The elements of plane trigonometry |
Dentro del libro
Resultados 1-5 de 52
Página v
... equal to the radius 88 103. Comparison of the unit of measurement in the two methods of esti- mating the magnitude of an angle .................................... .. 88 104. Sin sin ( 2nπ0 ) , & c ... and similar formulæ for Cos 0 ...
... equal to the radius 88 103. Comparison of the unit of measurement in the two methods of esti- mating the magnitude of an angle .................................... .. 88 104. Sin sin ( 2nπ0 ) , & c ... and similar formulæ for Cos 0 ...
Página vi
... equal to the angle itself , very nearly ......... Cos 0 = 3. ( co√ = 1 · § . ( e® √ = 1 + € - 0 √ = 1 ) . + ε - 0√ = 1 ) . Sin 03.V - 1 . ( e - T _ 6-0 √ = ï ) . 101 102 104 104 106 118 . 107 1 Tan0 = · 20 √ T +1 119. GREGORIE'S ...
... equal to the angle itself , very nearly ......... Cos 0 = 3. ( co√ = 1 · § . ( e® √ = 1 + € - 0 √ = 1 ) . + ε - 0√ = 1 ) . Sin 03.V - 1 . ( e - T _ 6-0 √ = ï ) . 101 102 104 104 106 118 . 107 1 Tan0 = · 20 √ T +1 119. GREGORIE'S ...
Página 1
... equal to C ' B C that given line , and if from AB we have to take a given line , we must cut off from BA a part BC ' equal to the given line , and AC ' will be the required remainder . Let AB be represented by a , and BC by b , and make ...
... equal to C ' B C that given line , and if from AB we have to take a given line , we must cut off from BA a part BC ' equal to the given line , and AC ' will be the required remainder . Let AB be represented by a , and BC by b , and make ...
Página 2
... equal in magnitude to the dif- ference of the lines b and a ; which difference we see lies in c this case to the left of Ay . y B Hence , if a line be represented by a negative quantity , it is meant that it is measured from Ay in a ...
... equal in magnitude to the dif- ference of the lines b and a ; which difference we see lies in c this case to the left of Ay . y B Hence , if a line be represented by a negative quantity , it is meant that it is measured from Ay in a ...
Página 3
... equal to the given angle , and the whole BAE will be the angle required . And if it be required to take a given angle from BAC , CA must evidently move in the contrary direction till it come into a position E'A , such that < CAE ' is equal ...
... equal to the given angle , and the whole BAE will be the angle required . And if it be required to take a given angle from BAC , CA must evidently move in the contrary direction till it come into a position E'A , such that < CAE ' is equal ...
Otras ediciones - Ver todas
Términos y frases comunes
A₁ AC AC angle containing Asin base C₁ centre circle coefficient cosec cosines decimal determined Diff difference digit equal errors Eucl expression formulæ given goniometric functions greater Hence increment integer last Article less m₁ magnitude mantissa measured Napier's rules nearly negative number of seconds P₁ perpendicular plane triangle planes AOB polar triangle pole polygon positive proved quantity radius Regular Polyhedron right angles right-angled triangle S₁ secants shew shewn Similarly sin A sin sines sines and cosines small angle solid angle sphere spherical excess spherical triangle SPHERICAL TRIGONOMETRY subtended subtraction tabular logarithmic tangents THEOREM triangle ABC triangle whose sides TRIGONOMETRY versin Wherefore π π
Pasajes populares
Página 141 - Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number.
Página 10 - Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle.
Página 56 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation. The operation of finding the unknown parts is called the solution of the triangle.
Página 57 - ... the three interior angles of a triangle are together equal to two right angles.
Página 12 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 143 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 27 - For example, let it be required to prove the formula sin ( A - B) = sin A. cos В - cos A. sin В from the annexed figure, where ВАC' = A, and C'AD — В ; each angle being greater than a right angle.
Página 5 - ... stretched taut from one point to the other. The string will not lie on the parallel, but will evidently be in a plane which passes through the centre of the sphere. If the two points be on a meridian, the stretched string will lie on the meridian. By angular distance between two points on a sphere is meant the angle subtended at the centre of the sphere by the arc joining the given points. Thus in Fig. 4 the angle NOA is the angular distance of A from N.
Página 6 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Página 200 - Three circles whose radii are a, b, c touch each other externally ; prove that the tangents at the points of contact meet in a point whose distance from any one of them is (aba Nj a+b + cj 12.