Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 231
... sine and cosine of the arc AB , CF and OF the sine and cosine of BC , and CE is the sine of the compound arc AC . Consequently , R sin AC sinAB cos BC + cos AB sin BC . 1 E GD Cor . 1. Hence , likewise , the rectangle under TRIGONOMETRY ...
... sine and cosine of the arc AB , CF and OF the sine and cosine of BC , and CE is the sine of the compound arc AC . Consequently , R sin AC sinAB cos BC + cos AB sin BC . 1 E GD Cor . 1. Hence , likewise , the rectangle under TRIGONOMETRY ...
Seite 232
... sine of the difference of two arcs , is equal to the difference of the rectangles under their alternate sines and cosines ; or R sinAC'sinAB cosBC - cos AB sin BC . Cor . 2. If the two arcs A and B be equal , it is obvious that R sin2A ...
... sine of the difference of two arcs , is equal to the difference of the rectangles under their alternate sines and cosines ; or R sinAC'sinAB cosBC - cos AB sin BC . Cor . 2. If the two arcs A and B be equal , it is obvious that R sin2A ...
Seite 233
... sine of the mean arc . Let A - B , A , and A + B represent three arcs increasing by the difference B ; then R ( sin ( A + B ) + sin ( A - B ) ) = 2cosB sinA . The property is easily deduced by combining the preced- ing TRIGONOMETRY . 233.
... sine of the mean arc . Let A - B , A , and A + B represent three arcs increasing by the difference B ; then R ( sin ( A + B ) + sin ( A - B ) ) = 2cosB sinA . The property is easily deduced by combining the preced- ing TRIGONOMETRY . 233.
Seite 234
... sine of the common difference and the cosine of the mean arc ; or R ( sin ( A + B ) —sin ( A — B ) ) = 2sinB cosA . Cor . 2. Hence R ( cos ( A − B ) + cos ( A + B ) ) = 2cos B cos A , and R ( cos ( A - B ) —cos ( A + B ) ) = 2sinB sinA ...
... sine of the common difference and the cosine of the mean arc ; or R ( sin ( A + B ) —sin ( A — B ) ) = 2sinB cosA . Cor . 2. Hence R ( cos ( A − B ) + cos ( A + B ) ) = 2cos B cos A , and R ( cos ( A - B ) —cos ( A + B ) ) = 2sinB sinA ...
Seite 235
... sine of 30 ° being ( cor . 1. def . ) equal to the chord of 60 ° or the radius , it is evident that sin ( 60 ° + B ) ... sine of half the arc IAC ' , or of half the sum of the arcs AC and AC ' , as CF is the sine of half their differ- ence ...
... sine of 30 ° being ( cor . 1. def . ) equal to the chord of 60 ° or the radius , it is evident that sin ( 60 ° + B ) ... sine of half the arc IAC ' , or of half the sum of the arcs AC and AC ' , as CF is the sine of half their differ- ence ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Beliebte Passagen
Seite 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Seite 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Seite 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Seite 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Seite 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Seite 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Seite 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Seite 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.