An Introduction to the Theory and Practice of Mechanics: In Five Books ... |
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Page 16
... fall the perpendiculars DE , DF ; the triangles BED , CFD , are similar ; for the angles at B and C. being both of them equal to the angle A , are equal to each other ; therefore , we have . DC : DB :: DF : DE , and , by the supposition ...
... fall the perpendiculars DE , DF ; the triangles BED , CFD , are similar ; for the angles at B and C. being both of them equal to the angle A , are equal to each other ; therefore , we have . DC : DB :: DF : DE , and , by the supposition ...
Page 24
... fall upon DB the perpendicular AC , and CB is the effective force required . For the force AB is equivalent to the two forces AC , CB , and AC being perpendicular to DB , can have no effect in urging the body along DB ; therefore , the ...
... fall upon DB the perpendicular AC , and CB is the effective force required . For the force AB is equivalent to the two forces AC , CB , and AC being perpendicular to DB , can have no effect in urging the body along DB ; therefore , the ...
Page 29
... fall upon the plane MN the perpendiculars AG , BH , CI , we shall have RxCI = QxBH + PXAG . 2. But when the point F is taken between A and B , the difference of the moments of the forces P , Q , will be equal to the moment of their ...
... fall upon the plane MN the perpendiculars AG , BH , CI , we shall have RxCI = QxBH + PXAG . 2. But when the point F is taken between A and B , the difference of the moments of the forces P , Q , will be equal to the moment of their ...
Page 31
... fall upon the plane MN , the perpendiculars Aa , Bb , Cc , Dd , also Ee , Ff , Gg . Then the moment of the resultant T , will be equal to the sum of the moments of the forces P , Q , ( art . 77. ) and we shall have TxEe PxAa + Q × Bb ...
... fall upon the plane MN , the perpendiculars Aa , Bb , Cc , Dd , also Ee , Ff , Gg . Then the moment of the resultant T , will be equal to the sum of the moments of the forces P , Q , ( art . 77. ) and we shall have TxEe PxAa + Q × Bb ...
Page 32
... fall the perpendiculars Aa , Bb , & c . Ee , Cc , & c . Dd , & c . Ff ; by art . 82 , we have VxEe PxAa + QxBb ; and Xx Ff Rx Cc + SxDd . Now if Y represent the resultant of the forces V , X , and G its point of application , this force ...
... fall the perpendiculars Aa , Bb , & c . Ee , Cc , & c . Dd , & c . Ff ; by art . 82 , we have VxEe PxAa + QxBb ; and Xx Ff Rx Cc + SxDd . Now if Y represent the resultant of the forces V , X , and G its point of application , this force ...
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An Introduction to the Theory and Practice of Mechanics: In Five Books William Marrat No preview available - 2020 |
Common terms and phrases
altitude angle Answ avoirdupois axis axle ball barometer beam bodies move body descend centre of gravity centre of motion centre of oscillation centrifugal force centripetal force circle circumference consequently curve cycloid cylinder denote density diameter direction distance draw effect elastic equal equation equilibrium fall find the centre fluent fluid fluxion force of gravity forces acting friction fulcrum given hence horizontal impact inches inclined plane inertia inversely length lever magnitude mercury moving force nearly orifice parallel parallelogram particles pendulum perpendicular piston pressure proportion PROPOSITION pulley quantity of matter radii radius ratio resistance resultant revolving right line Scholium screw side sine space described specific gravity sphere square suppose triangle tube uniformly velocity vertex vertical vessel vibrate water wheel weight whence whole
Popular passages
Page 264 - ... 2. The load at the maximum is nearly, but somewhat less than, as the square of the velocity of the wind, the shape and position of the sails being the same.
Page 264 - ... when the velocities compared are more than double of that where the given load produces a maximum, the effects increase nearly in a simple ratio of the velocity of the wind.
Page 265 - ... horizontal windmill, little more than one sail can be acting at once : whereas, in the common windmill, all the four act together : and, therefore, supposing each vane of a horizontal windmill, of the same dimensions as each vane of the vertical, it is...
Page 41 - Centre of gravity of any body, or system of bodies, is that point upon which the body or system of bodies...
Page 6 - Every body continues in its state of rest, or uniform motion in a straight line, unless it is compelled to change that state by forces impressed on it (inertia).
Page 264 - ... 7. The load at a maximum that sails of a similar figure and position will overcome, at a given distance from the centre of motion, will be as the cube of the radius.
Page 41 - The centre of gravity of a body is not always within the body itself : thus the centre of gravity of a ring is not in the substance of the ring, but in the axis of its circumscribing cylinder ; and the centre of gravity of a hollow staff, or of a bone, is not in the matter of which it is constituted, but somewhere in its imaginary axis ; every body, however, has a centre of gravity, and so has every system of bodies.
Page 261 - Were nothing more requisite than to cause the sails to acquire a certain degree of velocity by the wind, the position recommended by M. Parent would be the best. But if the sails are intended with given dimensions to produce the greatest effects possible in a given time, we must, if planes are made use of, confine our angle within the limits of 72 and 75 degrees.
Page 6 - To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal and directed to contrary pans.
Page 80 - ... exactly adapted to the above series, (the line itself being supposed inelastic, and of no magnitude) the necessity of using several pulleys in each frame will be obviated, and with that some of the inconveniences to which the use of the pulley is liable. In the figure referred to, the coils of rope, by which the Weight is supported, are represented by the lines a, b, c, &c.