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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 232
... ( BC + ( AB -AC ) ) ( BC- ( AB - AC ) ) :: ( cos . BAC ) : ( sin . 1 BAC ) . But the cosine of any arch is to the sine , as the radius to the tangent of the same arch ; therefore , ( AB + AC 232 PLANE TRIGONOMETRY : N ...
... ( BC + ( AB -AC ) ) ( BC- ( AB - AC ) ) :: ( cos . BAC ) : ( sin . 1 BAC ) . But the cosine of any arch is to the sine , as the radius to the tangent of the same arch ; therefore , ( AB + AC 232 PLANE TRIGONOMETRY : N ...
Página 234
... sine of any of the acute an- gles is the cosine of the other . This problem admits of several cases , and the solutions , or rules for calculation , which all depend on the first Proposition , may be conve- niently exhibited in the form ...
... sine of any of the acute an- gles is the cosine of the other . This problem admits of several cases , and the solutions , or rules for calculation , which all depend on the first Proposition , may be conve- niently exhibited in the form ...
Página 236
... 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 supple- ment 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 supple- ment of it , ( Cor . def . 4. ) . This ambiguity , however , does not arise from any ...
Página 237
... sine is the same with the sine of the sum of ABC and ACB . But BAC ' is the difference of the the angles ACB , ABC ; for it is the difference of the angles ACC and ABC , because ACC , that is ACC is equal to the sum of the angles ABC ...
... sine is the same with the sine of the sum of ABC and ACB . But BAC ' is the difference of the the angles ACB , ABC ; for it is the difference of the angles ACC and ABC , because ACC , that is ACC is equal to the sum of the angles ABC ...
Página 239
... sine or co- sine 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 instance , the natural sine .9998500 is given , it will be immediately ...
... sine or co- sine 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 instance , the natural sine .9998500 is given , it will be immediately ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore