A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and SurveyingDurrie and Peck, 1851 |
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Página 52
... extended till it meets a line drawn from the center through the other end . Thus , AD ( Fig . 3. ) is the tangent of the ... extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines ...
... extended till it meets a line drawn from the center through the other end . Thus , AD ( Fig . 3. ) is the tangent of the ... extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines ...
Página 58
... extend these tables beyond 90 ° ; because the sines , tangents , and secants , are of the same magnitude , in one of the quadrants of a circle , as in the others . Thus the sine of 30 ° is equal to that of 150 ° . ( Art . 90. ) 99. And ...
... extend these tables beyond 90 ° ; because the sines , tangents , and secants , are of the same magnitude , in one of the quadrants of a circle , as in the others . Thus the sine of 30 ° is equal to that of 150 ° . ( Art . 90. ) 99. And ...
Página 59
... extend from the center , to a point without the circle . 102. The numbers in the table here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined in arts . 82 , 83 ...
... extend from the center , to a point without the circle . 102. The numbers in the table here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined in arts . 82 , 83 ...
Página 81
... Extend CA to G , making AG equal to AB ; then CG is the sum of the two sides AB and AC . On AB , set off AD , equal to AC ; then BD is the difference of the sides AB and AC . The sum of the two angles ACB and ABC , is equal to the sum ...
... Extend CA to G , making AG equal to AB ; then CG is the sum of the two sides AB and AC . On AB , set off AD , equal to AC ; then BD is the difference of the sides AB and AC . The sum of the two angles ACB and ABC , is equal to the sum ...
Página 82
... extend BA to H. Then by Euc . 35. 3 . ABXAH ALXAD Therefore , AB AD : AL : AH But AD - CD + CA = CB + CA And AL - CL - CA - CB - CA And AH - HP - PA = BP - PA ( Euc . 3. 3. ) If , then , for the three last terms in the proportion , we ...
... extend BA to H. Then by Euc . 35. 3 . ABXAH ALXAD Therefore , AB AD : AL : AH But AD - CD + CA = CB + CA And AL - CL - CA - CB - CA And AH - HP - PA = BP - PA ( Euc . 3. 3. ) If , then , for the three last terms in the proportion , we ...
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Términos y frases comunes
ABCD arithmetical complement axis base calculation circle circular segment circumference column cone cosecant cosine cotangent course cylinder decimal diameter Diff difference of latitude difference of longitude divided earth equator feet figure find the area find the SOLIDITY frustum given side greater horizon hypothenuse inches JEREMIAH DAY length less line of chords logarithm measured Mercator's Merid meridional difference miles minutes multiplied negative number of degrees number of sides object oblique parallel of latitude parallelogram parallelopiped perimeter perpendicular plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right ascension right cylinder rods root scale secant segment sine sines and cosines slant-height sphere spherical spirit level square subtract surface tables tangent term theorem trapezium triangle ABC Trig trigonometry whole
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 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 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Página 61 - When a quantity is greater than any other of the same class, it is called a maximum. A multitude of straight lines, of different lengths, may be drawn within a circle. But among them all, the diameter is a maximum. Of all sines of angles, which can be drawn in a circle, the sine of 90° is a maximum. When a quantity is less than any other of the same class, it is called a minimum. Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given...
Página 69 - This will reduce the whole to the triangle MGD, which is equal to the original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice, it will not be necessary actually to draw the parallel lines BD, GC, &c. It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed,...
Página 21 - THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR.
Página 48 - PROBLEM VI. To find the SOLIDITY of a FRUSTUM of a cone. 68. ADD TOGETHER THE AREAS OF THE TWO ENDS, AND THE SQUARE ROOT OF THE PRODUCT OF THESE AREAS; AND MULTIPLY THE SUM BY 1 OF THE PERPENDICULAR HEIGHT.
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 14 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Página 56 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.