A Treatise on Plane and Spherical TrigonometryU. Hunt's Sons, 1872 |
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Page 37
Enoch Lewis. D H I Let BAC and BAD be two angles , whose sines adapted to the radius AC or AB , are EC and FD ; while the sines of the same angles adapted to the radius AG or AH , are KH and LI . Since ... ABC , ADF and AHE , SECTION I. 37.
Enoch Lewis. D H I Let BAC and BAD be two angles , whose sines adapted to the radius AC or AB , are EC and FD ; while the sines of the same angles adapted to the radius AG or AH , are KH and LI . Since ... ABC , ADF and AHE , SECTION I. 37.
Page 38
... Let ABC be a trian- gle ; make AE = BC ; from the centres B and A , with the radii BC and AE , describe the arcs CG and EH ; from C and E , let fall on AB ( produced if necessary ) the perpendiculars CD and EF ; these perpen- diculars ...
... Let ABC be a trian- gle ; make AE = BC ; from the centres B and A , with the radii BC and AE , describe the arcs CG and EH ; from C and E , let fall on AB ( produced if necessary ) the perpendiculars CD and EF ; these perpen- diculars ...
Page 39
... Let ABC be the tri- angle ; AC , AB , the sides . From the centre A , with the distance AC , describe the circle . DCEF ; meeting AB , produced in D and E ; and CB , produced in F ; join AF , DC ; and through E draw EG parallel to BC ...
... Let ABC be the tri- angle ; AC , AB , the sides . From the centre A , with the distance AC , describe the circle . DCEF ; meeting AB , produced in D and E ; and CB , produced in F ; join AF , DC ; and through E draw EG parallel to BC ...
Page 40
... Let ABC be the trian- gle ; AB the less , and AC the greater side . Draw AD at right angles to AC , and equal to AB ; cut off AE , also = AB ; and join DE and DC . Then , DAC being a right angle , DA AC rad : tangent : of ADC ( Art . 28 ) ...
... Let ABC be the trian- gle ; AB the less , and AC the greater side . Draw AD at right angles to AC , and equal to AB ; cut off AE , also = AB ; and join DE and DC . Then , DAC being a right angle , DA AC rad : tangent : of ADC ( Art . 28 ) ...
Page 41
... Let ABC be a trian- gle , whose base is AB . From the vertex C , with the greater side AC , de- scribe the circle AEGF , cutting BC produced in E and F , and AB pro- duced in G ; join AE , FG ; bisect AB in H , and draw CD at right ...
... Let ABC be a trian- gle , whose base is AB . From the vertex C , with the greater side AC , de- scribe the circle AEGF , cutting BC produced in E and F , and AB pro- duced in G ; join AE , FG ; bisect AB in H , and draw CD at right ...
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Common terms and phrases
ABDP adjacent angle angled spherical triangle base bisect C.cos c.sin centre circle Art common section Comp AC cone conical surface consequently construction cos² cosec cosine cotan directrix distance EC² ecliptic ED² ellipse equal equation given angle greater axis Hence hyperbola hypothenuse join latus rectum less circle Let ABC line of measures logarithms meet opposite ordinate original circle parabola parallel perpendicular plane of projection primitive circle projected circle projected pole projecting point Q. E. D. ART Q. E. D. Cor quadrant radius right angled spherical right ascension right line secant semicircle semitangent sides similar triangles sine sphere spherical angle tangent tangent of half touches the circle triangle ABC vertex vertical angle whence wherefore
Popular passages
Page 39 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. 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. By Theorem II. we have a : b : : sin. A : sin. B.
Page 32 - 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 78 - Required the height and distance of the steeple. Ans. Height, 210.4 feet; distance, 250.8 feet. 14. Two pulleys, whose diameters are 6 inches and 4 feet 3 inches, respectively, are placed at a distance of 3 feet 6 inches from centre to centre. What must be the length of a belt which shall connect them, by passing around their circumferences, without crossing...
Page 78 - From the top of a tower, whose height is 108 feet, the angles of depression of the top and bottom of a vertical column standing in the horizontal plane are found to be 30° and 60° respectively ; required the height of the column.
Page 80 - Ans. 41.9968. 6. tin a level garden there are two lofty firs, having their tops ornamented with gilt balls, one is 100 feet high, the other 80, and they are 120 feet distant at the bottom ; now the owner wants to place a fountain in a right line between the trees, to be equally distant from the top of each...
Page 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 98 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.
Page 36 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Page 117 - The straight line joining the vertex and the centre of the base is called the axis of the cone.
Page 40 - Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the remaining angle ECB will be their half difference.