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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 11
av Euclid, Robert Simson - 1821 - 516 sider
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Mathematical Questions and Solutions, from the "Educational Times ..., Volum 42

W. J. C. Miller - 1885
...that it " lies evenly between its extreme points "; but in Postulate ii. he says, " Let it be granted, that a terminated straight line may be produced to any length in a straight line," and this gives us the idea of an infinite straight line. But do we require more than two infinite straight...
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The Fundamental Science

Henry James Clarke - 1885 - 265 sider
...the unreasonableness of such a desire. What then am I to do ? I need not ask how I am to prove that things which are equal to the same are equal to one another : this truth is one of which I have a clear perception ; I feel sure that I know it by immediate intuition,...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885
...AB . BE is equal to the figure AE. Hence the rectangle AB . CB is equal to the figure AE. And since things which are equal to the same are equal to one another, the rectangle AC . CB, together with the square, on CB, is equal to the rectangle AB . CB. , Or thus...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 sider
...is the centre of the circle ACE, BC is equal to BA. Hence we have proved. AC = AB, and BC = AB. But things which are equal to the same are equal to one another (Axiom i.) ; therefore AC is equal to BC ; therefore the three lines AB, BC, CA are equal to one another....
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Christian Thought, Volum 1

1886
...same time be and not be ; (2) that if equals be added to equals the wholes are equal ; and (3) that things which are equal to the same are equal to one another. It so happens that each of these propositions which he has assumed to be true is, if true, much more...
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Picture Logic

Alfred James Swinburne - 1887 - 188 sider
...middle terms is called the minor premiss. The former always comes first. Unless the principle that " things which are equal to the same are equal to one another " were true, it would not follow that " Socrates " and " mortal," which are equal to the same (" man...
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The Passenger from Scotland Yard

H. Freeman Wood - 1888 - 398 sider
...DAB., producing the straight lines DA, DB, to E and F; in accordance with postulate 2, which states that a terminated straight line may be produced to any length in a straight line. From the centre B, at the distance BC, I describe the circle CGH, meeting DF at G, inasmuch as postulate...
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First and Fundamental Truths: Being a Treatise on Metaphysics

James McCosh - 1889 - 360 sider
...such that all straight lines drawn from a certain point within the figure are equal to one another ; " and that " A circle may be described from any centre at any distance from that centre." I shall have occasion, in speaking of the application of the principles laid down in this treatise...
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Alluring Absurdities: Fallacies of Henry George

Michael William Meagher - 1889 - 193 sider
...says the trunk lines of railroads unite to raise rates, just as robbers unite to plunder in concert. Things which are equal to the same are equal to one another. If, then, railroad companies unite to raise rates, and workingmen unite to raise rates of wages, and it...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...POSTULATES. Let it be granted 1. That a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. That a circle may be described from any centre at any distance from that centre. In practice this...
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