The mechanical Euclid, containing the elements of mechanics and hydrostatics1837 |
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Página i
... MANNER OF THE ELEMENTS OF GEOMETRY ; AND INCLUDING THE PROPOSITIONS FIXED UPON BY THE UNIVERSITY OF CAMBRIDGE AS REQUISITE FOR THE DEGREE OF B. A. TO WHICH ARE ADDED EL REMARKS ON MATHEMATICAL REASONING AND ON THE LOGIC OF INDUCTION ...
... MANNER OF THE ELEMENTS OF GEOMETRY ; AND INCLUDING THE PROPOSITIONS FIXED UPON BY THE UNIVERSITY OF CAMBRIDGE AS REQUISITE FOR THE DEGREE OF B. A. TO WHICH ARE ADDED EL REMARKS ON MATHEMATICAL REASONING AND ON THE LOGIC OF INDUCTION ...
Página 7
... manner , n a ” × a ” = a ” + ” ; and 3a2x3 × 5 a x y2 = 15a3x1y3 . 27. If the multiplier or multiplicand consist of several terms , each term of the latter must be mul- tiplied by every term of the former , and the sum of all the ...
... manner , n a ” × a ” = a ” + ” ; and 3a2x3 × 5 a x y2 = 15a3x1y3 . 27. If the multiplier or multiplicand consist of several terms , each term of the latter must be mul- tiplied by every term of the former , and the sum of all the ...
Página 10
... manner C = dy ; therefore , by the same axiom , ac = bday ; dividing these equal quantities , ac and bday by bd , we have * ( 8 ) . 35 . ac bd - a C xy = b To divide simple Algebraical Fractions . To divide a fraction by any quantity ...
... manner C = dy ; therefore , by the same axiom , ac = bday ; dividing these equal quantities , ac and bday by bd , we have * ( 8 ) . 35 . ac bd - a C xy = b To divide simple Algebraical Fractions . To divide a fraction by any quantity ...
Página 15
... - other when the two quantities depend wholly upon each other , in such a manner that if the one be changed the other is changed in the same proportion . If the altitude of a triangle be invariable , the ALGEBRA . 15 (11) Variation.
... - other when the two quantities depend wholly upon each other , in such a manner that if the one be changed the other is changed in the same proportion . If the altitude of a triangle be invariable , the ALGEBRA . 15 (11) Variation.
Página 16
... manner , but the reciprocal of the latter is changed in the same manner . If the area of a triangle be given the base varies as the perpendicular altitude . If A , a represent the altitudes , B , b the bases of two triangles , since a ...
... manner , but the reciprocal of the latter is changed in the same manner . If the area of a triangle be given the base varies as the perpendicular altitude . If A , a represent the altitudes , B , b the bases of two triangles , since a ...
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The Mechanical Euclid, Containing the Elements of Mechanics and Hydrostatics William Whewell Sin vista previa disponible - 2015 |
Términos y frases comunes
ABCD Accelerating Force algebraical quantities Axioms of Statics axis balance body falling body moving center of gravity column of fluid deductive deductive reasoner definition density destroy direction equilibrium exerted fluid displaced forces acting fulcrum Geometry heavy fluid Hence horizontal plane horizontal pressures hydrostatic balance Hydrostatics idea immersed inclined plane INDUCTIVE PRINCIPLE lever magnitude manner mathematical mercury opposite P's velocity parallel particle perpendicular piston portions pressure on LM prism produce proportion pully Q. E. D. PROP quantity of matter ratio reasoning represent rest right angle SCHOLIUM sides space described specific gravity straight line string supposed surface pressed tical tions triangles truth tube uniform force University of Cambridge upper surface valve velocity acquired vertical column vertical line vessel weight
Pasajes populares
Página 22 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. 5. The inclination of a straight line to a plane...
Página 46 - If three forces, represented in magnitude and direction by the sides of a triangle, act on a point, they will keep it at rest.
Página 9 - Sacred History, from the Creation of the World to the Destruction of Jerusalem. With Questions for Examination.
Página 18 - ... if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth.
Página 47 - There is an equilibrium upon the wheel and axle when the power is to the weight as the radius of the axle to the radius of the wheel.
Página 20 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Página 97 - ... gravity of the fluid : the specific gravity of the body. Prop. 10. To describe the hydrostatic balance, and to shew how to find the specific gravity of a body by means of it, 1st, when its specific gravity is greater than that of the fluid in which it is weighed ; 2ndly, when it is less.