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 51
... drawn , within and about the circle , a number of straight lines , called Sines , Tangents , Secants , & c . With these the learner should make himself perfectly familiar . 82. The SINE of an arc is a straight line drawn from one end of ...
... drawn , within and about the circle , a number of straight lines , called Sines , Tangents , Secants , & c . With these the learner should make himself perfectly familiar . 82. The SINE of an arc is a straight line drawn from one end of ...
Page 52
... drawn per- pendicular from the extremity of the diameter which passes through one end of the arc , and extended till it meets a line drawn from the center through the other end . Thus AD ( Fig . 3. ) is the tangent of the arc AG . 85 ...
... drawn per- pendicular from the extremity of the diameter which passes through one end of the arc , and extended till it meets a line drawn from the center through the other end . Thus AD ( Fig . 3. ) is the tangent of the arc AG . 85 ...
Page 57
... Draw BF perpendicular to AH . This will divide the right angled tri- angle ABH into two similar triangles . ( Euc . 8. 6. ) The an- gles ACD and AHB are equal . ( Euc . 20. 3. ) Therefore the four triangles ACG , AHB , FHB , and FAB are ...
... Draw BF perpendicular to AH . This will divide the right angled tri- angle ABH into two similar triangles . ( Euc . 8. 6. ) The an- gles ACD and AHB are equal . ( Euc . 20. 3. ) Therefore the four triangles ACG , AHB , FHB , and FAB are ...
Page 66
... drawn , with sides parallel to these , will all have the same angles . So that one of the parts given must always be ... drawing a perpen- dicular from one of the angles to the opposite side . 116. One of the six parts in a right angled ...
... drawn , with sides parallel to these , will all have the same angles . So that one of the parts given must always be ... drawing a perpen- dicular from one of the angles to the opposite side . 116. One of the six parts in a right angled ...
Page 80
... drawn perpendicular to the op- posite side . This will fall either within or without the tri- angle . 1. Let it fall within as in Fig . 23. Then , in the right an- gled triangles ACD and BCD , according to art . 126 , Rbsin A : p Rasin ...
... drawn perpendicular to the op- posite side . This will fall either within or without the tri- angle . 1. Let it fall within as in Fig . 23. Then , in the right an- gled triangles ACD and BCD , according to art . 126 , Rbsin A : p Rasin ...
Other editions - View all
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.