Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Ergebnisse 6-10 von 23
Seite 231
... 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 sin AB cos BC + cos AB sin BC . Cor . 1. Hence , likewise , the rectangle under TRIGONOMETRY . 231 PROP. I ...
... 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 sin AB cos BC + cos AB sin BC . Cor . 1. Hence , likewise , the rectangle under TRIGONOMETRY . 231 PROP. I ...
Seite 232
... cosine of the sum of two arcs , is equal to the difference of the rectangles under their respective cosines and sines . Let A and B denote two arcs , of which A is the great- er ; then R cos ( A + B ) = cos A cos B - sinA sinB . For ...
... cosine of the sum of two arcs , is equal to the difference of the rectangles under their respective cosines and sines . Let A and B denote two arcs , of which A is the great- er ; then R cos ( A + B ) = cos A cos B - sinA sinB . For ...
Seite 233
... cosine of the difference of two arcs is equal to the sum of the rectangles under their respective cosines and sines ; or R.cos AC ' = cos AB cosBC + sinAB sin BC . Cor . 2. If A and B represent two equal arcs , it will follow , that R ...
... cosine of the difference of two arcs is equal to the sum of the rectangles under their respective cosines and sines ; or R.cos AC ' = cos AB cosBC + sinAB sin BC . Cor . 2. If A and B represent two equal arcs , it will follow , that R ...
Seite 234
... 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 ) ) = 2cosB cos A , and R ( cos ( A - B ) —cos ( A + B ) ) = 2sinB sinA . For OB OD :: OF : OG :: 20F : 20G or ...
... 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 ) ) = 2cosB cos A , and R ( cos ( A - B ) —cos ( A + B ) ) = 2sinB sinA . For OB OD :: OF : OG :: 20F : 20G or ...
Seite 236
... cosine of 5A are found ; and this mode of procedure may be continually repeated . To abridge the notation , however , it will be proper to express the sine and the co- sine of the arc a , by s and c . The results are thus ex- pressed in ...
... cosine of 5A are found ; and this mode of procedure may be continually repeated . To abridge the notation , however , it will be proper to express the sine and the co- sine of the arc a , by s and c . The results are thus ex- pressed in ...
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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 sequently side AC sinB sine square of AB square of AC straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore