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 12
... angle at the base CAB . But if the base AB be made radius , the per- pendicular BC becomes the tangent , and the ... opposite to that side , or to the cosine of the angle adjacent to that side . C G D Let ABC be a right - angled triangle ...
... angle at the base CAB . But if the base AB be made radius , the per- pendicular BC becomes the tangent , and the ... opposite to that side , or to the cosine of the angle adjacent to that side . C G D Let ABC be a right - angled triangle ...
Σελίδα 13
... angle , and therefore is equal to the angle ABC . From the equian- gular triangles ABC , AEG , AB : BC : AE :: EG ... opposite side , the segments of that side will be to each other as the tangents of the parts into which the vertical angle ...
... angle , and therefore is equal to the angle ABC . From the equian- gular triangles ABC , AEG , AB : BC : AE :: EG ... opposite side , the segments of that side will be to each other as the tangents of the parts into which the vertical angle ...
Σελίδα 14
... opposite angles CAD , BAD . Hence AD : R :: DC : tan . CAD ( 50 ) , and AD : R :: DB : tan . BAD . A D consequently ... angle is equal to the cotan- gent of its complement ( 23 ) . PROP . IV . 54. The sides of any triangle are to one another ...
... opposite angles CAD , BAD . Hence AD : R :: DC : tan . CAD ( 50 ) , and AD : R :: DB : tan . BAD . A D consequently ... angle is equal to the cotan- gent of its complement ( 23 ) . PROP . IV . 54. The sides of any triangle are to one another ...
Σελίδα 15
... angle A of the triangle ABC draw AD perpendicular to BC . About the centres B and C , with the radii BA and CA ... opposite to one of them be given , the remaining side and angles may be found ; or , if two angles and a side opposite to ...
... angle A of the triangle ABC draw AD perpendicular to BC . About the centres B and C , with the radii BA and CA ... opposite to one of them be given , the remaining side and angles may be found ; or , if two angles and a side opposite to ...
Σελίδα 17
... angle C , it will fall within the triangle , and will divide it into two ... opposite angles is to the tangent of half their difference . F H Let ABC be ... angle HFB = half the an- gle HCB ( 20. 3 ) , half the sum of the angles at the ...
... angle C , it will fall within the triangle , and will divide it into two ... opposite angles is to the tangent of half their difference . F H Let ABC be ... angle HFB = half the an- gle HCB ( 20. 3 ) , half the sum of the angles at 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.