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 25
... side of the base . Therefore , the angles at the base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which sub ...
... side of the base . Therefore , the angles at the base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which sub ...
Σελίδα 26
... sides of the other each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having ...
... sides of the other each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having ...
Σελίδα 27
... sides which are terminated in one extremity of the base equal to one another , and likewise their sides terminated in the other extremity ; but this is impossible ( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the ...
... sides which are terminated in one extremity of the base equal to one another , and likewise their sides terminated in the other extremity ; but this is impossible ( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the ...
Σελίδα 30
... sides of AB , make the adjacent an- gles ABC , ABD equal together to two right angles . BD is in the same straight ... side of it , the angles ABC , ABE are together equal ( 13. 1. ) to two right an- gles ; but the angles ABC , ABD are ...
... sides of AB , make the adjacent an- gles ABC , ABD equal together to two right angles . BD is in the same straight ... side of it , the angles ABC , ABE are together equal ( 13. 1. ) to two right an- gles ; but the angles ABC , ABD are ...
Σελίδα 32
... side of every triangle has the greater angle opposite to it . Let ABC be a triangle of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . From AC , which is greater than AB , cut off ( 3 ...
... side of every triangle has the greater angle opposite to it . Let ABC be a triangle of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . From AC , which is greater than AB , cut off ( 3 ...
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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