Works, Volume 3G. Bell and sons, 1898 |
From inside the book
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Page 5
... infinitely small , used by foreign mathematicians instead of fluxions or velocities of nascent and evanescent increments . 6. Differences of various orders , i.e. quantities infinitely less than quantities infinitely little ; and ...
... infinitely small , used by foreign mathematicians instead of fluxions or velocities of nascent and evanescent increments . 6. Differences of various orders , i.e. quantities infinitely less than quantities infinitely little ; and ...
Page 6
... infinitely small supposed and rejected by Leibnitz and his followers . No quantity , according to them , greater or smaller for the addition or subduction of its infinitesimal . 19. Conclusions to be proved by the principles , and not ...
... infinitely small supposed and rejected by Leibnitz and his followers . No quantity , according to them , greater or smaller for the addition or subduction of its infinitesimal . 19. Conclusions to be proved by the principles , and not ...
Page 12
... infinitely small . The difference of a line is an infinitely little line ; of a plane an infinitely little plane . They sup- pose finite quantities to consist of parts infinitely little , and curves to be polygons , whereof the sides ...
... infinitely small . The difference of a line is an infinitely little line ; of a plane an infinitely little plane . They sup- pose finite quantities to consist of parts infinitely little , and curves to be polygons , whereof the sides ...
Page 13
... infinitely greater than some other real magnitude , and add them to the least given quantity , it shall never be the bigger . For this is one of the modest postulata of our modern mathematicians , and is a corner - stone or ground- work ...
... infinitely greater than some other real magnitude , and add them to the least given quantity , it shall never be the bigger . For this is one of the modest postulata of our modern mathematicians , and is a corner - stone or ground- work ...
Page 16
... infinitely small , yet it seems ineffectual . For aught I see , you can admit no quantity as a medium between a finite quantity and nothing , without admitting infinitesimals . An increment generated in a finite particle of time is ...
... infinitely small , yet it seems ineffectual . For aught I see , you can admit no quantity as a medium between a finite quantity and nothing , without admitting infinitesimals . An increment generated in a finite particle of time is ...
Common terms and phrases
abscissa acid admitted æther Analyst animal answer Aristotle balsam Berkeley Berkeley's better bodies cause circulation Cloyne commerce conceive consequently considered cure demonstration distemper diuretic Divine doctrine of fluxions doth drink Dublin Edited effect England equal error evanescent expression fevers finite quantities fire flowing quantities foreign geometry hath human increments industry infidels infinitely small infinitesimal Ireland isochronal kingdom labour less light manufactures mathematicians mathematics medicine method method of fluxions mind momentum motion nascent national bank nature nevertheless obscure observed opinion particles phænomena philosophers Plato Plotinus prejudices principles produce proportion reader reason rectangle religion saith salts scurvy sect sense shew similar triangles Sir Isaac Newton sophism soul spirit subducted subtangent supposed supposition tar-water Theophrastus thereof things third fluxions tion trade Translated triangle true truth vegetable velocities virtue vols Walton wealth whence wherein whole
Popular passages
Page 388 - I went by the field of the slothful, and by the vineyard of the man void of understanding ; and, lo, it was all grown over with thorns, and nettles had covered the face thereof, and the stone wall thereof was broken down.
Page 390 - Yet a little sleep, a little slumber, a little folding of the hands to sleep ; so shall thy poverty come as one that travelleth, and thy want as an armed man.