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 89
... segment NP - AP . ( Euc . 3. 3. ) But BP is greater than NP . 147. The two segments are to each other , as the tangents of the opposite angles , or the cotangents of the adjacent an- gles . For , in the right angled triangles ACP , and ...
... segment NP - AP . ( Euc . 3. 3. ) But BP is greater than NP . 147. The two segments are to each other , as the tangents of the opposite angles , or the cotangents of the adjacent an- gles . For , in the right angled triangles ACP , and ...
Página 90
... segments are as the tangents of the opposite angles . And the tangents of these are the cotangents of the adjacent angles A and B. ( Art . 89. ) Cor . The greater segment is opposite to the greater angle . And of the angles at the base ...
... segments are as the tangents of the opposite angles . And the tangents of these are the cotangents of the adjacent angles A and B. ( Art . 89. ) Cor . The greater segment is opposite to the greater angle . And of the angles at the base ...
Página 96
... segments may be found by Theorem III . ( Art . 145. ) There will then be given , in each of the right angled tri- angles , the hypothenuse and one of the legs , from which the angles may be determined , by rectangular trigonometry ...
... segments may be found by Theorem III . ( Art . 145. ) There will then be given , in each of the right angled tri- angles , the hypothenuse and one of the legs , from which the angles may be determined , by rectangular trigonometry ...
Página 97
... segments is AP , because it is next the side AC , which is greater than BC . ( Art . 146. ) 19.5 To and from half the sum of the segments Adding and subtracting half their difference , ( Art . 153. ) 6.36 We have the greater segment AP ...
... segments is AP , because it is next the side AC , which is greater than BC . ( Art . 146. ) 19.5 To and from half the sum of the segments Adding and subtracting half their difference , ( Art . 153. ) 6.36 We have the greater segment AP ...
Página 149
... segments made by the perpendicular . The demonstration is the same , as in the other case , ex- cept that AH - BP + PA , instead of BP — PA . Thus , in the circle BDHL , of which C is the centre , ABXAH - ALXAD ; therefore AB : AD :: AL ...
... segments made by the perpendicular . The demonstration is the same , as in the other case , ex- cept that AH - BP + PA , instead of BP — PA . Thus , in the circle BDHL , of which C is the centre , ABXAH - ALXAD ; therefore AB : AD :: AL ...
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.