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
... opposite sides of AB , make the adjacent an- gles ABC , ABD equal together to two right angles . BD is in the same straight line with CB . For if BD be not in the same straight line with CB , let BE be in the same straight line with it ...
... opposite sides of AB , make the adjacent an- gles ABC , ABD equal together to two right angles . BD is in the same straight line with CB . For if BD be not in the same straight line with CB , let BE be in the same straight line with it ...
Página 31
... opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite an- gles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and ...
... opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite an- gles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and ...
Página 32
... opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal ( 13. 1 ) to two right angles ; therefore the angles ABC , BCA are less ...
... opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal ( 13. 1 ) to two right angles ; therefore the angles ABC , BCA are less ...
Página 33
... 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 equal to AB , or less than it ; it is not ...
... 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 equal to AB , or less than it ; it is not ...
Página 34
... opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than the ...
... opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than 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