shewn that it is not equal to it : therefore A B ! E C D F the angle BAC ...
... less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; there- fore the angle BAC is not less than the angle EDF ; and it was shewn that it is not equal to it : therefore A B ! E C D F the angle BAC ...
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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 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