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 3
... means they could accurately express several parts of the periphery of the circle in whole numbers , which they considered far more clear , and less intricate than frac- tions . LEMMA II . 7. ALL angles are to one another as their arcs ...
... means they could accurately express several parts of the periphery of the circle in whole numbers , which they considered far more clear , and less intricate than frac- tions . LEMMA II . 7. ALL angles are to one another as their arcs ...
Σελίδα 4
... means of a set of tables called a Trigonometrical Canon . It is divided into two parts , Plane Trigonometry and Sphe- rical . The former has for its object rectilinear triangles , the latter , triangles formed by the intersection of ...
... means of a set of tables called a Trigonometrical Canon . It is divided into two parts , Plane Trigonometry and Sphe- rical . The former has for its object rectilinear triangles , the latter , triangles formed by the intersection of ...
Σελίδα 9
... mean proportional be- tween the cosine and secant , between the sine and cosecant , and between the tangent and cotangent . 42. The tangents and cotangents of any two arcs of a circle are reciprocally proportional ; that is , the ...
... mean proportional be- tween the cosine and secant , between the sine and cosecant , and between the tangent and cotangent . 42. The tangents and cotangents of any two arcs of a circle are reciprocally proportional ; that is , the ...
Σελίδα 11
... mean proportional between the diameter and the versed sine of that arc . 2. Again , the triangles AFB , DFB give the following analogy . AF : BF :: BF : DF . That is , the sine of any arc is a mean proportional between the versed sine ...
... mean proportional between the diameter and the versed sine of that arc . 2. Again , the triangles AFB , DFB give the following analogy . AF : BF :: BF : DF . That is , the sine of any arc is a mean proportional between the versed sine ...
Σελίδα 22
... means of which all the cases of right- angled triangles may be easily resolved . 1. a = - b sine Ab cos . C r or log . a = log . blog . sine A - log . r = log . blog . cos . C - log . r . 2 . c tan . A r or log . a = log . c + log . tan ...
... means of which all the cases of right- angled triangles may be easily resolved . 1. a = - b sine Ab cos . C r or log . a = log . blog . sine A - log . r = log . blog . cos . C - log . r . 2 . c tan . A r or log . a = log . c + log . tan ...
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.