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" Two straight lines which are each of them parallel to the same straight line, and not in the same plane with it, are parallel to one another. Let AB... "
The Elements of Descriptive Geometry ... - Página 7
por Thomas Grainger Hall - 1841 - 100 páginas
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 páginas
...which AB is at right angles. Therefore, if two straight lines, &c. QED PROPOSITION IX. THEOR. — Two straight lines, which are each of them parallel to...straight line, and not in the same plane with it, are par<Mel to one another. Let AB, CD be each of them parallel to EF, and not in the same plane with it...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...parallel to BE. Therefore AD and CF are each of them equal and parallel to BE. But straight lines that are parallel to the same straight line, and not in the same plane with it, are parallel to one another : (xi. 9.) therefore AD is parallel to CF ; and it is equal to it; (i. ax. 1.) and AC, D.Fjoin them...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 páginas
...(XI. 4) to the plane BDE in which those lines are. Wherefore, if one, &c. PROP. IX. THEOR. — Two straight lines -which are each of them parallel to the same straight line, and are not both in the same plane with it, are parallel to one another. Let AB, CD be each of them parallel...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...plane to which AB is at right angles. Wherefore, If two straight lines S$ca ED PROP. IX. THEOR. Two straight lines, which are each of them parallel to...plane with it, are parallel to one another. Let AB, CD be each of them parallel to EF, and not in the same plane with it : AB shall be parallel to CD....
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 páginas
...the other is also at right angles to the same plane. Recite p. 6 of this; ax. 11 of b. 1. 8 Th. Two straight lines, which are, each of them, parallel to the same straight line, though not both in the same plane with it, are parallel to each other. Recite p. 4, 7, 6 of this. 9...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 páginas
...AB, and are drawn through the same point D, which is impossible (11. Ax. 1.). PROP. VIII. THEOR. Two straight lines which are each of them parallel to the same straight line, though not both in the same plane with it, are parallel to one another. Let AB, CD be each of them...
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An elementary course of mathematics, Volume 2

Samuel Hunter Christie - 1847
...plane MN. Therefore, if two straight lines, &c.: which was to be proved. • PROP. XIX. THEOR. Two straight lines, which are each of them parallel to the same straight line, and not both in one plane with it, are parallel to one another. Let AB, CD (fig. 25) be each of them parallel...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...angles to a plane ; the other also shall be at right angles to the same plane. PROP. IX. THEOREM. Two straight lines which are each of them parallel to...the same plane with it, are parallel to one another. PROP. X. THEOREM. If two straight lines meeting one another be parallel to two others that meet one...
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General Report on Public Instruction in the Bengal Presidency

1863
...the equal angles are homologous sides. Cut a given straight line in extreme and mean ratio. 4. Two straight lines which are each of them parallel to the same straight line, but not in the same plane with it, are parallel to one another. 5. If 48 men working eight hours a...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Livro 1

Euclides - 1853
...right angles: therefore GH is parallel (i. 28) to AC, and for like reason FK is parallel to AC. Now straight lines which are each of them parallel to the same straight line are parallel (i. 30) ; therefore GH, FK are parallel. In the same manner it may be shewn that GF, HK...
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