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 22
... Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that C A is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
... Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that C A is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same ...
Página 52
... base BC , the angle DAC is equal ( 8. 1. ) to the angle BAC : But DAC is a right angle ; therefore also BAC is a right angle . There- fore , if the square , & c . Q. E. D. B C OF GEOMETRY . BOOK II . E DEFINITIONS . I. 52 ELEMENTS.
... base BC , the angle DAC is equal ( 8. 1. ) to the angle BAC : But DAC is a right angle ; therefore also BAC is a right angle . There- fore , if the square , & c . Q. E. D. B C OF GEOMETRY . BOOK II . E DEFINITIONS . I. 52 ELEMENTS.
Página 53
... DEFINITIONS . I. VERY right angled parallelogram , or rectangle , is said to be con- tained by any two of the straight lines which are about one of the right angles " Thus the right angled parallelogram AC is called the rectangle ...
... DEFINITIONS . I. VERY right angled parallelogram , or rectangle , is said to be con- tained by any two of the straight lines which are about one of the right angles " Thus the right angled parallelogram AC is called the rectangle ...
Página 65
... From this demonstration , it is manifest that the diameters of every parallelogram bisect one another . T OF GEOMETRY . BOOK III . DEFINITIONS . A. T OF GEOMETRY . BOOK II . 65 COR. From this demonstration, it is manifest that ...
... From this demonstration , it is manifest that the diameters of every parallelogram bisect one another . T OF GEOMETRY . BOOK III . DEFINITIONS . A. T OF GEOMETRY . BOOK II . 65 COR. From this demonstration, it is manifest that ...
Página 66
... DEFINITIONS . A. T HE radius of a circle is the straight line drawn from the centre to the circumference . I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are ...
... DEFINITIONS . A. T HE radius of a circle is the straight line drawn from the centre to the circumference . I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are ...
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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