An Elementary Treatise on Plane and Spherical Trigonometry and on the Application of Algebra to Geometry: From the Mathematics of Lacrois and BézoutHilliard and Metcalf, sold by W. Hiliard, 1826 - 165 Seiten |
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... construction of algebraic quantities Geometrical questions , and remarks upon the manner of put- ting them into equations , and upon the different solutions derived from these equations Other applications of algebra Of curved lines ...
... construction of algebraic quantities Geometrical questions , and remarks upon the manner of put- ting them into equations , and upon the different solutions derived from these equations Other applications of algebra Of curved lines ...
Seite 6
... construction , bisects the arc NN ' , we infer from the similar triangles NED , NN'G , that NG is also divided into two equal parts in the point D , and that DN = DG . Moreover , DQ EF , GQ = N'Q ' , DE = FQ ; and as DE is half of N'G ...
... construction , bisects the arc NN ' , we infer from the similar triangles NED , NN'G , that NG is also divided into two equal parts in the point D , and that DN = DG . Moreover , DQ EF , GQ = N'Q ' , DE = FQ ; and as DE is half of N'G ...
Seite 8
... from which we set out , to show , which of these two arcs it is proposed to divide , we ought to find the sine of the half of each . According to the construction we have AMPM + AP = -2 = 2 PM + ( 8 Plane Trigonometry .
... from which we set out , to show , which of these two arcs it is proposed to divide , we ought to find the sine of the half of each . According to the construction we have AMPM + AP = -2 = 2 PM + ( 8 Plane Trigonometry .
Seite 16
... construction , and which consists in this , that each value , which the expression in question assumes , is preceded and followed by values , which differ as little as we please , from the first , and that in describing a line , each ...
... construction , and which consists in this , that each value , which the expression in question assumes , is preceded and followed by values , which differ as little as we please , from the first , and that in describing a line , each ...
Seite 18
... construction and reasoning employed in the article referred to , if we apply them immediately to the proposed arcs . The application of these formulas would be a useful exercise for the learner . 24. By following the course of the ...
... construction and reasoning employed in the article referred to , if we apply them immediately to the proposed arcs . The application of these formulas would be a useful exercise for the learner . 24. By following the course of the ...
Häufige Begriffe und Wortgruppen
a² y² abscissas ac² algebraic altitude angle calculate centre circle circumference conjugate axis consequently construction cos a cos cos b sin cosine curve deduce describe determine diameter dividing draw ellipse equal equation y² expression formulas Geom give given line hyperbola hypothenuse known let fall manner mean proportional multiplying obtain opposite ordinates parabola parallel perpendicular PM plane point F question radius right-angled triangle secant side AC similar triangles sin a cos sin a sin sine sine and cosine solution spherical triangles Spherical Trigonometry square straight line substituting subtract supposed tang atang tangent tion transverse axis triangle ABC Trig trigonometry unknown quantity vertex whence α²
Beliebte Passagen
Seite 23 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Seite 26 - ... for this purpose an account is given in a note subjoined to this part. In the solution of this problem we have made use of the theorem, the sines of the angles are to each other as the sides opposite to these angles. We might also apply the rule given for right-angled triangles (Trig. 30), namely, radius is to the tangent of one of the acute angles, as the side adjacent to this angle is to the side opposite ; thus, As radius or sine of 90° . 10,00000 is to 6 c 2,30103 so is tang Abe 47° 30...
Seite 151 - E~JJ and E as centres, and a radius greater than DC or CE, describe two arcs intersecting in F. Then CF is the required perpendicular (I., Proposition XVIII.). 57. Another solution. Take any point O, without the given line, as a centre, and with a radius equal to the distance from O to C, describe a circumference A—V''' intersecting AB in C and in a second ''• •*
Seite 29 - ... others ; thus, 0,17032 2,30103 9,86763 2,33898 the same as before. t Of the manner of measuring the necessary angles and sides and of the instruments that are used for this purpose an account is given in a note subjoined to this part. In the solution of this problem we have made use of the theorem, the sines of the angles are to each other as the sides opposite to these angles.
Seite 85 - I asked whether they were perfectly convinced that in a right-angled triangle the square of the hypothenuse is equal to the squares of the other two sides ? He answered in the affirmative.
Seite 94 - ... both ; that is. their half sum, or their half difference, or a mean proportional between them, or &c., and we shall always arrive at an equation more simple than by employing either the one or the other.
Seite 46 - ABC, the three equations ; cos a = cos 6 cos c + cos A sin b sin c 1 cos b = cos a cos c -j- cos B sin a sin c > .... (B).