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 páginas |
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Página 29
... common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; but the base CF is also equal ( 11. Def . 1. ) to the base CG ; therefore the angle CHF is equal ( 8. 1. ) to the angle CHG ...
... common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; but the base CF is also equal ( 11. Def . 1. ) to the base CG ; therefore the angle CHF is equal ( 8. 1. ) to the angle CHG ...
Página 30
... common angle ABC , and the remain . ing angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be ...
... common angle ABC , and the remain . ing angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And in like manner , it may be ...
Página 31
... common angle AED , and the remaining angle CEA it A- -B E D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner may be demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c ...
... common angle AED , and the remaining angle CEA it A- -B E D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner may be demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c ...
Página 39
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . If a ...
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . If a ...
Página 42
... common ver- tex of the triangles : that is , ( 2 Cor . 15. 1. ) together with four right angles . Therefore , twice as many right angles as the figure has sides , are equal to all C E F A B the angles of the figure , together with four ...
... common ver- tex of the triangles : that is , ( 2 Cor . 15. 1. ) together with four right angles . Therefore , twice as many right angles as the figure has sides , are equal to all C E F A B the angles of the figure , together with four ...
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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