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 26
... greater also than BCD ; much more then is the angle BDC greater than the angle : A B BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but it has been demonstrated to be greater than it ...
... greater also than BCD ; much more then is the angle BDC greater than the angle : A B BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but it has been demonstrated to be greater than it ...
Página 31
... greater than either of the interior opposite an- gles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it ... greater than the angle ECF ; therefore the angle ECD , that is ACD , is greater than BAE : In the same manner , if ...
... greater than either of the interior opposite an- gles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it ... greater than the angle ECF ; therefore the angle ECD , that is ACD , is greater than BAE : In the same manner , if ...
Página 32
... greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a ... greater ( 16. 1. ) then the interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD ...
... greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a ... greater ( 16. 1. ) then the interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD ...
Página 33
... greater - side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . For , if it be not greater , AC must either be ...
... greater - side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . For , if it be not greater , AC must either be ...
Página 34
... greater than the angle BAC . Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are greater than the third side , the two sides BA , AE of the triangle ABE are greater than BE . To each of these add EC ; therefore the ...
... greater than the angle BAC . Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are greater than the third side , the two sides BA , AE of the triangle ABE are greater than BE . To each of these add EC ; therefore the ...
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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