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 37
... angle BAC is not equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) to EF ; but it is not ; there- fore the angle BAC is not equal to the angle EDF ; neither is it less ; because then the base BC would be A D ...
... angle BAC is not equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) to EF ; but it is not ; there- fore the angle BAC is not equal to the angle EDF ; neither is it less ; because then the base BC would be A D ...
Page 38
... angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the ...
... angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the ...
Page 101
... angle BAD is the fifth part of two right angles . " For since each of the angles ABD and ADB is equal to twice the " angle BAD , they are together equal to four times BAD , and there- " fore all the three angles ABD , ADB , BAD , taken ...
... angle BAD is the fifth part of two right angles . " For since each of the angles ABD and ADB is equal to twice the " angle BAD , they are together equal to four times BAD , and there- " fore all the three angles ABD , ADB , BAD , taken ...
Page 128
... angles by the straight line AD . Therefore , if the angle , & c , Q. E. D. PROP . A. THEOR . If the exterior angle of a triangle be bisected by a straight line which ... angle ABC equal to the angle DCE , and the angle ACB 128 ELEMENTS.
... angles by the straight line AD . Therefore , if the angle , & c , Q. E. D. PROP . A. THEOR . If the exterior angle of a triangle be bisected by a straight line which ... angle ABC equal to the angle DCE , and the angle ACB 128 ELEMENTS.
Page 129
... equal to the angle DCE , and the angle ACB to the angle DEC , and consequently ( 32. 1. ) the angle BAC equal to the angle CDE . The sides about the equal angles of the triangles ABC , DCE are propor- tionals ; and those are the ...
... equal to the angle DCE , and the angle ACB to the angle DEC , and consequently ( 32. 1. ) the angle BAC equal to the angle CDE . The sides about the equal angles of the triangles ABC , DCE are propor- tionals ; and those are 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 BD THEOR third touches the circle triangle ABC triangle DEF wherefore