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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 20
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they ...
... common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they ...
Página 23
... common vertex of the triangles ; that is , ( 2 Cor . 8. 1. ) together with four right angles . Therefore , twice as many right angles as the figure has sides , are equal to all the angles of the figure , to- gether with four right ...
... common vertex of the triangles ; that is , ( 2 Cor . 8. 1. ) together with four right angles . Therefore , twice as many right angles as the figure has sides , are equal to all the angles of the figure , to- gether with four right ...
Página 26
... common to the two triangles ; therefore their other sides are equal , each to each , and the third angle of the one to the third angle of the other ( Th . 2. ) ; viz . the side AB to the side CD , and AC to BD , and the angle BAC equal ...
... common to the two triangles ; therefore their other sides are equal , each to each , and the third angle of the one to the third angle of the other ( Th . 2. ) ; viz . the side AB to the side CD , and AC to BD , and the angle BAC equal ...
Página 31
... common to the two triangles DAC , BAC , and the base DC likewise equal to the base BC , the angle DAC is equal ( 5. 1. ) to the angle BAC ; But DAC is a right angle ; therefore also BAC is a right angle . B PROBLEMS RELATING TO THE ...
... common to the two triangles DAC , BAC , and the base DC likewise equal to the base BC , the angle DAC is equal ( 5. 1. ) to the angle BAC ; But DAC is a right angle ; therefore also BAC is a right angle . B PROBLEMS RELATING TO THE ...
Página 33
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; but the base DF is also equal to the base EF ; there- fore the angle DAF is equal ( 5. 1. ) to the angle EAF wherefore ...
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; but the base DF is also equal to the base EF ; there- fore the angle DAF is equal ( 5. 1. ) to the angle EAF wherefore ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore