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 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 36.
Σελίδα 20
... required to find the other three parts of the triangle . If one angle of a triangle be right , the other two angles are acute , and together make a right angle ( 32. 1 ) . Therefore when one of the acute angles of a right - angled ...
... required to find the other three parts of the triangle . If one angle of a triangle be right , the other two angles are acute , and together make a right angle ( 32. 1 ) . Therefore when one of the acute angles of a right - angled ...
Σελίδα 21
... required , may be made radius to find a side ; but a given side must always be made radius to find an angle . Hence , to find an angle , begin the proportion with a side op- posite to a given angle ; and to find a side , begin the ...
... required , may be made radius to find a side ; but a given side must always be made radius to find an angle . Hence , to find an angle , begin the proportion with a side op- posite to a given angle ; and to find a side , begin the ...
Σελίδα 22
... required , it is sufficient , after tan . A is found by this proportion , to take from the tri- gonometrical tables the cosine which corresponds to tan . A , and then to compute AC by this proportion , cos . A :: R :: AB : AC . 71. If ...
... required , it is sufficient , after tan . A is found by this proportion , to take from the tri- gonometrical tables the cosine which corresponds to tan . A , and then to compute AC by this proportion , cos . A :: R :: AB : AC . 71. If ...
Σελίδα 23
... required to find the other three parts . This problem contains four cases , and the solutions of them depend upon the preceding propositions . Case 1. When two angles and a side are given , to find the rest . 2. When two sides and an ...
... required to find the other three parts . This problem contains four cases , and the solutions of them depend upon the preceding propositions . Case 1. When two angles and a side are given , to find the rest . 2. When two sides and an ...
Σελίδα 28
... required . If logarithms be used , add the loga- rithms of the second and third terms , and from the sum sub- * F. Nichols proposes to reprint De La Lande's Stereotype Tables of the Logarithms of Numbers , Sines and Tangents , with the ...
... required . If logarithms be used , add the loga- rithms of the second and third terms , and from the sum sub- * F. Nichols proposes to reprint De La Lande's Stereotype Tables of the Logarithms of Numbers , Sines and Tangents , with 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.