A Treatise of Plane Trigonometry, and the Mensuration of Heights and Distances: To which is Prefixed a Summary View of the Nature and Use of Logarithms. Adapted to the Method of Instruction in Schools and AcademiesIvison & Phinney, 1855 - 237 páginas |
Dentro del libro
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Página 50
... chord of double the arc . The sine BG is half PG , which is the chord of the arc PAG , double the are AG . 83. The VERSED SINE of an arc is that part 50 TRIGONOMETRY .
... chord of double the arc . The sine BG is half PG , which is the chord of the arc PAG , double the are AG . 83. The VERSED SINE of an arc is that part 50 TRIGONOMETRY .
Página 55
... chord of 60 ° are , in any circle , each equal And the tangent of 45 ° to the radius , and therefore equal to each other . Demonstration . 1. In the quadrant ACH , ( figure on the next page , ) the arc AH is 90 ° . The sine of this ...
... chord of 60 ° are , in any circle , each equal And the tangent of 45 ° to the radius , and therefore equal to each other . Demonstration . 1. In the quadrant ACH , ( figure on the next page , ) the arc AH is 90 ° . The sine of this ...
Página 56
... chord of 60 ° , is equal to CS , the radius . 3. Let AR be an arc of 45 ° . AD will be its tangent , and the angle ... chord of 60 ° . ( Art . 82. cor . But by the preceding article , the chord of 60 ° is equal to radius . Its half ...
... chord of 60 ° , is equal to CS , the radius . 3. Let AR be an arc of 45 ° . AD will be its tangent , and the angle ... chord of 60 ° . ( Art . 82. cor . But by the preceding article , the chord of 60 ° is equal to radius . Its half ...
Página 57
... chord , as the chord to the versed sine . Let the arc AD - a , and ADB - 2a . Draw BF perpen- dicular to AH . This will divide the right angled triangle ABH into two similar triangles . ( Euc . 8. 6. ) The angles ACD and AHB are equal ...
... chord , as the chord to the versed sine . Let the arc AD - a , and ADB - 2a . Draw BF perpen- dicular to AH . This will divide the right angled triangle ABH into two similar triangles . ( Euc . 8. 6. ) The angles ACD and AHB are equal ...
Página 99
... chords . In forming a given triangle , or any other right lined figure , the parts which must be made to agree with the conditions proposed , are the lines and the angles . For the former , a scale of equal parts is used ; for the ...
... chords . In forming a given triangle , or any other right lined figure , the parts which must be made to agree with the conditions proposed , are the lines and the angles . For the former , a scale of equal parts is used ; for the ...
Otras ediciones - Ver todas
A Treatise of Plane Trigonometry, and the Mensuration of Heights and ... Jeremiah Day Vista completa - 1848 |
A Treatise of Plane Trigonometry, and the Mensuration of Heights and ... Jeremiah Day Sin vista previa disponible - 2016 |
A Treatise Of Plane Trigonometry, And The Mensuration Of Heights And ... Jeremiah Day Sin vista previa disponible - 2008 |
Términos y frases comunes
ac AC arithmetical complement base bung diameter calculation cask centre circle circular segment circumference cosecant Cosine Sine Cotang cube cubic decimal dicular difference distance divided equal to half equal to radius extend feet figure find the angles frustum given angle given side gles greater hypothenuse inches inscribed lateral surface length less line of chords line of numbers loga logarithm measure miles multiplied natural number negative number of degrees number of sides oblique parallelogram parallelopiped perimeter perpen perpendicular perpendicular height plane prism PROBLEM proportion pyramid quadrant quantity quotient radius regular polygon right angled triangle right cylinder rithm rods root scale secant sector segment slant-height sphere square subtended subtracting tables Tang tangent term Theorem Thomson's Legendre trapezium triangle ABC Trig trigonometry vulgar fraction whole wine gallons zone
Pasajes populares
Página 19 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 19 - 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 fraction. Or the logarithm may be found, by first reducing the vulgar fraction to a decimal. If the numerator is less than the denominator, the index of the logarithm must be negative, because the value of the fraction is less than a unit. ( Art* 9.) Required the logarithm of f 4.
Página 129 - From half the sum of the sides, subtract each side severally; multiply together the half sum and the three remainders; and extract the square root of the product.
Página 56 - A cylinder is a solid described by the revolution of a rectangle about one of its sides, which remains fixed.
Página 92 - One of the required angles is found, by beginning with a side, and, according to Theorem I, stating the proportion, As the side opposite the given angle, To the sine of that angle ; So is the side opposite the required angle, To the sine of that angle. The third angle is found, by subtracting the sum of the other two from 180° ; and the remaining side is found, by the proportion in the preceding article.
Página 39 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 34 - But the difference of two squares is equal to the product of the sum and difference of their roots.
Página 27 - ... base. For the area of a circle is equal to the product of half the diameter into half the circumference ; (Art.
Página 18 - The sum of the logarithms of two numbers, is the logarithm of the product of those numbers ; and the difference of the logarithms of two numbers, is the logarithm of the quotient of one of the numbers divided by the other. (Art. 2.) In Briggs' system, the logarithm of 10 is 1.
Página 38 - Find the amount of 1 dollar for 1 year ; multiply its logarithm by the number of years ; and to the product, add the logarithm of the principal. The 'sum will be the logarithm of the amount for the given time. From the amount subtract the principal, and the remainder will be the interest.