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
Resultados 1-5 de 51
Página 25
... obvious that all propositions requiring demon- stration , must be founded , either directly or indirectly , upon those which do not , or on axioms ; and hence our first proposition be- comes the source of a vast amount of knowledge ...
... obvious that all propositions requiring demon- stration , must be founded , either directly or indirectly , upon those which do not , or on axioms ; and hence our first proposition be- comes the source of a vast amount of knowledge ...
Página 26
... obviously have the same number of units whether we diminish the a + b units by taking the c units from b or from a . Q. E. D. PROPOSITION IV . Multiplications , divisions , multiplications and divisions , ( 4 ) are relatively free ...
... obviously have the same number of units whether we diminish the a + b units by taking the c units from b or from a . Q. E. D. PROPOSITION IV . Multiplications , divisions , multiplications and divisions , ( 4 ) are relatively free ...
Página 27
... obviously the same as assuming Q to be resolvable into factors , two of which are b and c ; hence , Q being divisible by b and c , denoting the third factor by a , we have .. ( 112 ) Q = abc ; Q : cab , dividing both sides by c , and ...
... obviously the same as assuming Q to be resolvable into factors , two of which are b and c ; hence , Q being divisible by b and c , denoting the third factor by a , we have .. ( 112 ) Q = abc ; Q : cab , dividing both sides by c , and ...
Página 28
... obviously 1 + 1 + 1 + ... .. + 1 + 1 + 1 + ... .. 1 + 1 + 1 + ... + 1 + 1 + 1 + ... 1 + 1 + 1 + ... + 1 + 1 + 1 + ... ... ... ... may be done , since it is only asserting the same proposition in an inverted order ; = . ( 111 ) ( a + b ) c - ...
... obviously 1 + 1 + 1 + ... .. + 1 + 1 + 1 + ... .. 1 + 1 + 1 + ... + 1 + 1 + 1 + ... 1 + 1 + 1 + ... + 1 + 1 + 1 + ... ... ... ... may be done , since it is only asserting the same proposition in an inverted order ; = . ( 111 ) ( a + b ) c - ...
Página 39
... obviously be ex- tended to three or more unknown quantities , embraced in three or more independent equations - equations not convertible into each other ; and it will become manifest , by making the elimination , that the number of ...
... obviously be ex- tended to three or more unknown quantities , embraced in three or more independent equations - equations not convertible into each other ; and it will become manifest , by making the elimination , that the number of ...
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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.