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Bøker Bok 3140 av 189If a side of any triangle be produced, the exterior angle is equal to the two interior...
" If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Side 41
av John Playfair - 1832 - 333 sider
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...drawn from the eertex to the point of section dieides the outward angle of the triangle into two equal angles. Let ABC be a triangle, and let one of its sides BA be produced to E; and let the outward angle CAE be divided into two equal angles by the straight...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...point A, parallel to the given straight line BC. Which was to he done. . PROP. XXXII. THEOR. If a side of any triangle be produced, the exterior angle is...sides BC be produced to D; the exterior angle ACD shall be equal to_ the two interior and opposite angles CAB, ABC: and the three interior angles of...
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A System of Crystallography,: With Its Application to Mineralogy

John Joseph Griffin - 1841 - 489 sider
...Acuic-anylcd, when the triangle has three acute angles. See the triangular planes on Model 73. «7, The three interior angles of every triangle are equal to two right angles. — It, If two angles of a triangle be given, the third is equal to the difference between their sum...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...through the given point A parallel to the given straight line в c. QEF PROP. XXXII. THEOR. IF a side of any triangle be produced, the exterior angle is...angles. Let ABC be a triangle, and let one of its sides, вc be produced to D; the exterior angle AC D is equal to the two interior and opposite angles CAB,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...angles are also equal. Now, this being demonstrated, it is easy to prove that the three angles of any triangle are equal to two right angles. Let ABC be a triangle right angled at A, draw AD perpendicular to BC. The triangles ABD, ABC have the angles BAC, BDA right...
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On school education

James Pycroft - 1843 - 216 sider
...complicated nature, any more than the Moralist should suppose he can render it highly probable that the three interior angles of every triangle are equal to two right angles, or the Orator exhaust his powers of persuasion in trying to enlist the affections in favour of the...
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The Necessary Existence of God

William Honyman Gillespie - 1843 - 391 sider
...subjective mind. § 65. To illustrate this doctrine by an example taken from the science of magnitude. That the three interior angles of every triangle are equal to two right angles, is a truth which, if the demonstration has been followed, cannot but be believed, when the subject...
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The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - 1845 - 358 sider
...equal to that which is described by eitner extremity of the base.* BOOK I. PKOP. XXXII.— If a side of any triangle be produced, the exterior angle is equal to the two interior and remote angles ; and the three interior angles of every triangle are together equal to two right angles....
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...straight line EAF parallel to the given straight line BC. QEF PROPOSITION XXXII. THEOREM. If a side of any triangle be produced, the exterior angle is equal to the Iwo interior and opposite angles; and Ihe three interior angles of every triangle are together equal...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...the given point A parallel to the given straight line BC. Qur PROP. XXXII. THEOR. If any side of a triangle be produced, the exterior angle is equal...sides BC be produced to D : the exterior angle ACD shall be equal to the two interior and opposite angles CAB, ABC; and the . . n three interior angles...
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