The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to the Method of Instruction in the American CollegesHowe & Spalding, S. Converse, printer, 1824 - Geometry |
From inside the book
Results 1-5 of 16
Page 53
... cosecant of an angle is the secant of the complement of the angle . Thus CF is the cosecant of GCA . Hence , as in a right angled triangle , one of the acute an- gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent ...
... cosecant of an angle is the secant of the complement of the angle . Thus CF is the cosecant of GCA . Hence , as in a right angled triangle , one of the acute an- gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent ...
Page 54
... cosecant . By comparing the triangles CBG and CAD , 1. AC : BC :: AD : BG , that is , R : cos :: tan ; sin . 2. CG CD :: BG : AD 3. CB CA :: CG : CD R secsin tan . cos : R :: R : sec . Therefore R2 = = cos X sec . By comparing the ...
... cosecant . By comparing the triangles CBG and CAD , 1. AC : BC :: AD : BG , that is , R : cos :: tan ; sin . 2. CG CD :: BG : AD 3. CB CA :: CG : CD R secsin tan . cos : R :: R : sec . Therefore R2 = = cos X sec . By comparing the ...
Page 59
... cosecant of an angle , are the sine , tangent , and secant of the complement of the angle . ( Art . 89. ) As the complement of an angle is the difference between the angle and 90 ° , and as 45 is the half of 90 ; if any given angle ...
... cosecant of an angle , are the sine , tangent , and secant of the complement of the angle . ( Art . 89. ) As the complement of an angle is the difference between the angle and 90 ° , and as 45 is the half of 90 ; if any given angle ...
Page 60
... cosecant of an angle greater than 45 ° , has its equal , among the sines , tangents , and secants of an- gles less than 45 ° , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to ...
... cosecant of an angle greater than 45 ° , has its equal , among the sines , tangents , and secants of an- gles less than 45 ° , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to ...
Page 61
... cosecants , the correction is to be subtracted For , as the sines increase , the cosines decrease . Ex . 1. What is the logarithmic sine of 14 ° 43 ' 10 " ? The sine of 14 ° 43 ' is 9.40490 of 14 ° 44 ' Difference 9.40538 48 Here it is ...
... cosecants , the correction is to be subtracted For , as the sines increase , the cosines decrease . Ex . 1. What is the logarithmic sine of 14 ° 43 ' 10 " ? The sine of 14 ° 43 ' is 9.40490 of 14 ° 44 ' Difference 9.40538 48 Here it is ...
Other editions - View all
The Second [-Fifth and Sixth] Part of a Course of Mathematics: Adapted to ... Jeremiah Day,Matthew Rice Dutton No preview available - 2016 |
Common terms and phrases
axis base calculation centre circle circular segment circumference column cone cosecant cosine cotangent course cylinder decimal diameter Diff difference of latitude difference of longitude distance divided earth equator errour feet figure find the SOLIDITY frustum given sides gles greater horizon hypothenuse inches JEREMIAH DAY lateral surface length less line of chords loga logarithm measured Mercator's Merid meridian meridional difference miles minutes multiplied number of degrees number of sides object oblique parallel of latitude parallelogram parallelopiped perimeter perpendicular plane sailing polygon prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rods root scale secant segment ship sails sine sines and cosines slant-height sphere square stations subtract tables tance tangent tangent of half term theorem trapezium triangle ABC Trig trigonometry whole
Popular passages
Page 75 - 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 88 - BBOWN, of the said district, hath deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : " Sertorius : or, the Roman Patriot.
Page 49 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 108 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 89 - III. Two sides and the included angle being given ; to find the other side and angles. Draw one of the given sides. From one end of it lay off the given angle, and draw the other given side. Then connect the extremities of this and the first line. Ex. 1. Given the angle A 26° 14', the side b 78, and the side c 106 ; to find B, C, and a.
Page 121 - 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 26 - Icosaedron, whose sides are four triangles ; six squares ; eight triangles ; twelve pentagons ; twenty triangles.* Besides these five, there can be no other regular solids. The only plane figures which can form such solids, are triangles, squares, and pentagons. For the plane angles which contain any solid angle, are together less than four right angles or 360°. (Sup. Euc. 21, 2.) And the least number which can form a solid angle is three.
Page 88 - ... for the encouragement of learning by securing the copies of Maps, charts, and books, to the Authors and Proprietors of such copies during the times therein mentioned, and extending the benefits thereof to the arts of designing, engraving and etching historical and other prints.
Page 50 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
Page 125 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.