A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the Nature and Use of Logarithms : Being the Second Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges |
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Page 124
... = 1 ' , 2 ' , 3 ' , & c . successively , we shall have expressions for the sines and cosines of a series of arcs increasing regularly by one minute . Thus , * See note H. sin ( 1 ' + 1 ' ) = 2 124 COMPUTATION OF THE CANON .
... = 1 ' , 2 ' , 3 ' , & c . successively , we shall have expressions for the sines and cosines of a series of arcs increasing regularly by one minute . Thus , * See note H. sin ( 1 ' + 1 ' ) = 2 124 COMPUTATION OF THE CANON .
Page 143
... regular polygon , or to inscribe one in a given circle . Thus , to make a pentagon with the transverse distance from 6 to 6 for radius , describe a circle , and the distance from 5 to 5 will be the length of one of the sides of a ...
... regular polygon , or to inscribe one in a given circle . Thus , to make a pentagon with the transverse distance from 6 to 6 for radius , describe a circle , and the distance from 5 to 5 will be the length of one of the sides of a ...
Page 1
... regular polygon has all its sides equal , and all its angles equal . III . The height of a triangle is the length of a perpendicu- lar , drawn from one of the angles to the opposite side ; as CP . ( Fig . 5. ) The height of a four sided ...
... regular polygon has all its sides equal , and all its angles equal . III . The height of a triangle is the length of a perpendicu- lar , drawn from one of the angles to the opposite side ; as CP . ( Fig . 5. ) The height of a four sided ...
Page 11
... REGULAR POLYGÓN . 15. MULTIPLY ONE OF ITS SIDES INTO HALF ITS PERPEN- DICULAR DISTANCE FROM THE CENTER , AND THIS PRODUCT INTO THE NUMBER OF SIDES . A regular polygon contains as many equal triangles as the figure has sides . Thus the ...
... REGULAR POLYGÓN . 15. MULTIPLY ONE OF ITS SIDES INTO HALF ITS PERPEN- DICULAR DISTANCE FROM THE CENTER , AND THIS PRODUCT INTO THE NUMBER OF SIDES . A regular polygon contains as many equal triangles as the figure has sides . Thus the ...
Page 12
... regular hexagon ( Fig . 7. ) be 38 inches , what is the area ? The angle BCP of 360 ° 30 ° . Then , R : 19 :: cot 30 ° 32.909 - CP , the perpendicular . And the area = 19 × 32.909 × 6 = 3751.6 . 2. What is the area of a regular decagon ...
... regular hexagon ( Fig . 7. ) be 38 inches , what is the area ? The angle BCP of 360 ° 30 ° . Then , R : 19 :: cot 30 ° 32.909 - CP , the perpendicular . And the area = 19 × 32.909 × 6 = 3751.6 . 2. What is the area of a regular decagon ...
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A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2017 |
A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2018 |
A Treatise of Plane Trigonometry: To Which Is Prefixed a Summary View of the ... Jeremiah Day No preview available - 2018 |
Common terms and phrases
ABC Fig ABCD altitude axis base breadth bung diameter calculation cask circle circular sector circular segment circumference column cosecant cosine cotangent course cube cubic decimal departure Diff difference of latitude difference of longitude distance divided earth equal to half equator figure find the area find the SOLIDITY frustum given sides gles greater hypothenuse inches inscribed lateral surface length less logarithm longitude measured Mercator's meridian meridional difference middle diameter miles multiply the sum number of degrees number of sides oblique parallelogram parallelopiped perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rods rule secant sector segment ship sine sines and cosines slant-height sphere spherical subtract tables tangent term theorem trapezium triangle ABC Trig trigonometry wine gallons zone
Popular passages
Page 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.
Page 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.
Page 50 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 69 - 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 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.
Page 89 - Divide the height of the segment by the diameter of the circle ; look for the quotient in the column of heights in the table ; take out the corresponding number in the column of areas ; and multiply it by the square of the diameter.