A Course of Mathematics ...: Designed for the Use of the Officers and Cadets of the Royal Military College, Volume 2C. Glendinning, 1806 - Mathematics |
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Page 243
... axis EC , the greatest inscribed rectangle OC will be when OD bisects the base AC , or the subtangent DA the base , and the tangent AB is bisected at the point of contact O. = A ED B 246. The sines and cosines of two arcs ( BD , DG ) ...
... axis EC , the greatest inscribed rectangle OC will be when OD bisects the base AC , or the subtangent DA the base , and the tangent AB is bisected at the point of contact O. = A ED B 246. The sines and cosines of two arcs ( BD , DG ) ...
Page 248
... the frustum , and sup- pose the cone or pyramid to be com- pleted . Put the area of the base HB , that of the top DA , h = the height CO , and x = OV , CV being the axis . , H C Then 62 : { * :: ( h + 2 248 APPLICATION OF ALGEBRA.
... the frustum , and sup- pose the cone or pyramid to be com- pleted . Put the area of the base HB , that of the top DA , h = the height CO , and x = OV , CV being the axis . , H C Then 62 : { * :: ( h + 2 248 APPLICATION OF ALGEBRA.
Page 252
... axis . If the incident ray is indefinitely near the axis DA , then b may be taken r , and x becomes , or FC FA . Suppose the radius CO or r = 6 feet = 72 inches , aud OR 20 inches , then CR 69.166 inches nearly , = b ; whence CF37.47 ...
... axis . If the incident ray is indefinitely near the axis DA , then b may be taken r , and x becomes , or FC FA . Suppose the radius CO or r = 6 feet = 72 inches , aud OR 20 inches , then CR 69.166 inches nearly , = b ; whence CF37.47 ...
Page 255
... axis or transverse diameter is the line connecting the vertices . Thus CG is the axis of the ellipse ; and Gg that of the hyper- bola . But the axis of the parabola is infinite in length ; GO being a part of that axis . 262. The center ...
... axis or transverse diameter is the line connecting the vertices . Thus CG is the axis of the ellipse ; and Gg that of the hyper- bola . But the axis of the parabola is infinite in length ; GO being a part of that axis . 262. The center ...
Page 256
... axis CG , are equal at equal distances from the vertices C and G. Now suppose NO is the diameter of another circular section of the cone ; then IT ( in the plane of that circle , and also in that of the oblique section CPGTR ) will be ...
... axis CG , are equal at equal distances from the vertices C and G. Now suppose NO is the diameter of another circular section of the cone ; then IT ( in the plane of that circle , and also in that of the oblique section CPGTR ) will be ...
Other editions - View all
A Course of Mathematics, Vol. 1: Designed for the Use of the Officers and ... Isaac Dalby No preview available - 2018 |
A Course of Mathematics ...: Designed for the Use of the Officers and Cadets ... Isaac Dalby No preview available - 2016 |
Common terms and phrases
Arith arithmetical progression axis bisect body center of gravity center of oscillation center of percussion circle coefficients column completing the square consequently Corol cube cubic curve cylinder denominator denote depth descending described diameter difference direction distance divided divisor ellipse equal equation equilibrio example expression feet per second fluid force fraction fulcrum Geom given gives horizontal inches infinite lever logarithms motion multiplied nearly number of terms ordinate ounces parabola parallel pendulum perpendicular plane pressure proportional quadratic equation quotient radius ratio rectangle reduced respectively right angles SCHOLIUM shot sides sine specific gravity square root subtangent subtracted Suppose surds surface tangent theorem triangle velocity vertex vertical vulgar fraction weight whence whole number
Popular passages
Page 238 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page 55 - If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents.
Page 67 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 66 - Subtract the power from the given quantity, and divide the first term of the remainder by the...
Page 302 - Every body continues in its state of rest, or uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Page 116 - How much gold of 15, of 17, and of 22 carats fine, must be mixed with 5 oz. of 18 carats fine, so that the composition may be 20 carats fine ? Ans.
Page 134 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 94 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 23 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Page 39 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.