Higher Geometry and Trigonometry: Being the Third Part of a Series on Elementary and Higher Geometry, Trigonomentary and Mensuration : Containing Many Valuable Discoveries and Improvements in Mathematical Science, Especially in Relation to the Quadrature of the Circle, and Some Other Curves, as Well as the Cubature of Certain Curvilinear Solids : Designed as a Text-book for Collegiate and Academic Instruction, and as a Practical Compendium of Mensuration |
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Results 1-5 of 95
Page 49
... square of the sine of the given angle . To determine the tangent of twice a given angle . By formula ( e ) : tan . ( +6 ) = tan . + tan . B 1 = 1. -tan . tan . B 2 tan . tan . 20 = 1 — - tan . 2 Let 6 , the above becomes - ( i ) The ...
... square of the sine of the given angle . To determine the tangent of twice a given angle . By formula ( e ) : tan . ( +6 ) = tan . + tan . B 1 = 1. -tan . tan . B 2 tan . tan . 20 = 1 — - tan . 2 Let 6 , the above becomes - ( i ) The ...
Page 92
... square , cube , & c . these must of course be divided by R2 R3 , & c . As observed above , R may be any given number whatever , the number usually employed in the ordinary tables being 10 " , and therefore log . R = 10 Take as an ...
... square , cube , & c . these must of course be divided by R2 R3 , & c . As observed above , R may be any given number whatever , the number usually employed in the ordinary tables being 10 " , and therefore log . R = 10 Take as an ...
Page 129
... square of the sine and versed sine of an arc , is equal to the square of double the sine of half the arc . Ex . 7. Demonstrate that the sine of an arc is a mean pro- portional between half the radius and the versed sine of dou- ble the ...
... square of the sine and versed sine of an arc , is equal to the square of double the sine of half the arc . Ex . 7. Demonstrate that the sine of an arc is a mean pro- portional between half the radius and the versed sine of dou- ble the ...
Page 161
... square . If , for example , the quan- a2 + a2 b tity to be constructed be a + c a2 + ab a + c Now a + ab a + c is easily it may be considered as a x constructed , after what has been laid down , by considering it a + b a + c of the line ...
... square . If , for example , the quan- a2 + a2 b tity to be constructed be a + c a2 + ab a + c Now a + ab a + c is easily it may be considered as a x constructed , after what has been laid down , by considering it a + b a + c of the line ...
Page 165
... and , that , in a right angled triangle the square of the hypothenuse is equivalent to the sum of the squares of 15 ALGEBRA TO GEOMETRY . 165 Geometrical Questions, the modes of forming Equations therefrom, and their Solutions,
... and , that , in a right angled triangle the square of the hypothenuse is equivalent to the sum of the squares of 15 ALGEBRA TO GEOMETRY . 165 Geometrical Questions, the modes of forming Equations therefrom, and their Solutions,
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abscissa altitude arithmetical progression axes base bisected chord circle circular circular segment circumference cone conjugate construction convex surface corresponding cosec cosine cylinder described diameter distance divided draw drawn ellipse equal to half equation expression feet formed formula frustum Geom geometrical given height hence hyperbola inches infinite series latus rectum length logarithm major axis multiplied opposite ordinates parabola parallel parallelogram perpendicular plane portion prism Prop PROPOSITION pyramid quadrant quadrature quantity radii radius ratio rectangle represent revoloidal surface right angles Scholium sector segment sides similar similar triangles sine solidity specific gravity sphere spherical triangle spheroid spindle square straight line tangent THEOREM tion trian triangle ABC trigonometrical ungula versed sine vertex vertical virtual centre whence
Popular passages
Page 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 81 - N .-. by definition, x — x" is the logarithm of ^ ; that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the nth power. N"=a".
Page 68 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 7 - The radius of a sphere is a straight line, drawn from the centre to any point of the surface ; the diameter, or axis, is a line passing through this centre, and terminated on both sides by the surface.
Page 138 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 8 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 27 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 78 - In a system of logarithms all numbers are considered as the powers of some one number, arbitrarily chosen, which is called the base of the system, and the exponent of that power of the base which is equal to any given number, is called the logarithm of that number. Thus, if a be the base of a system of logarithms, N any number, and x such that N = a* then x is called the logarithm of N in the system whose base is a.