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 222
... sine , as the radius to the tangent of the same arc ; therefore , ( AB + AC + BC ) ( AB + AC - BC ) : ( BČ + ( AB − AC ) ) BC— ( AB — AC ) ) :: R2 : ( tan . BAC ) 2 ; and √ ( AB + AC + BC ) ( AB + AC - BC : √ ( BC + AB - AC ) ( BC ...
... sine , as the radius to the tangent of the same arc ; therefore , ( AB + AC + BC ) ( AB + AC - BC ) : ( BČ + ( AB − AC ) ) BC— ( AB — AC ) ) :: R2 : ( tan . BAC ) 2 ; and √ ( AB + AC + BC ) ( AB + AC - BC : √ ( BC + AB - AC ) ( BC ...
Página 223
... sine of any of the acute angles is the cosine of the other . This problem admits of several cases , and the solutions , or rules for cal- culation , which all depend on the first Proposition , may be conveniently exhibited in the form ...
... sine of any of the acute angles is the cosine of the other . This problem admits of several cases , and the solutions , or rules for cal- culation , which all depend on the first Proposition , may be conveniently exhibited in the form ...
Página 225
... sine being found by the proportion above , the angle belonging to that sine may either be that which is found in the tables , or it may be the supplement of it ( Cor . def . 4. ) . This ambiguity , however , does not arise from any ...
... sine being found by the proportion above , the angle belonging to that sine may either be that which is found in the tables , or it may be the supplement of it ( Cor . def . 4. ) . This ambiguity , however , does not arise from any ...
Página 226
... sine is the same with the sine of the sum of ABC and ACB . But BAC ' is the difference of the angles ACB , ABC : for it is the diffe- rence of the angles AC'C and ABC , because AC'C , that is , ACC ' is equal to the sum of the angles ...
... sine is the same with the sine of the sum of ABC and ACB . But BAC ' is the difference of the angles ACB , ABC : for it is the diffe- rence of the angles AC'C and ABC , because AC'C , that is , ACC ' is equal to the sum of the angles ...
Página 228
... sine or cosine of such an angle is given ( that is , a sine or cosine nearly equal to the radius , ) the angle itself cannot be very accurately found . If , for in- stance , the natural sine .9998500 is given , it will be immediately ...
... sine or cosine of such an angle is given ( that is , a sine or cosine nearly equal to the radius , ) the angle itself cannot be very accurately found . If , for in- stance , the natural sine .9998500 is given , it will be immediately ...
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Términos y frases comunes
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