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 Trigonometry |
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Page 25
... 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- tend , or are opposite to them , are also equal to one another ...
... 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- tend , or are opposite to them , are also equal to one another ...
Page 26
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two 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 ...
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two 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 ...
Page 27
... 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 given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1 ...
... 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 given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1 ...
Page 30
... Q. E. D. L PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the oppo- site sides of it , make the adjacent angles together equal to two right angles , these two straight lines are in one and the ...
... Q. E. D. L PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the oppo- site sides of it , make the adjacent angles together equal to two right angles , these two straight lines are in one and the ...
Page 32
... Q. E. D. PROP . XVII . THEOR . Any two angles of a 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 . Produce BC to D ; and be- cause ACD is the ...
... Q. E. D. PROP . XVII . THEOR . Any two angles of a 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 . Produce BC to D ; and be- cause ACD is 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 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