A new treatise on mechanics, by the author of A new introduction to the mathematics |
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Page ii
Joseph Denison. LONDON : GILBERT AND RIVINGTON , PRINTERS , ST . JOHN'S SQUARE . PREFACE . THE present work has originated in consequence of.
Joseph Denison. LONDON : GILBERT AND RIVINGTON , PRINTERS , ST . JOHN'S SQUARE . PREFACE . THE present work has originated in consequence of.
Page 32
... square of one second is to the square of two seconds ; that is , 16 64 1a : 22 : 1 : 4 · So 64 So 144 144 :: 22 : 32 :: 4 : 9 256 : 32 : 42 :: 9:16 · Also 256 And 400 400 : 42 : 52 :: 16 : 25 576 52 : 62 : 25 : 36 :: 52 and so on . ( 5 ...
... square of one second is to the square of two seconds ; that is , 16 64 1a : 22 : 1 : 4 · So 64 So 144 144 :: 22 : 32 :: 4 : 9 256 : 32 : 42 :: 9:16 · Also 256 And 400 400 : 42 : 52 :: 16 : 25 576 52 : 62 : 25 : 36 :: 52 and so on . ( 5 ...
Page 34
... square a 3 de , de- scribed upon the right line a 3 , which represents 3 " , and the square a6bc , described upon a 6 , would represent e the spaces described by a gravitating body in 3 " and 6 " , respectively ; for those squares ...
... square a 3 de , de- scribed upon the right line a 3 , which represents 3 " , and the square a6bc , described upon a 6 , would represent e the spaces described by a gravitating body in 3 " and 6 " , respectively ; for those squares ...
Page 35
... square , ai eh ) , and be then stopped for an instant , and then let fall again , and gravitate as from rest for 4 " . Had it gravitated for the entire time , 5 " , without interruption , it would have described the space i represented ...
... square , ai eh ) , and be then stopped for an instant , and then let fall again , and gravitate as from rest for 4 " . Had it gravitated for the entire time , 5 " , without interruption , it would have described the space i represented ...
Page 39
... square root , t = g = = 12 ; 9 ( ) + And the · time being thus found , the velocity may be found by arti- cle 26 . ( 29. ) In the six following theorems we have enunciated and demonstrated the propositions of which the several formulę ...
... square root , t = g = = 12 ; 9 ( ) + And the · time being thus found , the velocity may be found by arti- cle 26 . ( 29. ) In the six following theorems we have enunciated and demonstrated the propositions of which the several formulę ...
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A New Treatise on Mechanics, by the Author of a New Introduction to the ... Joseph Denison No preview available - 2016 |
A New Treatise on Mechanics, by the Author of a New Introduction to the ... Joseph Denison No preview available - 2016 |
Common terms and phrases
16 feet 2lbs 32 feet 4lbs abscissa acquired by gravity acquired velocity acting simultaneously action body falling body impelled body moving uniformly chap circumference contiguous threads Coroll cylinder demonstrated descent describe a space described by gravity diagonal distance dividing equal velocity equilibrio Euclid falling from rest feet per second find the space fixed pulley force applied force of gravity forces acting formula fulcrum gravitating body heavier weight heavy body height of ascent Hence hypothenuse inches inclined plane length lever momenta momentum moveable pulleys moving body moving force obstruction parallelogram perpendicular Problem proposition quantity ratio reaction rectangle repre represents the space required to find resistance right angles right line right-angled triangle Scholium screw sides Solution sought space described spiral square theorem uniform velocity velo velocity acquired WABC wedge weight of 3lbs wheel and axle wherefore
Popular passages
Page 162 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 24 - In any proportion, the product of the means is equal to the product of the extremes.
Page 180 - ... we substitute the causes which produce them, it may be said that the accelerative force is as the moving force directly, and the quantity of matter moved inversely,
Page 157 - THE WEDGE. The wedge is a double inclined plane, consequently its principles are the same : Hence when two bodies are forced asunder by means of the wedge in a direction parallel to its head, — Multiply the resisting power by half the thickness of the head or back of the wedge, and divide the product by the length of one of its inclined sides ; the quotient is the force equal to the resistance.
Page 33 - ... passed over in the 4th second is seven times that passed over in the 1st ; that the space of the 5th second is nine times that of the first ; and the space of the 6th second eleven times that of the first. Hence, we arrive at the important conclusion that the spaces described in the succeeding seconds increase in the ratio of the odd numbers 1, 3, 5, 7, 9, 1 1, 13, &c. &c. Fig. 9. 15. "We shall now consider the spaces passed over, not in the seconds taken singly, but in any number of them taken...
Page 143 - ... The movable pulley changes its position with that of the weight, and effects a saving equal to half the power. An equilibrium is preserved between the power and weight, when the weight is equal to the product of the power and twice the number of movable pulleys. RULE. Divide the weight to be raised by twice the number of pulleys in the lower block ; the quotient will give the power necessary to raise the weight. EXAMPLE. Required the power to raise 600 Ibs. when the lower block contains six pulleys....
Page v - Motion, or change of motion, is proportional to the force impressed, and is produced in the right line in which that force acts.
Page 130 - So that the length of the winch doubles the power gained by each trundle. As the power gained by any machine, or engine whatever, is in direct proportion as the velocity of the power is to the velocity of the weight ; the powers of this crane are easily estimated, and they are as follows.
Page 1 - FIRST LAW.—A body continues always in a state of rest, or of uniform rectilinear motion, until by some external force, it is made to change its state.—This law contains the doctrine of INERTIA, expressed in four particulars. First, that unless put in motion by some external force, a body always remains at rest; secondly, that when once in motion it continues always in motion, unless stopped by some force; thirdly...
Page ix - ... as the distance between the threads to the circumference of the cylinder in which the spiral moves.