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We must now show that on some component of the graph there exist two points for which the corresponding diagonal points in the C-plane are on opposite sides of C.
from Brown Corpus
Some Related Sentences
We and must
We must be ever alert that freedom does not wither through the careless amassing of restrictive controls or the lack of courage to deal boldly with the issues of the day.
We must avoid the notion, suggested to some people by examples such as those just mentioned, that ideas are `` units '' in some way comparable to coins or counters that can be passed intact from one group of people to another or even, for that matter, from one individual to another.
We must, therefore, have a look at the new archaeological material and re-examine the literary and place-name evidence which bears upon the problem.
We expect him to be noble, and to make us so -- yet he knows, and tries to tell us, how very humble man must be.
`` We were on our vacation in Canada '', Howard explained, in a muffled voice that must have been used to booming, `` and the news didn't catch up with us till we were nearly home.
We must ask ourselves which of the two alternatives will help the commuter -- the two-way B. & O. - C. & O. merger, or the three-way New York Central - B. & O. - C. & O. merger.
We must build a corps of highly professional teachers of interior design who have had education, experience in the profession and are willing to take on the usual accompaniments of teaching -- minimal income and minimal status among their confreres.
Says Clarence Thompson: `` We dealers must earn our mark-up by performing a service for the builder cheaper than he could do it himself ''.
We must realize with Prof. Charles Morris in his The Open Self that `` Man is the being that can continually remake himself, the artisan that is himself the material for his own creation ''.
Denouncing the view that the sexual union is an end in itself, the Conference declared: `` We steadfastly uphold what must always be regarded as the governing considerations of Christian marriage.
We had nearly decided that all the tales of Lao lethargy must be true, when we were invited to take a trip with the Prime Minister.
`` We must solve the problems which have forced these people to depend upon ADC for subsistence '', Martin said.
He said, `` We Democrats must resolve our issues on the test of what is right and just, and not what is expedient at the time ''.
We and now
We get some clue from a few remembrances of childhood and from the circumstance that we are probably not much more afraid of people now than man ever was.
We have now a quiet city, fewer automobiles, less congestion, and fewer retail customers shopping in center city.
We now have to think not only of our national security but also of the future generations who will suffer from any tests we might undertake.
We know now that a 15-degree differential in temperature is the maximum usually desirable, and accurate controls assure the comfort we want.
We now have not only what has been called over here the comedy of menace but we also have horror jokes, magazines known as Horror Comics, and sick comedians.
We now shall show that any involution with these characteristics is necessarily of the type we have just described.
We now observe that the case in which **zg is a Af curve on a quadric is impossible if the complex of singular lines consists exclusively of the lines which meet Aj.
We now know that things rarely ever work out in such cut-and-dried fashion, and that car loadings, while perhaps interesting enough, are nevertheless not the magic formula that will always turn before stock prices turn.
We turn now to a type of fully distributed cost analysis which, unlike the `` railroad type '', draws no distinction between cost allocation and cost apportionment: the single-step type.
We cannot now speak of maximizing the value of the objective function, since this function is now known only in a probabilistic sense.
We have learned from earthquakes much of what we now know about the earth's interior, for they send waves through the earth which emerge with information about the materials through which they have traveled.
We may now take up for consideration a hard case which seems to require either no action employing economic pressure or else action that would seem to violate the principles set forth above.
`` We are now witnessing an effort to transfer to Mr. Mitchell some of the glow of Sen. Case's candidacy of last year.