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ABCD according added algebraic answer arises assume ball Baron base becomes centre circle common consequently considered contains continually Corollary course cube definition demonstrated denominator described difference digits direction distance ditto divided dollars draw drawn easily equal equation evident expressed figure fluxion force formula four fourth fraction given gives greater Hence increase James John kind known latitude length less limit manner marked mathematical means measure meridian method multiple nature New-York parallel Pennsylvania perpendicular Philadelphia plane principles prop properties proportional proposed proposition quantity QUEST question radius ratio reasoning rectangle remainder represent right angles root rule side signs similar sine solutions Solved square straight line subtracted suppose theorem third Thomas tion triangle true tube unit whence whole York
151. lappuse - What principles you proceed upon; how sound they may be; and how you apply them? It must be remembered that I am not concerned about the truth of your theorems, but only about the way of coming at them; whether it be legitimate or illegitimate, clear or obscure, scientific or tentative.
150. lappuse - ... to demonstrate any proposition a certain point is supposed, by virtue of which certain other points are attained; and such supposed point be itself afterwards destroyed or rejected by a contrary supposition ; in that case all the other points attained thereby and consequent thereupon, must also be destroyed and rejected, so as from thenceforward to be no more supposed or applied in the demonstration.
124. lappuse - We must therefore be careful to distinguish between the ratio of two evanescent quantities, and the limit of their ratio ; the former ratio never arriving at the latter, as the quantities vanish at the instant that such a circumstance is aboBt to take place.
151. lappuse - C's part being lost by his death, it is required to divide the whole sum, properly, between the other two. Ans. A's part is $ 57,142$, and B's $ 42,857}.
21. lappuse - The fourth term is equal to the product of the second and third terms, divided by the first term.
197. lappuse - ... the product of the sum and difference of any two quantities, is equal to the difference of their squares.
20. lappuse - If the answer is to be greater, place the greater of the two remaining numbers for the second term, and the less number for the first term; but if it is to be less, place the less of the...
70. lappuse - ... They themselves also speak in the most contemptuous manner of Col. Jared Mansfield, superintendent of the Military Academy at West Point. The writer has a copy of No. 2. stitched in a blue cover, on which is an advertisement of a Lecture delivered in New York by G. Baron, which contains (as he says) "a complete refutation of the false and spurious principles, ignorantly imposed on the public, in the 'New American Practical Navigator,
120. lappuse - ... by the motion of lines ; solids by the motion of superficies ; angles by the rotation of the sides ; portions of time by a continual flux ; and so in other quantities. These geneses really take place in the nature of things, and are daily seen in the motion of bodies.