Elements of Geometry and Trigonometry from the Works of A. M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes, 1857 - 432 σελίδες |
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Σελίδα 264
... comp . 3.274107 3.274107 2.104729 its ar . comp . 7.895271 Diff . 1.169378 Sum 1.169378 after sub- tracting 10 . Hence , to perform division by means of the arithmetical complement , we have the following RULE . To the logarithm of the ...
... comp . 3.274107 3.274107 2.104729 its ar . comp . 7.895271 Diff . 1.169378 Sum 1.169378 after sub- tracting 10 . Hence , to perform division by means of the arithmetical complement , we have the following RULE . To the logarithm of the ...
Σελίδα 282
... comp . 0.005705 sin A 58 ° 07 ' 9.928972 :: AB 408 2.610660 BC 351.024 ( after rejecting 10 ) 2.545337 . REMARK . The logarithm of the fourth term of a pro- portion is obtained by adding the logarithm of the second terin to that of the ...
... comp . 0.005705 sin A 58 ° 07 ' 9.928972 :: AB 408 2.610660 BC 351.024 ( after rejecting 10 ) 2.545337 . REMARK . The logarithm of the fourth term of a pro- portion is obtained by adding the logarithm of the second terin to that of the ...
Σελίδα 283
... comp . 7.931814 2.334454 • 9.584968 : sin B 45 ° 13 ′ 55 ′′ , or ABC 134 ° 46 ′ 05 ′′ 9.851236 . The ambiguity in this , and similar examples , arises in consequence of the first proportion being true for either of the angles ABC , or ...
... comp . 7.931814 2.334454 • 9.584968 : sin B 45 ° 13 ′ 55 ′′ , or ABC 134 ° 46 ′ 05 ′′ 9.851236 . The ambiguity in this , and similar examples , arises in consequence of the first proportion being true for either of the angles ABC , or ...
Σελίδα 285
... comp . 7.004365 BC - BA 90 1.954243 10.076187 6 ° 11 ' . · 9.034795 . · :: tan ( A + C ' ) : tan ( A – α ) 50 ° • • Hence , 50 ° + 6 ° 11 ' 56 ° 11 ' A ; and 50 ° - 6 ° 11 ′ = 43 ° 49 ' = C. = To find the third side AC . sin C 43 ° 49 ...
... comp . 7.004365 BC - BA 90 1.954243 10.076187 6 ° 11 ' . · 9.034795 . · :: tan ( A + C ' ) : tan ( A – α ) 50 ° • • Hence , 50 ° + 6 ° 11 ' 56 ° 11 ' A ; and 50 ° - 6 ° 11 ′ = 43 ° 49 ' = C. = To find the third side AC . sin C 43 ° 49 ...
Σελίδα 286
... In the triangle DAC , to find the angle DAC . AC 34 ar . comp . ᎠᏟ 26.6375 . :: sin D 90 ° : sin DAC 51 ° 34 ' 40 " 8.468521 1.425493 · 10.000000 9.894014 . In the triangle BAD , to find the angle BAD 286 PLANE TRIGONOMETRY .
... In the triangle DAC , to find the angle DAC . AC 34 ar . comp . ᎠᏟ 26.6375 . :: sin D 90 ° : sin DAC 51 ° 34 ' 40 " 8.468521 1.425493 · 10.000000 9.894014 . In the triangle BAD , to find the angle BAD 286 PLANE TRIGONOMETRY .
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cos² cosine Cotang cubes cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar similar triangles sin² sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM three angles triangle ABC triangular prism triedral angles vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 34 - If two right-angled triangles have the hypothenuse and a side of the one, equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Σελίδα 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Σελίδα 278 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Σελίδα 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Σελίδα 43 - BtSL hence the sum of all the interior and exterior angles, is equal to twice as many right angles as the polygon has sides.
Σελίδα 119 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Σελίδα 30 - B : hence the two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each : hence, the two triangles are equal (Th.
Σελίδα 97 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.