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 60
... positive , and increases till it is equal to radius , as before . Since the cosine of the arc AB is equal to the sine of its complement BH , it follows , reversedly , from what has been said respecting the variation of the rate of ...
... positive , and increases till it is equal to radius , as before . Since the cosine of the arc AB is equal to the sine of its complement BH , it follows , reversedly , from what has been said respecting the variation of the rate of ...
Σελίδα 62
... investigations it is common to em- ploy , indifferently , arcs of all magnitudes , whether positive or negative , greater or less than 360 ° ; in which cases their sines , cosines , & c . , may be derived from 62 PLANE TRIGONOMETRY .
... investigations it is common to em- ploy , indifferently , arcs of all magnitudes , whether positive or negative , greater or less than 360 ° ; in which cases their sines , cosines , & c . , may be derived from 62 PLANE TRIGONOMETRY .
Σελίδα 63
... positive or negative sine , cosine , & c . as the single arc AB . Whence , if C denote the whole circum- ference of a circle , or 360 ° , and x any arc AB ; then sine x = sine ( C + x ) sine ( 2 C + x ) = sine ( 3 C + x ) = & c . The ...
... positive or negative sine , cosine , & c . as the single arc AB . Whence , if C denote the whole circum- ference of a circle , or 360 ° , and x any arc AB ; then sine x = sine ( C + x ) sine ( 2 C + x ) = sine ( 3 C + x ) = & c . The ...
Σελίδα 64
... positive . If a line , supposed to be positive in one direction , vanish , and then be set off in a contrary direction , it becomes negative . Hence CF , the cosine of the arc AB , is positive ; but Cf , the cosine of the arc Ab or As ...
... positive . If a line , supposed to be positive in one direction , vanish , and then be set off in a contrary direction , it becomes negative . Hence CF , the cosine of the arc AB , is positive ; but Cf , the cosine of the arc Ab or As ...
Σελίδα 65
... positive arc . The secant radius cosine ; therefore the secant has the same sign both for a positive arc and a negative arc ; for it has been shown that the sign of the cosine is the same for both arcs . Hence , if A , B denote two arcs ...
... positive arc . The secant radius cosine ; therefore the secant has the same sign both for a positive arc and a negative arc ; for it has been shown that the sign of the cosine is the same for both arcs . Hence , if A , B denote two arcs ...
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.