A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying. Adapted to the Method of Instruction in the American CollegesDurrie & Peck, 1853 - 5 páginas |
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Página 55
... hypothenuse is equal to the sum of the squares of the perpendicular sides . ( Euc . 47. 1. ) In the right angled triangles CBG , CAD , and CHF , ( Fig . 3. ) 1. CG2 = CB3 + BG3 , that is , R2 = cos2 + sin2 , * 2. CD2 = CA2 + AD3 3. CF2 ...
... hypothenuse is equal to the sum of the squares of the perpendicular sides . ( Euc . 47. 1. ) In the right angled triangles CBG , CAD , and CHF , ( Fig . 3. ) 1. CG2 = CB3 + BG3 , that is , R2 = cos2 + sin2 , * 2. CD2 = CA2 + AD3 3. CF2 ...
Página 67
... hypothenuse . If the tables used be logarithmic , they will give the logarithms of the lengths of the two sides . In the same manner , any right angled triangle whatever , whose base is equal to the radius of the tables , will have its ...
... hypothenuse . If the tables used be logarithmic , they will give the logarithms of the lengths of the two sides . In the same manner , any right angled triangle whatever , whose base is equal to the radius of the tables , will have its ...
Página 69
... HYPOTHENUSE be made radius , one of the legs will be a SINE of its opposite angle , and the other leg a COSINE of the same angle . Thus , if to the triangle ABC ( Fig . 14. ) a circle be applied , whose radius is AC , and whose center ...
... HYPOTHENUSE be made radius , one of the legs will be a SINE of its opposite angle , and the other leg a COSINE of the same angle . Thus , if to the triangle ABC ( Fig . 14. ) a circle be applied , whose radius is AC , and whose center ...
Página 70
... hypothenuse is the secant of the angle C , and the cosecant of the angle A. 124. Whenever a right angled triangle is proposed , whose sides or angles are required ; a similar triangle may be form- ed , from the sines , tangents , & c ...
... hypothenuse is the secant of the angle C , and the cosecant of the angle A. 124. Whenever a right angled triangle is proposed , whose sides or angles are required ; a similar triangle may be form- ed , from the sines , tangents , & c ...
Página 71
... hypothenuse be given , and the base or perpen- dicular be required ; then , in Fig . 14 , where ac is the tabular radius , be the tabular sine of a , or its equal A , and ab the tabular sine of C ; ( Art . 124. ) ac AC bc : BC , that is ...
... hypothenuse be given , and the base or perpen- dicular be required ; then , in Fig . 14 , where ac is the tabular radius , be the tabular sine of a , or its equal A , and ab the tabular sine of C ; ( Art . 124. ) ac AC bc : BC , that is ...
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Términos y frases comunes
acute angles arithmetical complement axis base bung diameter calculation cask circle circular sector circular segment circumference cosecant cosine cotangent cube cubic decimal difference distance divided equal to radius equation feet figure find the area find the SOLIDITY frustum given angle given number given side greater hypothenuse inches inscribed JEREMIAH DAY lateral surface length less line of chords loga middle diameter natural number negative number of degrees number of sides oblique opposite angles parallelogram parallelopiped perimeter perpendicular perpendicular height plane prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rithms rods root scale secant sector segment sine sines and cosines slant-height sphere spherical square subtract tables tangent tangent of half term theorem trapezium triangle ABC trigonometry wine gallons zone
Pasajes populares
Página 81 - 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.
Página 52 - The VERSED SINE of an arc is that part of the diameter which is between the sine and the arc. Thus, BA is the versed sine of the arc AG.
Página 43 - A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 98 - For, by art. 14, the decimal part of the logarithm of any number is the same, as that of the number multiplied into 10, 100, &c.
Página 131 - 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.
Página 38 - To the sum of the areas of the two ends add four times the area of a section parallel to and equally distant from both ends, and this last sum multiplied by | of the height will give the solidity.
Página 14 - To find then the logarithm of a vulgar fraction, subtract the logarithm of the denominator from that of the numerator. The difference will be the logarithm of the fraciion.
Página 100 - ... term. (Art. 52.) But it is more convenient in practice to begin by subtracting the first term from one of the others. If four quantities are proportional, the quotient of the first divided by the second, is equal to the quotient of the third divided by the fourth.
Página 49 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Página 41 - TO ONE OF THE SIDES. Or, MULTIPLY THE CUBE OF ONE OF THE EDGES, BY THE SOLIDITY OF A SIMILAR SOLID WHOSE EDGES ARE 1...