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 213
H K AC , perpendicular to the diameter passing through the other extremity A , is called the Sine of the arc AC , or of the angle ABC , of which AC is the measure . I A D Cor . 1. The sine of a quadrant , or of a right angle , is equal ...
H K AC , perpendicular to the diameter passing through the other extremity A , is called the Sine of the arc AC , or of the angle ABC , of which AC is the measure . I A D Cor . 1. The sine of a quadrant , or of a right angle , is equal ...
Página 214
Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of the same angle : CL or BD is the cosine , HK the cotangent , and BK the cosecant of the angle ABC . Cor . 1.
Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of the same angle : CL or BD is the cosine , HK the cotangent , and BK the cosecant of the angle ABC . Cor . 1.
Página 215
Therefore , B CB : BA :: CD : DF ; but CD is the radius , and DF the sine of the angle C , ( Def . 4. ) ; therefore CB : BA :: R : sin . C. Also , because EG touches the circle in E , CEG is a right angle , and therefore equal to the ...
Therefore , B CB : BA :: CD : DF ; but CD is the radius , and DF the sine of the angle C , ( Def . 4. ) ; therefore CB : BA :: R : sin . C. Also , because EG touches the circle in E , CEG is a right angle , and therefore equal to the ...
Página 216
... or to the sine of the arc AC ; and BH or LK F being the sine of AB , DK is the sum of the sines of the arcs AC and AB , and CK is the difference of their sines ; DAB also is the sum of the arcs AC G ! A and AB , because AD is equal ...
... or to the sine of the arc AC ; and BH or LK F being the sine of AB , DK is the sum of the sines of the arcs AC and AB , and CK is the difference of their sines ; DAB also is the sum of the arcs AC G ! A and AB , because AD is equal ...
Página 220
... by the difference of the two sides , and the other the base diminished by the difference of the same sides , as the square of the radius to the square of the sine of half the angle included between the two sides of the triangle .
... by the difference of the two sides , and the other the base diminished by the difference of the same sides , as the square of the radius to the square of the sine of half the angle included between the two sides of the triangle .
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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 distance 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 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 |
| Editor | W. E. Dean, 1836 |
| Largo | 311 páginas |
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