A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical ApplicationsJ. Johnson, 1806 - 419 páginas |
Dentro del libro
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Página xxxii
... base a circle of the sphere ; but , easy as this step appears , it was not achieved till fifteen hundred years after the time of Hipparchus . It is uncertain , indeed , by whom , or at what time , these two useful propositions were ...
... base a circle of the sphere ; but , easy as this step appears , it was not achieved till fifteen hundred years after the time of Hipparchus . It is uncertain , indeed , by whom , or at what time , these two useful propositions were ...
Página 11
... base and the ver- tical angle . 8. In a right - angled triangle the hypothenuse is equal to the square root of the sum of the squares of the other two sides ; and either of the sides is equal to the square root of the difference of the ...
... base and the ver- tical angle . 8. In a right - angled triangle the hypothenuse is equal to the square root of the sum of the squares of the other two sides ; and either of the sides is equal to the square root of the difference of the ...
Página 16
... base are each equal to half the supplement of the given angle , or that at the ver- tex ; whence the third side may be found directly by Case I. And if the included angle be a right angle , or 90 ° , the third side , or hypothenuse ...
... base are each equal to half the supplement of the given angle , or that at the ver- tex ; whence the third side may be found directly by Case I. And if the included angle be a right angle , or 90 ° , the third side , or hypothenuse ...
Página 18
... base , and let fall a per- pendicular upon it from the opposite angle . Then , as the base , or sum of its 18.
... base , and let fall a per- pendicular upon it from the opposite angle . Then , as the base , or sum of its 18.
Página 19
... base . And half this difference , being added to half the base , will give the greater segment ; and , subtracted from it , will give the less . Then , in each of the right - angled triangles , formed by the perpendicular , there will ...
... base . And half this difference , being added to half the base , will give the greater segment ; and , subtracted from it , will give the less . Then , in each of the right - angled triangles , formed by the perpendicular , there will ...
Otras ediciones - Ver todas
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Sin vista previa disponible - 2014 |
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Sin vista previa disponible - 2018 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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...
Página 75 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.