A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and BonnycastleF. Nichols, 1811 - 128 σελίδες |
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Σελίδα 5
... quadrants , each arc containing 90 degrees ( 6 ) . Draw tAT touching the circle in A ; and draw the radius CB , and produce it till it meet the line tAT in T. . 13. DEF . 1. The difference of any arc from a quadrant , or of any angle ...
... quadrants , each arc containing 90 degrees ( 6 ) . Draw tAT touching the circle in A ; and draw the radius CB , and produce it till it meet the line tAT in T. . 13. DEF . 1. The difference of any arc from a quadrant , or of any angle ...
Σελίδα 6
... quadrant , produced thence till it meets the radius ( produced ) drawn through the end of the arc . Thus , draw HK , touching the circle in H , and meeting the radius produced in K ; then HK is the cotangent of the arc AB , or of the ...
... quadrant , produced thence till it meets the radius ( produced ) drawn through the end of the arc . Thus , draw HK , touching the circle in H , and meeting the radius produced in K ; then HK is the cotangent of the arc AB , or of the ...
Σελίδα 7
... quadrant in such parts , of which 10,000,000 make the radius , is called a trigo- nometrical canon ; and it will always be , as the tabular radius is to any other given radius , so is the tabular sine , & c . of any angle to the sine ...
... quadrant in such parts , of which 10,000,000 make the radius , is called a trigo- nometrical canon ; and it will always be , as the tabular radius is to any other given radius , so is the tabular sine , & c . of any angle to the sine ...
Σελίδα 8
... quadrant , or a right angle , is equal to radius . This is manifest from an inspection of the figure . 28. The tangent of 45 degrees is radius . For then the angle ACT being half a right angle , the other acute angle ATC must also be ...
... quadrant , or a right angle , is equal to radius . This is manifest from an inspection of the figure . 28. The tangent of 45 degrees is radius . For then the angle ACT being half a right angle , the other acute angle ATC must also be ...
Σελίδα 9
... quadrant , but under two quadrants , is equal to the difference between the versed sine of its supplement and the diameter ; that is , Af AD - AF . For CF - Cf , therefore Af = DF = AD - AF . 40. The versed sine of an arc above two ...
... quadrant , but under two quadrants , is equal to the difference between the versed sine of its supplement and the diameter ; that is , Af AD - AF . For CF - Cf , therefore Af = DF = AD - AF . 40. The versed sine of an arc above two ...
Συχνά εμφανιζόμενοι όροι και φράσεις
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest geometry Given the side greater than 90 half the sum half their difference height Hence hypothenuse AC included angle less than 90 logarithmic sines mathematics measured mechanical philosophy negative opposite angle perp perpendicular plane triangle plane trigonometry PROP propositions quadrant AH quantity right-angled spherical triangle right-angled triangle Scholium secant side AB side AC sides and angles sine a sine sine and cosine sine² sines and tangents solution spherical angle spherical triangle ABC spherical trigonometry supplement tables tangent of half theorems third side three angles three sides triangle are given trigono versed sine yards
Δημοφιλή αποσπάσματα
Σελίδα 12 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα ix - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα 23 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.
Σελίδα 13 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.
Σελίδα 87 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Σελίδα 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.