A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical Applications |
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Page x
... side to 45 ° , and then returning backwards , from the right hand side , to 90 ° ; so that each number and its complement stand on the same line . The second part of this volume , which is entitled Universalium inspectionum ad canonem ...
... side to 45 ° , and then returning backwards , from the right hand side , to 90 ° ; so that each number and its complement stand on the same line . The second part of this volume , which is entitled Universalium inspectionum ad canonem ...
Page 8
... side and its opposite angle . 2. When two sides and their included angle are given . 3. When the three sides are given . Each of which cases may be resolved , either by geometrical construction , by arithmetical computation , or ...
... side and its opposite angle . 2. When two sides and their included angle are given . 3. When the three sides are given . Each of which cases may be resolved , either by geometrical construction , by arithmetical computation , or ...
Page 10
... side is opposite to the greater angle ; and the less side to the less angle . 3. The sum of any two sides is greater than the third ; and the difference of any two sides is less than the third . 4. The triangle is equilateral ...
... side is opposite to the greater angle ; and the less side to the less angle . 3. The sum of any two sides is greater than the third ; and the difference of any two sides is less than the third . 4. The triangle is equilateral ...
Page 11
... side will fall within the triangle ; and the greater and less segment will be next the greater and less side ( g ) . 7. In an isosceles triangle , a perpendicular drawn from the vertex ... side . As any side is to the sine of its opposite 11.
... side will fall within the triangle ; and the greater and less segment will be next the greater and less side ( g ) . 7. In an isosceles triangle , a perpendicular drawn from the vertex ... side . As any side is to the sine of its opposite 11.
Page 12
... side to the sine of its opposite angle . Or , As the sine of any angle is to its opposite side , so is the sine of any other angle to its opposite side . Hence , to find an angle , begin the proportion with a side opposite to a given ...
... side to the sine of its opposite angle . Or , As the sine of any angle is to its opposite side , so is the sine of any other angle to its opposite side . Hence , to find an angle , begin the proportion with a side opposite to a given ...
Other editions - View all
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle No preview available - 2014 |
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle No preview available - 2018 |
Common terms and phrases
A B C acute adjacent angle Aldebaran ambiguous azimuth centre complement cos² cosec cosine describe a circle diff difference distance draw the diameters ecliptic equal equation Example extent will reach find the rest former formulæ given leg given side Given two sides greater than 90 Greenwich height horizon hypothenusal angle incd latitude leg BC less than 90 Log sine logarithms longitude meridian moon's oblique oblique-angled spherical triangle observed obtuse opposite angle parallax perpendicular plane triangle point of aries points pole quadrantal spherical triangle radius required to find right ascension right-angled spherical triangle RULE scale of chords secant semitangent side AC sides and angles sin a sin sin² sines sphere spherical angle spherical triangle ABC spherical trigonometry star subtracted sun's declination supplement tangents THEOREM three angles three sides trigonometry whence
Popular passages
Page xxxi - 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.
Page 6 - ... for the second term, and the greater for the first ; and in either case multiply the second and third terms together, and divide the product by the first for the answer, which will always be of the same denomination as the third term.
Page 329 - 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.
Page 363 - The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side.
Page vii - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page 13 - To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference...
Page 17 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page 2 - SECANT of an arc, is a straight line drawn from the centre, through one end of the arc, and extended to the tangent which is drawn from the other end.
Page 181 - The AMPLITUDE of any object in the heavens is an arc of the horizon, contained between the centre of the object when rising, or setting, and the east or west points of the horizon. Or, it is...
Page 75 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.