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 11.
Σελίδα 5
... chord of any arc is a right line drawn from one extremity of the arc to the other . Let the points B and E be in the circle , and join B , E ; then the straight line BE is the chord of the arc BAE , or of the angle BCE , of which the ...
... chord of any arc is a right line drawn from one extremity of the arc to the other . Let the points B and E be in the circle , and join B , E ; then the straight line BE is the chord of the arc BAE , or of the angle BCE , of which the ...
Σελίδα 7
... chord of 60 degrees is equal to radius . For then the angles ABC , BAC being equal ( 5. 1 ) , each of them is 60 degrees = angle ACB ; therefore the triangle ACB being equiangular , is also equilateral ( Cor . 6. 1 ) ; therefore the chord ...
... chord of 60 degrees is equal to radius . For then the angles ABC , BAC being equal ( 5. 1 ) , each of them is 60 degrees = angle ACB ; therefore the triangle ACB being equiangular , is also equilateral ( Cor . 6. 1 ) ; therefore the chord ...
Σελίδα 10
... chord of double that arc . For the radius CA , perpendicular to BE , bisects the chord BE in F ( 3. 3 ) , and also the arc BAE subtended by it ( 26. 3 ) , because the angle BCA = ECA ; therefore BF , the sine of the arc BA , is half the ...
... chord of double that arc . For the radius CA , perpendicular to BE , bisects the chord BE in F ( 3. 3 ) , and also the arc BAE subtended by it ( 26. 3 ) , because the angle BCA = ECA ; therefore BF , the sine of the arc BA , is half the ...
Σελίδα 11
... chord of any arc is a 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 ...
... chord of any arc is a 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 ...
Σελίδα 28
... chords , or a protractor . The unknown parts of the triangle thus constructed are found by measuring them on the same scale or instrument from which the known parts were taken . In the second method let the analogy be formed according ...
... chords , or a protractor . The unknown parts of the triangle thus constructed are found by measuring them on the same scale or instrument from which the known parts were taken . In the second method let the analogy be formed according ...
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.