## A Treatise on Plane and Spherical Trigonometry: With an Introduction, Explaining the Nature and Use of Logarithms. : Adapted to the Use of Students in Philosophy |

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againſt alſo angle oppoſite angled ſpherical triangle Anſwer arithmetic complement baſe becauſe caſe circle cofine common logarithms comp computation conſtant correſponding coſec coſine cotangent decimal different affections diſtance ecliptic equation expreſſed fides fimilar firſt firſt term given number greater than 90 hence hypothenuſe increaſe inſtance laſt leſs than 90 Let ABC meaſured multiply muſt negative index obſervations oppoſite angle perpendicular plane pole poſitive produćt Prop Propoſition quadrant quantity quotient r x coſ radius repreſent reſpectively reſult right angled ſpherical right angled triangle ſame affection ſecant ſecond ſee ſet ſhow ſides ſign ſignificant figure ſin ſine ſmall ſphere ſquare ſtands ſubſtituting ſubtract ſuch ſum ſun ſupplement ſuppoſe Tables tangent theſe thoſe triangle ABC true logarithm unity uſed whole numbers whoſe x fin

### Popular passages

Page 43 - The Circumference of every Circle is fuppofed to be divided into 360 equal Parts...

Page 44 - The difference of an arc from 90 degrees, or a quarter, is called its complement ; thus FC is the complement of CB. The chord of an arc is a line drawn from one extremity of the arc to the other ; thus CK is the chord of the arc CBK. The sine of an arc is a line drawn from one extremity of the arc perpendicular to the diameter passing through the other extremity ; thus CD is the sine of the arc CB, or angle CAB, which it measures ; and CE is the sine of the arc CF, or angle CAF...

Page 108 - ... equal to the radius of the sphere. 4. Through the centre of a sphere and any two points on the surface a plane can be drawn ; and only one plane can be drawn, except when the two points are the extremities of a diameter of the sphere, and then an infinite number of such planes can be drawn. Hence only one great circle can be drawn through two given points on the surface of a sphere, except when the points are the extremities of a diameter of the sphere. When only one great 'circle can be drawn...

Page 44 - The versed sine of an arc is that part of the diameter which is intercepted between the sine and the arc; as BD or BE.

Page 29 - To evolve by logarithms, divide the logarithm of the given number by the number denoting the root to be taken ; the quotient will be the logarithm of the root.

Page 2 - Multiply the logarithm of the root by the exponent of the power and the product is the logarithm of the power.

Page 30 - RULE. Multiply the logarithm of the number by the numerator of the fraction denoting the index, and divide the product by the denominator, and the quotient is the logarithm of the quantity required. But if the given...

Page 44 - ... 90° ; and the Supplement of an arc, or of an angle, is what it wants of 180°.

Page 44 - Hence, the arc MB is the complement of the arc MA, and the angle MCB is the complement of the angle MCA...

Page 3 - ... 4, 5, &c. The properties mentioned in the preceding article may be -verified in this series $ thus if we add together the logarithms of 10 and 1000, which are 1 and 3, we perceive, that their sum 4 is found directly under 10000, which is the product of the proposed numbers. 243. The logarithms of the intermediate numbers, between 1 and 10, 10 and 100, 100 and 1000, &c. can be found only by approximation. To obtain, for example, the logarithm of 2, we must resolve the equation (10).r = 2, by the...