. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. Thus CH, which is thesecant of A B, is the cosecant of B D. 1045. From the above definitions follow some remarkable properties. 1. That an arc and its supplement have the same sine, tangent, and secant; but the twolatter, that is. the tangent and the secant, are accounted negative when the arc exceeds a (pia-draiu, or 90 degrees. II. Wlien the arc is 0, cr nothing, the secant then becomes theradius C A, which is the least it can be. As the arc incre
. An encyclopaedia of architecture, historical, theoretical, & practical. New ed., rev., portions rewritten, and with additions by Wyatt Papworth. Thus CH, which is thesecant of A B, is the cosecant of B D. 1045. From the above definitions follow some remarkable properties. 1. That an arc and its supplement have the same sine, tangent, and secant; but the twolatter, that is. the tangent and the secant, are accounted negative when the arc exceeds a (pia-draiu, or 90 degrees. II. Wlien the arc is 0, cr nothing, the secant then becomes theradius C A, which is the least it can be. As the arc increases from 0, the sines, tangents, andsecants all increase, till the arc becomes a whole quailrant ; and then the sine is thegreatest it can be, being equal to the radius of the circle; under which circumstance thetangent and secant are infinite. III. In every arc AB, the versed sine AF, and thecosine BKor CF, are together equal to the radius of the circle. The radius CA, thetangent AH, and the secant CH, form a right-anged triiinge CAH. Again, the radius,sine, and cosine form another right-angled triangle CBF or CBK. So alao the radius,. Chap. I. PLANE TRIGONOMETRY. 297 cutanjieiit, and cosecant form a right-angled triangle CDL. All these right-angled trianglesare similar to each other. 1046. The sine, tangent, or secant of an angle is tliesine, tangent, or secant of the arc by which the angle ismeasured, or of the degrees. &c. in the same arc or method of constructing the scales of chords, ,tangents, and secants engraved on mathematical instru-ments is shown in the annexed figure. 1047. A trigonometrical canon {fig. .396.) is a tablewherein is given tlie length of the sine, tangent, andsecant to every degree and minute of the (|uadrant,compared with the radius, which is expressed by imityor 1 with any number of ciphers. The logarithms, more-over, of these sines, tangents, and secants, are tabulated, sothat trigonometrial calculations are performed by onlyad
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