## A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical Applications (Google eBook) |

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### Common terms and phrases

2d quadrant acute adjacent angle Aldebaran ambiguous azimuth centre complement cosec cosine describe a circle diff difference distance draw the diameters ecliptic equal equation Example expressions extent will reach find the hypothenuse find the rest following formula former given leg given side greater than 90 Greenwich height horizon hyp1 hypothenusal angle incd latitude leg ac less than 90 Log sine 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 remaining side required to find right ascension right-angled spherical triangle RULE scale of chords Scholium secant semitangent side ac side is less sides and angles sphere spherical angle spherical triangle abc spherical trigonometry star subtracted sun's declination supplement tables tangents THEOREM three angles three sides true altitude true longitude whence

### Popular passages

Page xxxiii - 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 4 - ... 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 325 - 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 359 - 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 v - 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 11 - 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 15 - 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 xxxvi - 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 179 - 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 73 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.