Elements of Geometry, Theoretical and Practical: Containing a Full Explanation of the Construction and Use of Tables, and a New System of SurveyingPratt, Woodford, 1848 - 324 páginas |
Dentro del libro
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Página 6
... construct his , to us , clumsy book of proportion , the best and only algebra at his command ? Why , when so much labor is saved and greater clearness ob- tained , should we refuse to employ an equation like ( a + b ) 2 : a2 + b2 + 2ab ...
... construct his , to us , clumsy book of proportion , the best and only algebra at his command ? Why , when so much labor is saved and greater clearness ob- tained , should we refuse to employ an equation like ( a + b ) 2 : a2 + b2 + 2ab ...
Página 69
... sides parallel . Application . Draw parallel lines upon paper with the straightedge and rightangle , and construct them in the field by aid of the cross . Fig . 83 . Fig . 8 . PROPOSITION IV . The sum of the external angles of.
... sides parallel . Application . Draw parallel lines upon paper with the straightedge and rightangle , and construct them in the field by aid of the cross . Fig . 83 . Fig . 8 . PROPOSITION IV . The sum of the external angles of.
Página 71
... construct about the vertex of a triangle angles equal to those at the base , and do this for triangles of different forms . 2o . Through the vertex of any triangle draw a line paral- Fig . 10 . lel to the base and prove ( 92 ) . 3 ...
... construct about the vertex of a triangle angles equal to those at the base , and do this for triangles of different forms . 2o . Through the vertex of any triangle draw a line paral- Fig . 10 . lel to the base and prove ( 92 ) . 3 ...
Página 77
... bisected by the lines AO , BO , and from O draw OP , OQ , parallel to the sides CA , CB , and terminating in the base in P and Q. Prove that AP PQ = QB . [ The student will construct the figure . ] = 8 ° . Prove that any side of a triangle.
... bisected by the lines AO , BO , and from O draw OP , OQ , parallel to the sides CA , CB , and terminating in the base in P and Q. Prove that AP PQ = QB . [ The student will construct the figure . ] = 8 ° . Prove that any side of a triangle.
Página 81
... construct the triangle ( h ' , a , b ' ) making bb and the ( a , b ) , there will result h2 = a2 + b2 = a2 + b2 = h2 , ... h ' = h , and < ( a , b ) = ( a , b ' ) = L. a Fig . 212 . Cor . 6. The diagonal of a square is incommensurable 6.
... construct the triangle ( h ' , a , b ' ) making bb and the ( a , b ) , there will result h2 = a2 + b2 = a2 + b2 = h2 , ... h ' = h , and < ( a , b ) = ( a , b ' ) = L. a Fig . 212 . Cor . 6. The diagonal of a square is incommensurable 6.
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Otras ediciones - Ver todas
Elements of Geometry, Theoretical and Practical: Containing a Full ... George Clinton Whitlock Sin vista previa disponible - 2016 |
Elements of Geometry, Theoretical and Practical: Containing a Full ... George Clinton Whitlock Sin vista previa disponible - 2016 |
Términos y frases comunes
A₁ abscissa algebraical altitude base becomes BINOMIAL THEOREM bisects C₁ centre chains chord circle circumference coefficients constant continuous function cosb cosc cosine cota cotb curve D₂ denominator denote derivative determine diameter difference diminished distance divided draw drawn ellipse embraced equal equation exponent fraction function geometry given greater horizontal hyperbola hypothenuse increment intersect logarithm measured minus multiplied observe operation opposite parabola parallel parallelogram perpendicular plane polygon polynomial problem proportional PROPOSITION quantities quotient radii radius ratio rectangle right angled triangle Scholium secant line segments sides sinb sine sinx square straight line subtangent subtracting tana tanb tangent theorem variable vertical whence y₁
Pasajes populares
Página 11 - If two triangles have two sides of the one equal to two sides of the...
Página 256 - ... greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle, shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to...
Página 62 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Página 187 - As the sine of the angle opposite the given side, is to the sine of the angle opposite the required side ; so is the given side to the required side.
Página 37 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 75 - ... by four times the square of the line joining the middle points of the diagonals.
Página 296 - N. by E. NNE NE by N. NE NE by E. ENE E. by N. East E. by S. ESE SE by E. SE SE by S.
Página 169 - The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference.
Página 256 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Página 72 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those angles equal which subtend the homologous sides.