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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Página 83
To draw a tangent to any point in a circular arc , without finding the centre . From B the given point , take two equal distances BC , CD on the arc ; join BD , and draw the chords BC , CD : make the angle CBG = CBD , and the straight ...
To draw a tangent to any point in a circular arc , without finding the centre . From B the given point , take two equal distances BC , CD on the arc ; join BD , and draw the chords BC , CD : make the angle CBG = CBD , and the straight ...
Página 149
Upon the given line AB as a diameter , describe a semi- circle at the extremity of the diameter draw the tangent AD equal to the side of the square C ; through the point D , and the centre O , draw the D A E FB secant DF ; then will DE ...
Upon the given line AB as a diameter , describe a semi- circle at the extremity of the diameter draw the tangent AD equal to the side of the square C ; through the point D , and the centre O , draw the D A E FB secant DF ; then will DE ...
Página 213
A straight line AE touching the circle at A , one extremity of the arc AC , and meeting the diameter BC , which passes through C the other extremity , is called the Tangent of the arc AC , or of the angle ABC COR . The tangent of half a ...
A straight line AE touching the circle at A , one extremity of the arc AC , and meeting the diameter BC , which passes through C the other extremity , is called the Tangent of the arc AC , or of the angle ABC COR . The tangent of half a ...
Página 214
therefore , if tables be constructed , exhibiting in numbers the sines , tan- gents , secants , and versed sines of certain angles to a given radius , they will exhibit the ratios of the sines , tangents , & c . of the same angles to ...
therefore , if tables be constructed , exhibiting in numbers the sines , tan- gents , secants , and versed sines of certain angles to a given radius , they will exhibit the ratios of the sines , tangents , & c . of the same angles to ...
Página 215
... FE A and since the angle at C is common to the triangles CBA , CGE , these triangles are equiangular , wherefore CA : AB :: CE EG ; but CE is the radius , and EG the tangent of the angle C ; therefore , CA : AB :: R : tan . C. COR .
... FE A and since the angle at C is common to the triangles CBA , CGE , these triangles are equiangular , wherefore CA : AB :: CE EG ; but CE is the radius , and EG the tangent of the angle C ; therefore , CA : AB :: R : tan . C. COR .
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Términos y frases comunes
ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid spherical square straight line taken tangent THEOR third touch triangle ABC wherefore whole
Información bibliográfica
| Título | 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 |
| Autor | John Playfair |
| Edición | 6 |
| Editor | W.E. Dean, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |