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 σελίδες |
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Σελίδα 23
... angle BAC be also equal to the angle EDF : then shall the base BC be equal to the base EF ; and the triangle ABC to the tri- angle DEF ; and the other angles , to which the equal sides are op- AA B C E posite , shall be equal , each to ...
... angle BAC be also equal to the angle EDF : then shall the base BC be equal to the base EF ; and the triangle ABC to the tri- angle DEF ; and the other angles , to which the equal sides are op- AA B C E posite , shall be equal , each to ...
Σελίδα 24
... angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor ...
... angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor ...
Σελίδα 27
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
Σελίδα 32
... angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore if one side , & c ... BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII .
... angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore if one side , & c ... BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII .
Σελίδα 34
... angle BAC . A E D 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 sides BA , AC ...
... angle BAC . A E D 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 sides BA , AC ...
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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 definition 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 MDCCCXX 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