Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 23
... that arc , or angle ( Arts . 26 and 28 ) : hence , the columns designated sine and tang at the top of the page , are designated cosine and cotang at the bottom . 1 USE OF THE TABLE . To find the logarithmic functions PLANE 23 TRIGONOMETRY .
... that arc , or angle ( Arts . 26 and 28 ) : hence , the columns designated sine and tang at the top of the page , are designated cosine and cotang at the bottom . 1 USE OF THE TABLE . To find the logarithmic functions PLANE 23 TRIGONOMETRY .
Page 24
... tang , or cotang , as the case may be ; the number there found is the logarithm required . Thus , log sin 19 ° 55 ' log tan 19 ° 55 ' 9.532312 9.559097 If the arc , or angle , is 45 ° or more , look for the de- grees at the bottom of ...
... tang , or cotang , as the case may be ; the number there found is the logarithm required . Thus , log sin 19 ° 55 ' log tan 19 ° 55 ' 9.532312 9.559097 If the arc , or angle , is 45 ° or more , look for the de- grees at the bottom of ...
Page 20
... Tang . D. Cotang . 8.543084 60.12 11.456916 60 546691 59.62 453309 59 550268 59.14 449732 58 553817 58.66 557336 ... Tang . M. M. Sine . D. Cosine . D. Tang . D. 20 ( 2 DEGREES . ) A TABLE OF LOGARITHMIC.
... Tang . D. Cotang . 8.543084 60.12 11.456916 60 546691 59.62 453309 59 550268 59.14 449732 58 553817 58.66 557336 ... Tang . M. M. Sine . D. Cosine . D. Tang . D. 20 ( 2 DEGREES . ) A TABLE OF LOGARITHMIC.
Page 21
... Tang . D. Cotang . 08.718800 40.06 9.999404 11 8.719396 40.17 11.280604 60 1 721204 39.84 999398 11 721806 39.95 278194 59 723595 39.62 999391 11 724201 39.74 275796 58 3 725972 39.41 999384 11 726588 39.52 273412 57 728337 39.19 730688 ...
... Tang . D. Cotang . 08.718800 40.06 9.999404 11 8.719396 40.17 11.280604 60 1 721204 39.84 999398 11 721806 39.95 278194 59 723595 39.62 999391 11 724201 39.74 275796 58 3 725972 39.41 999384 11 726588 39.52 273412 57 728337 39.19 730688 ...
Page 22
... Tang . 8.844644 30.19 846455 30.07 D. Cotang . 11.155356 60 153545 59 998923 15 848971 29.67 848260 29.95 151740 58 998914 • 15 850751 29.55 850057 29.82 149943 57 998905 15 851846 852525 29.43 29.70 148154 56 998896 15 853628 29.58 ...
... Tang . 8.844644 30.19 846455 30.07 D. Cotang . 11.155356 60 153545 59 998923 15 848971 29.67 848260 29.95 151740 58 998914 • 15 850751 29.55 850057 29.82 149943 57 998905 15 851846 852525 29.43 29.70 148154 56 998896 15 853628 29.58 ...
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Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.