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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Page xiii
... cosines of arches , which are the ounda- tion of those applications of Trigonometry lately in- troduced , with so much advantage , into the higher Geometry . In the Spherical Trigonometry , the rules for pre- venting the ambiguity of ...
... cosines of arches , which are the ounda- tion of those applications of Trigonometry lately in- troduced , with so much advantage , into the higher Geometry . In the Spherical Trigonometry , the rules for pre- venting the ambiguity of ...
Page 225
... 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 the same angle ; CLor BD is the co- sine , HK the cotangent , and BK 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 the same angle ; CLor BD is the co- sine , HK the cotangent , and BK the ...
Page 227
... 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 . FDK = cotan . DFK , because DFK 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 . FDK = cotan . DFK , because DFK is the ...
Page 230
... cosine of the angle included by the two sides . Let ABC be any triangle , 2AB.BC is to the difference between AB + BC2 and AC as radius to cos . B. A From A draw AD perpendicular to BC , and ( 12. and 13. 2. ) the difference between the ...
... cosine of the angle included by the two sides . Let ABC be any triangle , 2AB.BC is to the difference between AB + BC2 and AC as radius to cos . B. A From A draw AD perpendicular to BC , and ( 12. and 13. 2. ) the difference between the ...
Page 231
... 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 great- er of the other two sides , 4AB.AC : ( AB + AC + BC ) ( AB + AC - BC ) :: R2 : ( cos . BAC ) ...
... 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 great- er of the other two sides , 4AB.AC : ( AB + AC + BC ) ( AB + AC - BC ) :: R2 : ( cos . BAC ) ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition 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 MDCCCXX 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