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 |
From inside the book
Results 1-5 of 87
Page 8
... altitude of a zone or of a segment is the distance between the two parallel planes , which form the bases of the zone or segment . 15. Whilst the semicircle DAE ( Def . 1. ) revolving round its diameter DE , describes the sphere , any ...
... altitude of a zone or of a segment is the distance between the two parallel planes , which form the bases of the zone or segment . 15. Whilst the semicircle DAE ( Def . 1. ) revolving round its diameter DE , describes the sphere , any ...
Page 127
... altitude of the given triangle , draw a right line IL parallel to AB , and the point where this line cuts the circum- ference will determine the position of the vertical angle ; hence the sides DA and DB may be drawn . By Analysis ...
... altitude of the given triangle , draw a right line IL parallel to AB , and the point where this line cuts the circum- ference will determine the position of the vertical angle ; hence the sides DA and DB may be drawn . By Analysis ...
Page 161
... altitude and m the base of a rhomboid , we shall have a xm for the surface of this rhom- boid , ( Prop . VI , B. IV , El . Geom . ) therefore , reciprocally , a2 + a2b a + c this surface will represent a × m , or a2 + b c2 + ď3 In like ...
... altitude and m the base of a rhomboid , we shall have a xm for the surface of this rhom- boid , ( Prop . VI , B. IV , El . Geom . ) therefore , reciprocally , a2 + a2b a + c this surface will represent a × m , or a2 + b c2 + ď3 In like ...
Page 162
... altitude is a and base p . 4. Lastly , if the dimensions of the numerator exceed the dimensions of the denominator by three , the quantity expresses a solid , the construction of which may always be reduced to a parallelopiped . If ...
... altitude is a and base p . 4. Lastly , if the dimensions of the numerator exceed the dimensions of the denominator by three , the quantity expresses a solid , the construction of which may always be reduced to a parallelopiped . If ...
Page 167
... altitude , & c . , are known . ) It will be perceived that this question resolves itself into the determination of some point , G , in the altitude EF , through which a line AB , drawn parallel to HI , shall be equal to GF ; we may ...
... altitude , & c . , are known . ) It will be perceived that this question resolves itself into the determination of some point , G , in the altitude EF , through which a line AB , drawn parallel to HI , shall be equal to GF ; we may ...
Other editions - View all
Common terms and phrases
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.