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 213
... sine of a quadrant , or of a right angle , is equal to the radius . COR . 2. The sine of an arc is half the chord of twice that arc : this is evi- dent by producing the sine of any arc till it cut the circumference . H K L E 14 5. The ...
... sine of a quadrant , or of a right angle , is equal to the radius . COR . 2. The sine of an arc is half the chord of twice that arc : this is evi- dent by producing the sine of any arc till it cut the circumference . H K L E 14 5. The ...
Página 214
... sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . 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 ...
... sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . 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 ...
Página 215
... sine of the angle C , ( Def . 4. ) ; therefore CB : BAR sin . C. B G D 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 ...
... sine of the angle C , ( Def . 4. ) ; therefore CB : BAR sin . C. B G D 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 ...
Página 216
... sinę of the arc AC ; and BH or LK 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 and AB , because AD is equal to AC , and BC is ...
... sinę of the arc AC ; and BH or LK 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 and AB , because AD is equal to AC , and BC is ...
Página 220
... sine 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 two sides ; 4AB.AC : ( BC + ( AB — AC ) ) × ( BC— ( AB — AC ) ) : : R2 : ( sin.BAC ) 2 ...
... sine 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 two sides ; 4AB.AC : ( BC + ( AB — AC ) ) × ( BC— ( AB — AC ) ) : : R2 : ( sin.BAC ) 2 ...
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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