Elements of Geometry and Trigonometry Translated from the French of A.M. Legendre by David Brewster: Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page 234
... the horizontal line into the columns designated tang . , cotang . , sine , cosine , as the case may be the number so pointed out is the logarithm required . It will be seen , that the column designated sine 234 PLANE TRIGONOMETRY .
... the horizontal line into the columns designated tang . , cotang . , sine , cosine , as the case may be the number so pointed out is the logarithm required . It will be seen , that the column designated sine 234 PLANE TRIGONOMETRY .
Page 235
... cotang . , and the one designated cotang . , by tang . The angle found by taking the degrees at the top of the page , and the minutes from the first vertical column on the left , is the complement of the angle , found by taking the ...
... cotang . , and the one designated cotang . , by tang . The angle found by taking the degrees at the top of the page , and the minutes from the first vertical column on the left , is the complement of the angle , found by taking the ...
Page 236
... cotang blog . tang a + log . cotang a ; or , log , tang blog . tang a = log . cotang a - log . cotang b . Now , if it were required to find the logarithmic sine of an arc expressed in degrees , minutes , and seconds , we have only to ...
... cotang blog . tang a + log . cotang a ; or , log , tang blog . tang a = log . cotang a - log . cotang b . Now , if it were required to find the logarithmic sine of an arc expressed in degrees , minutes , and seconds , we have only to ...
Page 237
... cotang . 10.008688 . Cotang 44 ° 26 ' , next less in the table 10.008591 Tab . Diff . 421 ) 9700 ( 23 " Hence , 44 ° 26 ' - 23 ′′ -44 ° 25 ′ 37 ′′ is the arc corresponding to the given cotangent 10.008688 . PRINCIPLES FOR THE SOLUTION ...
... cotang . 10.008688 . Cotang 44 ° 26 ' , next less in the table 10.008591 Tab . Diff . 421 ) 9700 ( 23 " Hence , 44 ° 26 ' - 23 ′′ -44 ° 25 ′ 37 ′′ is the arc corresponding to the given cotangent 10.008688 . PRINCIPLES FOR THE SOLUTION ...
Page
... Cotang . M. Sine | D. 00.000000 ] Cosine D. Tang . D. 10.000000 0.0000001 Cotang . 16.463726 501717 Inmite . 60 000000 00 6.463726 501717 13.536274 59 2 764756 293485 000000 00 764756 293483 235244 58 3 940847 208231 000000 00 940847 ...
... Cotang . M. Sine | D. 00.000000 ] Cosine D. Tang . D. 10.000000 0.0000001 Cotang . 16.463726 501717 Inmite . 60 000000 00 6.463726 501717 13.536274 59 2 764756 293485 000000 00 764756 293483 235244 58 3 940847 208231 000000 00 940847 ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 251 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Page 109 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sides (Book IV.
Page 91 - Two similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E.
Page 169 - THEOREM. 7?/6 convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.
Page 41 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 155 - AK. The two solids AG, AQ, having the same base AEHD are to each other as their altitudes AB, AO ; in like manner, the two solids AQ, AK, having the same base AOLE, are to each other as their altitudes AD, AM. Hence we have the two proportions, sol.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 282 - ... 1. To find the length of an arc of 30 degrees, the diameter being 18 feet. ' Ans. 4.712364. 2. To find the length of an arc of 12° 10', or 12£°, the diameter being 20 feet.
Page 93 - ABC : FGH : : ACD : FHI. By the same mode of reasoning, we should find ACD : FHI : : ADE : FIK; and so on, if there were more triangles. And from this series of equal ratios, we conclude that the sum of the antecedents...