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 vii
... Sine of Half an Angle ,. 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a Polygon , 113 Area of a Regular Polygon , 114 .... To find the Circumference of a Circle , To find the Diameter of a Circle , To find the ...
... Sine of Half an Angle ,. 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a Polygon , 113 Area of a Regular Polygon , 114 .... To find the Circumference of a Circle , To find the Diameter of a Circle , To find the ...
Page 19
... sine of AM , and P'M ' is the sine of AM ' . If AM is equal to M'C , AM and AM ' will be supple- ments of each other ; and be- cause MM ' is parallel to AC , PM will be equal to P'M ' ( B. I. , P. XXIII . ) : hence , the sine of an arc ...
... sine of AM , and P'M ' is the sine of AM ' . If AM is equal to M'C , AM and AM ' will be supple- ments of each other ; and be- cause MM ' is parallel to AC , PM will be equal to P'M ' ( B. I. , P. XXIII . ) : hence , the sine of an arc ...
Page 21
... sine , cosine , tangent , and cotangent of the angle AOM , as well as of the arc AM . 1 30. It is often convenient ... sine ; A'M ' an arc described from 0 as a centre , with any ra- radius R , and P'M ' its sine . Then , because OPM and ...
... sine , cosine , tangent , and cotangent of the angle AOM , as well as of the arc AM . 1 30. It is often convenient ... sine ; A'M ' an arc described from 0 as a centre , with any ra- radius R , and P'M ' its sine . Then , because OPM and ...
Page 23
... sine and the tangent of the complement of that are ( Arts . 26 and 28 ) : hence , the columns designated sine and tang , at the top of the page , are designated cosiné and cotang at the bottom . USE OF THE TABLE . To find the ...
... sine and the tangent of the complement of that are ( Arts . 26 and 28 ) : hence , the columns designated sine and tang , at the top of the page , are designated cosiné and cotang at the bottom . USE OF THE TABLE . To find the ...
Page 24
... sine , cosine , tang , or cotang , as the case may be ; the number there found is the logarithm required . log sin 19 ° 55 ' log tan 19 ° 55 ' Thus , • · • · • 9.532312 9.559097 If the angle is greater than 45 ° , look for the degrees ...
... sine , cosine , tang , or cotang , as the case may be ; the number there found is the logarithm required . log sin 19 ° 55 ' log tan 19 ° 55 ' Thus , • · • · • 9.532312 9.559097 If the angle is greater than 45 ° , look for the degrees ...
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Common terms and phrases
ABCD altitude apothem Applying logarithms centre chord circle circumference circumscribed complement cone consequently convex surface cosec cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium segment semi-circumference side BC similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex vertices volume whence write the following
Popular passages
Page 85 - 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 28 - If 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, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 90 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.
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 58 - ABM'" ; that is, the functions of — a are the same as the functions of 360° — a. From an inspection of the figure, we shall discover the following relations, viz. : sin (— a) = — sin a ; cos (— a) = cos a ; tan (—a) = — tan a ; cot (— a) = — cot a ; sec ( - a) = sec a ; cosec ( — a) = — cosec a.
Page 243 - AD c, have two sides, and the included angle of the one equal to two sides and the included angle of the other, each \ to each, and are equal in all their parts...
Page 154 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.
Page 57 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 16 - A DIAGONAL of a polygon is a line joining the vertices of two angles, not consecutive.