A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying : Adapted to the Method of Instruction in the American Colleges, Volumes 1-3Durrie and Peck, 1838 - Geometry |
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Page 82
... SEGMENTS MADE BY THE PERPENDICULAR . In the triangle ABC , ( Fig . 26. ) if a perpendicular be drawn from C upon AB ; AB ... segment is next the greater side . If BC is greater than AC , ( Fig . 26. ) PB is * See note F. greater than AP ...
... SEGMENTS MADE BY THE PERPENDICULAR . In the triangle ABC , ( Fig . 26. ) if a perpendicular be drawn from C upon AB ; AB ... segment is next the greater side . If BC is greater than AC , ( Fig . 26. ) PB is * See note F. greater than AP ...
Page 83
... 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 ...
Page 88
... segments may be found by theorem III . ( Art . 145. ) There will then be given , in each of the right angled trian- gles , 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 trian- gles , the hypothenuse and one of the legs , from which the angles may be determined , by rectangular trigonometry ...
Page 89
... segments is AP , because it is next the side AC , which is greater than BC . ( Art . 146. ) To and from half the sum of the segments 19.5 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. ) To and from half the sum of the segments 19.5 Adding and subtracting half their difference , ( Art . 153. ) 6.36 We have the greater segment AP ...
Page 140
... , the side on which the perpendicular falls , is to the sum of the other two ; as the difference of the latter , to the sum of the segments made by the perpendicular . The demonstration is the same , as in the other 140 NOTES .
... , the side on which the perpendicular falls , is to the sum of the other two ; as the difference of the latter , to the sum of the segments made by the perpendicular . The demonstration is the same , as in the other 140 NOTES .
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Common terms and phrases
ABCD altitude angle of elevation axis base calculation cask chord circle circular segment circumference column cosecant cosine cotangent cube cubic decimal departure and difference Diff difference of latitude difference of longitude divided earth equator feet field figure find the area find the SOLIDITY frustum given sides greater hypothenuse inches inscribed lateral surface length logarithm measured Mercator's Merid meridian distances meridional difference middle diameter middle latitude miles minutes number of degrees number of sides object oblique parallel of latitude parallel sailing parallelogram parallelopiped perimeter perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quotient radius regular polygon right angled triangle right cylinder rods secant sector segment ship sails sine slant-height sphere spherical square subtract tables tangent theorem trapezium triangle ABC Trig trigonometry wine gallons zone
Popular passages
Page 120 - 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.
Page 83 - 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.
Page 45 - 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.
Page 57 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 73 - 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, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.
Page 63 - 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...
Page 16 - 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.
Page 124 - From half the sum of the three sides subtract each side separately ; multiply together the half sum and the three remainders, and extract the square root of the product.
Page 100 - 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.
Page 58 - CoR. 9. 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.