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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Αποτελέσματα 1 - 5 από τα 10.
Σελίδα 8
... increases from 90 degrees to 180 degrees , its sine , tangent , and secant decrease . Thus , as Ab increases , it is evident that the sine bf , the tangent At , and the secant Ct must decrease till the point b coincides with D. Conse ...
... increases from 90 degrees to 180 degrees , its sine , tangent , and secant decrease . Thus , as Ab increases , it is evident that the sine bf , the tangent At , and the secant Ct must decrease till the point b coincides with D. Conse ...
Σελίδα 37
... increases fast , we shall thus obtain the arc or angle A true to a second . In like manner , if an arc very near 90 ° be expressed by its sine , it can be known only within certain limits , by reason of the small variation of the sine ...
... increases fast , we shall thus obtain the arc or angle A true to a second . In like manner , if an arc very near 90 ° be expressed by its sine , it can be known only within certain limits , by reason of the small variation of the sine ...
Σελίδα 59
... increases from 0 ( nothing ) du- ring the first quadrant AH , till it becomes equal to radius at the point H. Then it decreases during the second quadrant HD , till it again becomes O at the end of it . After this the sine passes to the ...
... increases from 0 ( nothing ) du- ring the first quadrant AH , till it becomes equal to radius at the point H. Then it decreases during the second quadrant HD , till it again becomes O at the end of it . After this the sine passes to the ...
Σελίδα 60
... increase of the sines , that the cosine CF decreases slower in the first part AB of the quadrant AH , than when it approaches near the end of it , at H ; and , on the contrary , that it increases faster in the first part Hb of the ...
... increase of the sines , that the cosine CF decreases slower in the first part AB of the quadrant AH , than when it approaches near the end of it , at H ; and , on the contrary , that it increases faster in the first part Hb of the ...
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.