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 27
... triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC ...
... triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC ...
Σελίδα 28
... triangle ABC , and bisect ( 9. 1. ) the angle ACB by the straight line CD . AB is cut into two equal parts in the point D. C Because AC is equal to CB , and CD common to the two triangles ACD , BCD : the two sides AC , CD , are equal to ...
... triangle ABC , and bisect ( 9. 1. ) the angle ACB by the straight line CD . AB is cut into two equal parts in the point D. C Because AC is equal to CB , and CD common to the two triangles ACD , BCD : the two sides AC , CD , are equal to ...
Σελίδα 31
... triangle be produced , the exterior angle is greater than either of the interior , 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 ...
... triangle be produced , the exterior angle is greater than either of the interior , 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 ...
Σελίδα 32
... triangle are together 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 ...
... triangle are together 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 ...
Σελίδα 33
... triangle is subtended by the 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 ...
... triangle is subtended by the 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 ...
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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