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 AcademiesM.H. Newman & Company, 1848 - 153 páginas |
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Página 50
... radius of the circle . In many calculations , it is convenient to consider the radius , whatever be its length , as a unit . ( Alg . 510. ) To this must be referred the numbers expressing the lengths of other lines . Thus , 20 will be ...
... radius of the circle . In many calculations , it is convenient to consider the radius , whatever be its length , as a unit . ( Alg . 510. ) To this must be referred the numbers expressing the lengths of other lines . Thus , 20 will be ...
Página 53
... radius . But the versed sine of an obtuse angle is equal to the sum of the cosine and radius . Thus , the versed sine of ACG is AB = AC - BC . ( Art . 83. ) But the versed sine of MCG is MB MC + BC . Relations of Sines , Tangents ...
... radius . But the versed sine of an obtuse angle is equal to the sum of the cosine and radius . Thus , the versed sine of ACG is AB = AC - BC . ( Art . 83. ) But the versed sine of MCG is MB MC + BC . Relations of Sines , Tangents ...
Página 54
... radius , sin for sine , cos for cosine , tan for tangent , cot for cotangent , sec for secant , cosec for cosecant . H F L G C B M O By comparing the triangles CBG and CAD , 1. AC BC : AD : BG , that is , R 2. CG CD :: BG : AD cos : tan ...
... radius , sin for sine , cos for cosine , tan for tangent , cot for cotangent , sec for secant , cosec for cosecant . H F L G C B M O By comparing the triangles CBG and CAD , 1. AC BC : AD : BG , that is , R 2. CG CD :: BG : AD cos : tan ...
Página 55
... 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 , according to the definition , ( Art . 82. ) is CH , the radius of the circle ...
... 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 , according to the definition , ( Art . 82. ) is CH , the radius of the circle ...
Página 56
... radius . For Cor . The cotangent of 45 ° is also equal to radius . the complement of 45 ° is itself 45 ° . Thus , HD , the cotan- gent of ACD , is equal to AC the radius . 96. The sine of 30 ° is equal to half radius . For the sine of ...
... radius . For Cor . The cotangent of 45 ° is also equal to radius . the complement of 45 ° is itself 45 ° . Thus , HD , the cotan- gent of ACD , is equal to AC the radius . 96. The sine of 30 ° is equal to half radius . For the sine of ...
Otras ediciones - Ver todas
A Treatise of Plane Trigonometry, and the Mensuration of Heights and ... Jeremiah Day Vista completa - 1855 |
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
ABCD altitude axis base breadth bung diameter calculated capacity cask centre circular sector circular segment circumference convex surface cosecant Cosine Cotang cube decimal dicular difference divided earth equal to half figure find the area find the SOLIDITY frustum given sides gles greater head diameter hypothenuse inscribed lateral surface length less line of chords logarithm measure miles MULTIPLY THE SUM number of degrees number of sides oblique parallel parallelogram parallelopiped perpen perpendicular perpendicular height plane prism PROBLEM product of half proportion pyramid quadrant quantity quotient radius regular polygon regular solids right angled triangle right cone right cylinder right prism rods root secant sector sine sphere square feet subtracted tables tabular Tang tangent term Theorem Thomson's Legendre trapezium triangle ABC Trig trigonometry ullage whole surface wine gallons zone
Pasajes populares
Página 39 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 19 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 51 - 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 101 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that fronc '>ence the annexed first two figures of the Logarithm in the colvvran stand in the next lower line. N.
Página 47 - The circumference of every circle, whether great or small, is supposed to be divided into 360 equal parts, called degrees ; and every degree into 60 parts, called minutes ; and every minute into 60 seconds.
Página 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Página 4 - QUADRANT. NB The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right-hand column, belong to the degrees below.
Página 12 - We have then this important property, j -f 14. The DECIMAL PART of the logarithm of any number is the same, as that of the number multiplied or divided by 10, 100, 1000, &c.
Página 34 - But the difference of two squares is equal to the product of the sum and difference of their roots.
Página 18 - ... 1.84148. 31. To find the. logarithm of a VULGAR FRACTION. From the nature of a vulgar fraction, the numerator may be considered as a dividend, and the denominator as a divisor; in other words, the value of the fraction is equal to the quotient, of the numerator divided by the denominator.