Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1851 Excerpt: ...of the octant-lines, AN will be greater than PN, or the cosine will as to magnitude (without regard to sign) be greater than the sine; whereas for any angle, whose bounding line lies between DD ' and either of the octant-lines, PN will be greater than AN, or the sine will be greater than the cosine. Now sin.4 + cos, A is positive, (1) when sin is (+) and cos (+), that is, in the whole of the first quadrant; or (2) when sin is (+) and cos--), if sin cos, that is, in the former half of the second quadrant; or (3) when sin is (--) and cos (+), if cos sin, that is, in the latter half of the fourth quadrant: collecting which results, we may say that sin A + cos.4 = + V(l + sin 2.4), when A is an angle in the first quadrant, or in either of the two adjacent half-quadrants. Similarly, sin.4-f-cos A =--»J(1 + sm2A)y when A is an angle in the third quadrant, or in either of the two adjacent half-quadrants. Again, smA--cos.4 is positive, (1) when sin is (+) and cos (--), that is, in the whole of the second quadrant; or (2) when sin is (+) and cos (+), if sin cos, that is, in the latter half of the first quadrant; or (3) when sin is (--) and cos (--), if cos sin, that is, in the former half of the third quadrant: collecting which results, we may say that ein A--cos A = + V(l--sin21), when A is an angle in the second quadrant, or in either of the two adjacent half-quadrants. Similarly, sinA--cos.4 =--V(l--sin2.4), when A is an angle of the fourth quadrant, or in either of the two adjacent half-quadrants. It will be seen that each of these formulae holds good for 180 together, between alternate octant-lines, and that any pair of them, (namely, one for sinL + cos.4, and one for sin.4--cos.4,) holds good for 90 together, between successive lines of octants: that is, ...
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About the Author
John William Colenso was consecrated the first Bishop of Natal on 30th November 1853 and died at Bishopstowe in 1883. The publication of this Commentary on Romans in 1861 sparked a controversy over the legitimate lengths to which the Church could go in accommodating itself to African culture, with major consequences for church and society in South Africa. This remarkable book is now made available again in the hope that Colenso's courageous engagement with African culture may resonate with and inspire contemporary work on enculturation of the gospel.
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