The mechanical Euclid, containing the elements of mechanics and hydrostatics1837 |
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Página 11
... less than b , c is less than d , and if a be greater than b , c is greater than d . 12 39. When four quantities are proportionals , the product ALGEBRA . 11 (9) Definition of Proportion (10) Consequences of Proportion.
... less than b , c is less than d , and if a be greater than b , c is greater than d . 12 39. When four quantities are proportionals , the product ALGEBRA . 11 (9) Definition of Proportion (10) Consequences of Proportion.
Página 20
... less than that of the second , the multiple of the third is also less than that of the fourth ; or if the multiple of the first be equal to the multiple of the second , the multiple of the third is also equal to that of the fourth ; or ...
... less than that of the second , the multiple of the third is also less than that of the fourth ; or if the multiple of the first be equal to the multiple of the second , the multiple of the third is also equal to that of the fourth ; or ...
Página 21
... less than nb , mc is less than nd ; greater , greater . ( Art . 38. ) and if equal , equal ; and if Therefore the magnitudes . a , b , c , d are proportionals according to the geome- trical definition . LEMMA 2. If magnitudes be ...
... less than nb , mc is less than nd ; greater , greater . ( Art . 38. ) and if equal , equal ; and if Therefore the magnitudes . a , b , c , d are proportionals according to the geome- trical definition . LEMMA 2. If magnitudes be ...
Página 30
... weight . 2. A force may be taken equal to the excess of a greater given force over a less . 3. A force may be taken in a given ratio to a given force . PROPOSITION I. If a weight be supported on a horizontal 30 MECHANICS .
... weight . 2. A force may be taken equal to the excess of a greater given force over a less . 3. A force may be taken in a given ratio to a given force . PROPOSITION I. If a weight be supported on a horizontal 30 MECHANICS .
Página 31
... less , and by Post . 2 take X , the force which is the excess of Q above P , so that P + X is equal to Q ; therefore ... less than Q ; and in the same manner it may be shewn that Q is not less than P. Therefore P and Q are equal . Hence ...
... less , and by Post . 2 take X , the force which is the excess of Q above P , so that P + X is equal to Q ; therefore ... less than Q ; and in the same manner it may be shewn that Q is not less than P. Therefore P and Q are equal . Hence ...
Otras ediciones - Ver todas
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.