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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Seite 13
... diameter is 1 , being 3,141592653 , this number will express the semicircumference when the diameter is 2 , or radius 1. Hence , = 0,000 015 707 963 , sin 0,00001 = π 100000 = 3,141592653 100000 so also , sin 1 " = 12 π2 = 324000 3 ...
... diameter is 1 , being 3,141592653 , this number will express the semicircumference when the diameter is 2 , or radius 1. Hence , = 0,000 015 707 963 , sin 0,00001 = π 100000 = 3,141592653 100000 so also , sin 1 " = 12 π2 = 324000 3 ...
Seite 16
... diameter AB on the side of the point C oppo- site to that in which it was before , increases . This is evident ... diameter AA ' . The sine , which then becomes P " M " , falls also below the diameter , and increases , according as the ...
... diameter AB on the side of the point C oppo- site to that in which it was before , increases . This is evident ... diameter AA ' . The sine , which then becomes P " M " , falls also below the diameter , and increases , according as the ...
Seite 18
... diameter AA ' , and the cosines , when they pass from one side to the other of the point C , or according as they fall on this side or that of the diameter BB ' perpendicu- lar to AA ' . By attending to these things we shall be able to ...
... diameter AA ' , and the cosines , when they pass from one side to the other of the point C , or according as they fall on this side or that of the diameter BB ' perpendicu- lar to AA ' . By attending to these things we shall be able to ...
Seite 19
... diameter AA ' , and AN is the tangent of AA'M " . The radius becomes again parallel to AN at the point B ' , and the tangent is infinite ; beyond this point it falls below the diameter , and the arc AA'M " " has AN ' for its tangent ...
... diameter AA ' , and AN is the tangent of AA'M " . The radius becomes again parallel to AN at the point B ' , and the tangent is infinite ; beyond this point it falls below the diameter , and the arc AA'M " " has AN ' for its tangent ...
Seite 30
... diameter of the circle a b c . It is thus that Carnot has presented them in a work entitled Géomé- trie de Position , where may be found , according to this definition a very simple and elegant demonstration of the proposition given in ...
... diameter of the circle a b c . It is thus that Carnot has presented them in a work entitled Géomé- trie de Position , where may be found , according to this definition a very simple and elegant demonstration of the proposition given in ...
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).