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" ... we enquire after, may furnish out a train of obvious and known truths, serving distinctly to investigate the said relations. Euclid, in the first book of the elements, has demonstrated, that the three inward angles of a triangle taken together, are... "
The Elements of Logic: In Four Books ... - Page 227
by William Duncan - 1802 - 239 pages
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The Elements of Logick: In Four Books ... Design'd Particularly for Young ...

William Duncan - Logic - 1748 - 380 pages
...Relations. Euclid in the firft Book of the Elements has demonftrated, that the three in* ward jingles of a Triangle taken together, are equal to two Right Angles. The Reafoning by which he eftablifhes that Proportion, refolves hfelf into this general Principle : Things...
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An essay on mechanical geometry, explanatory of a set of models

Benjamin Donne - 1796 - 120 pages
...confequently the two internal 'angles A and C are equal to the whole external angle. THEOREM 14. The t hree angles of a triangle taken together, are equal to two right angles, or 1^Qdegrees. 32 E. I, or II DI For For through the vertex C of the triangle C. 18 ABC, draw a line...
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The Elements of Logic: In Four Books ...

William Duncan - Logic - 1802 - 256 pages
...elements, has demonstrated, that the three inward angles of a triangle taken together, an equal to t*,vo right angles. The reasoning, by which he establishes...things equal to one and the same thing, are equal ~tu~ one another, Will any one, however, pretend 10 say, that a bare consideration of the principle«tself...
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The Elements of Logic: In Four Books ...

William Duncan - Logic - 1802 - 244 pages
...distinctly to investigate the said relations. Euclid, 'in the first book of the elements, hasHlemonstrated, that the three inward angles of a triangle taken together, are equal to ting right angles. The reasoning, by which he establishes that proposition, resolves itself into this...
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The Monthly Mirror: Reflecting Men and Manners: With Strictures on ..., Volume 6

1809 - 418 pages
...pleasure to the receiver. But when a man publishes a mathematical truth, telling the world that the three angles of a triangle, taken together, are equal to two right angles; or when he broaches au arithmetical truism, such, for instance, as that four multiplied by four, produces...
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The Elements of Logic: In Four Books ...

William Duncan - Logic - 1811 - 272 pages
...singling out such intermediate ideas, as, being compared with those others •whose relations we inquire after, may furnish out a train of obvious and known...resolves itself into this general principle : things tgualto one and the same thing, are equal tu one another. Will any one, however, pretend to say, that...
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The Elements of Logic: In Four Books ...

William Duncan - Logic - 1814 - 276 pages
...singling out such intermediate ideas, as, being compared with those others whose relations we inquire after, may furnish out a train of obvious and known...angles of a triangle taken together, are equal to tworight angles. The reasoning, by which he establishes that proposition, resolves itself into this...
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The Western Monthly Review, Volume 3

Timothy Flint - Mississippi River Valley - 1830 - 696 pages
...is connected with happiness, and the infringement nf it with certain misery as it is, that the three angles of a triangle, taken together, are equal to two right angles. The study of these laws, then, is the science of education and morality. On p. 202 the author proceeds...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...that to proposition XXIV. Book II. of the aforesaid treatise, where it is demonstrated that The three angles of a triangle taken together are equal to two right angles, there is subjoined the following corollary, viz., " It follows from this, that if two lines are cut...
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Memoirs, Letters, and Comic Miscellanies in Prose and Verse: Of the Late ...

James Smith - 1840 - 758 pages
...pleasure to the receiver." But when a man publishes a mathematical truth, telling the world that the three angles of a triangle, taken together, are equal to two right angles ; or when he broaches an arithmetical truism, such, for instance, as that four multiplied by four produces...
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