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 214
The radius is a mean proportional between the cosine and secant of any angle ABC ; or cos . ABC X sec . ABC = R2 , Since CD , AE are parallel , BD is to BC or BA , as BA to BE . l PROP . I. In a right angled plane triangle , as the ...
The radius is a mean proportional between the cosine and secant of any angle ABC ; or cos . ABC X sec . ABC = R2 , Since CD , AE are parallel , BD is to BC or BA , as BA to BE . l PROP . I. In a right angled plane triangle , as the ...
Página 216
BC . But DK is the sum of the sines of the arcs AB and AC ; and KC is the difference of the sines ; also BD is the sum of the arcs AB and AC , and BC the differonce of those arcs E Cor . 1. Because EL is the cosine of AC 816 PLANE ...
BC . But DK is the sum of the sines of the arcs AB and AC ; and KC is the difference of the sines ; also BD is the sum of the arcs AB and AC , and BC the differonce of those arcs E Cor . 1. Because EL is the cosine of AC 816 PLANE ...
Página 217
Because EL is the cosine of AC , and EH of AB , FK is the sum of these cosines , and KB their difference ; for FK = { FB + EL = EH + EL , and KB = LH = EH - EL . Now , FK : KB : : tan . FDK : tan . BDK ; and tan . DFK = cotan .
Because EL is the cosine of AC , and EH of AB , FK is the sum of these cosines , and KB their difference ; for FK = { FB + EL = EH + EL , and KB = LH = EH - EL . Now , FK : KB : : tan . FDK : tan . BDK ; and tan . DFK = cotan .
Página 219
In any triangle , twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides , and the square of the " base , as the radius to the cosine of the angle included by the two sides .
In any triangle , twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides , and the square of the " base , as the radius to the cosine of the angle included by the two sides .
Página 221
... as the square of the radius to the square of the cosine of half the angle included between the two sides of the triangle . Let ABC be a triangle , of which BC is the base , and AB the greater of the other two sides , 4AB.
... as the square of the radius to the square of the cosine of half the angle included between the two sides of the triangle . Let ABC be a triangle , of which BC is the base , and AB the greater of the other two sides , 4AB.
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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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