A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical ApplicationsJ. Johnson, 1806 - 419 σελίδες |
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Σελίδα xxvi
... expressions of this kind as founded upon principles which are repugnant to all our ideas of magnitude or quantity , yet their com- modious form , and the ease and certainty with which they can be applied in many intricate inquiries ...
... expressions of this kind as founded upon principles which are repugnant to all our ideas of magnitude or quantity , yet their com- modious form , and the ease and certainty with which they can be applied in many intricate inquiries ...
Σελίδα 25
... expression to which it is prefixed . And the sign expresses the difference of the two quantities between which it is placed , when it is not known which of them is the greater . ( 1 ) The reason of this deficiency of the sines and ...
... expression to which it is prefixed . And the sign expresses the difference of the two quantities between which it is placed , when it is not known which of them is the greater . ( 1 ) The reason of this deficiency of the sines and ...
Σελίδα 28
... the hypothenuse by case v . RULE II . 1.2 a2 c = √2 + b = a√√ / 1 + 6 = b√√√1 + 00 a2 b2 Vita a2 which formulæ do not admit of convenient logarithmic expressions . SOLUTIONS OF ALL THE CASES OF OBLIQUE - ANGLED PLANE 28.
... the hypothenuse by case v . RULE II . 1.2 a2 c = √2 + b = a√√ / 1 + 6 = b√√√1 + 00 a2 b2 Vita a2 which formulæ do not admit of convenient logarithmic expressions . SOLUTIONS OF ALL THE CASES OF OBLIQUE - ANGLED PLANE 28.
Σελίδα 31
... expression . Area A = b sin A ( l cos A + √ r2 a2 — b2 sin3A ) 22 IV . Given two sides and their included angle , to find the other two angles . tan RULE . As sum of the two given sides : their difference :: supplement included : tan ...
... expression . Area A = b sin A ( l cos A + √ r2 a2 — b2 sin3A ) 22 IV . Given two sides and their included angle , to find the other two angles . tan RULE . As sum of the two given sides : their difference :: supplement included : tan ...
Σελίδα 32
... expressions . Area A = bc sin A 2r V. Given two sides and their included angle , to find the other side . RULE ... expression . If the A be isosceles , or have a = b , the rule will give 2 a sinc T or LC La + L sinc + 12-10 . VI . Given ...
... expressions . Area A = bc sin A 2r V. Given two sides and their included angle , to find the other side . RULE ... expression . If the A be isosceles , or have a = b , the rule will give 2 a sinc T or LC La + L sinc + 12-10 . VI . Given ...
Άλλες εκδόσεις - Προβολή όλων
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2014 |
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 75 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.