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" Since the three angles of the triangle ABC are equal to two right angles, .-.the angles DAB, DBA, DCF are together equal to one right angle, ie to DCF, and CDF; whence the two angles DAB, DBA are together... "
Lessons on form, for teachers [of geometry]. - Page 21
by Richard Pears Wright - 1882
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ...

Euclid, James Williamson - Euclid's Elements - 1781 - 324 pages
...angle ABD is equal to the angle ADB ; and fince (by 32. i.) the three angles of every triangle are equal to two right angles; therefore the three angles of the triangle ABD viz. ABD, ADB, BAD are equal to two right angles ; but BAD is a right angle (being an angle of...
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The philosophical and mathematical commentaries of Proclus ... on the first ...

Proclus (Diadochus.) - 1789 - 474 pages
...be added. The angles, therefore, acd, acb, are equal to the three angles of the triangle ab c. But the three angles of the triangle abc , are equal to two right. 1 66 COMMENTARIES OF PROCLUS. right. And hence, the angles acd^ acb, are equal to two right. But if...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...BD, CD; produce BD to Et and from D draw DF perpendicular to AC; the angle ADE is equal to CDF. Since the three angles of the triangle ABC are equal to two right angles, .-. the angles DAB, DBA, DCF are together equal to one right angle, ie to DCF, and CDF; whence the...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...produce BD to E, and from D draw DF perpendicular to AC; the angle ADE is equal to CDF. *- EĽ c Since the three angles of the triangle ABC are equal to two right angles, .-.the angles DAB, DBA, DCF are together equal to one right angle, ie to DCF, and CDF; whence the two...
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Elements of Geometry with Notes

John Radford Young - Geometry, Modern - 1833 - 238 pages
...AD to E, and from D draw DF perpendicular to BC ; the angle BDE is equal to CDF. -- E IT . O Because the three angles of the triangle ABC are equal to two right angles (Prop. XVI. Cor. 1.); therefore the angles DBA, DAB, DCF, are together equal to one right angle, that...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...right angles. Again : each of the interior angles at A, B, and c, with the adjacent exterior angle, are together equal to two right angles ; therefore the three angles of the triangle, together with the three exterior angles, are equal to six right angles. Thus the angles A, B, and c...
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The Theory of Reasoning

Samuel Bailey - Logic - 1851 - 256 pages
...persons. IMPLIED FACTS. This horned animal is ruminant. The lines A and B are equal to each other. The three angles of the triangle ABC are equal to two right angles. He could not be guilty of the offence committed at that time in London. He could not be robbed of a...
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The Student's Handbook: Synoptical and Explanatory, of Mr. J.S. Mill's ...

John Stuart Mill, Alfred Henry Killick - Logic - 1888 - 288 pages
...of this are : — (a.) Proving a geometrical theorem ly means of a diagram. Thus having proved that the three angles of the triangle ABC are equal to two right angles, we conclude that this is true of every triangle, not because we find it true of ABC, but for the same...
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A Commentary on the First Book of Euclid's Elements

Proclus - Mathematics - 1992 - 432 pages
...be added to both. The angles ACD and ACB are then equal to the three angles of the triangle ABC. But the three angles of the triangle ABC are equal to two right angles; [and therefore angles ACD and ACB are equal to two right angles].44 And if upon a straight line and...
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The Mechanic's Magazine, Museum, Register, Journal and Gazette, Volume 33

1840 - 632 pages
...of a right angle." The inference that Mr. S. attempts to deduce from the above proposition is, that the three angles of the triangle ABC, are equal to two right angles. He remarks, " Now, from this it might V somewhat inferred (this is rather an equilateral triangle to...
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