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 24
... BC shall coincide with the base EF ( cor . def . 3 , ) , and shall be equal to it . Therefore also the whole ... side of the base shall also be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and ...
... BC shall coincide with the base EF ( cor . def . 3 , ) , and shall be equal to it . Therefore also the whole ... side of the base shall also be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and ...
Σελίδα 25
... side of the base . Therefore , the angles at the base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle ... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is ...
... side of the base . Therefore , the angles at the base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle ... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is ...
Σελίδα 27
... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the ... side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of ...
... BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the ... side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of ...
Σελίδα 30
... BC , BD upon the opposite sides of AB , make the adjacent an- gles ABC , ABD equal together to two right angles . BD ... side of it , the angles ABC , ABE are together equal ( 13. 1. ) to two right an- gles ; but the angles ABC ...
... BC , BD upon the opposite sides of AB , make the adjacent an- gles ABC , ABD equal together to two right angles . BD ... side of it , the angles ABC , ABE are together equal ( 13. 1. ) to two right an- gles ; but the angles ABC ...
Σελίδα 31
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite an- gles CBA , BAС ... side BC be bisected , it may be demonstrated that the OF GEOMETRY . BOOK I. 31.
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite an- gles CBA , BAС ... side BC be bisected , it may be demonstrated that the OF GEOMETRY . BOOK I. 31.
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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