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
... cosine of any arc is to the 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 ...
... cosine of any arc is to the 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 ...
Página 223
... 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 of a table ; where the first column ...
... 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 of a table ; where the first column ...
Página 224
... , AC : AB :: R : tan . C ; but if C itself is not required , it is sufficient , having found tan . C by this proportion , to take from the Trigonometric Tables the cosine that corresponds to tan . C , 224 PLANE TRIGONOMETRY .
... , AC : AB :: R : tan . C ; but if C itself is not required , it is sufficient , having found tan . C by this proportion , to take from the Trigonometric Tables the cosine that corresponds to tan . C , 224 PLANE TRIGONOMETRY .
Página 225
... cosine that corresponds to tan . C , and then to compute CB from the proportion cos . C : R :: AC : CB . PROBLEM II . In an oblique angled triangle , of the three sides and three angles , any three being given , and one of these three ...
... cosine that corresponds to tan . C , and then to compute CB from the proportion cos . C : R :: AC : CB . PROBLEM II . In an oblique angled triangle , of the three sides and three angles , any three being given , and one of these three ...
Página 228
... cosine nearly equal to the radius , ) the angle itself cannot be very accurately found . If , for in- stance , the ... cosine of the arc BD , and CG the cosine of the half of BD ; whence the cosine of the half of any arc BD , of a circle ...
... cosine nearly equal to the radius , ) the angle itself cannot be very accurately found . If , for in- stance , the ... cosine of the arc BD , and CG the cosine of the half of BD ; whence the cosine of the half of any arc BD , of a circle ...
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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