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" We assume that but one straight line can be drawn through a given point parallel to a given straight line. "
Euclid's plane geometry, practically applied; book i, with explanatory notes ... - Σελίδα 41
των Euclides - 1863
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...line intersect one of two parallel right lines it must also intersect the other.' ' Only one right line can be drawn through a given point parallel to a given right line.' The axiom expressed by the first of these ways appears to me to be as unobjectionable,...

Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 σελίδες
...axiom and its converse should be so obvious as not to require demonstration. 3. ' ' The Twelfth A xiom may be expressed in any of the following ways : —...must also intersect the other : or, Only one rt. line cau be drawn through a given point parallel to a given rt. line." — LARDNER, p. 316. 4. The least...

Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870 - 270 σελίδες
...both the assumed axiom and its converse should be so obvious as not to require demonstration. 3. " The Twelfth Axiom may be expressed in any of the following...drawn through a given point parallel to a given rt. line." — LARDXER, p. 316. 4. The least objectionable definition of parallel st. lines is — " Parallel...

Elements of Analytical Geometry, and of the Differential and Integral Calculus

Gerardus Beekman Docharty - 1865 - 328 σελίδες
...parallel to a given line, then the angle which the line makes with the axis is known, and only one line can be drawn through a given point parallel to a given line. Illustration. If we were required to draw a line through the point P, whose abscissa AB is 8,...

Euclid's Elements of Geometry, Βιβλία 1-6

Henry Martyn Taylor - 1893 - 486 σελίδες
...intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3. If two straight lines, each of which is parallel to a third straight line, meet,...

The Elements of Geometry

Webster Wells - 1894 - 400 σελίδες
...plane are parallel.] (§ 411.) But through C, only one parallel can be drawn to AB. [But one straight line can be drawn through a given point parallel to a given straight line.] (§ 53.) Whence, CD is perpendicular to MN. 413. COB. II. If each of two straight lines...

Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - 1894 - 412 σελίδες
...greater than one of two equal magnitudes is less or greater, respectively, than the other. 18. Only one line can be drawn through a given point parallel to a given line. POSTULATE i. — A line can be revolved about a given point until it embraces another point or...

Euclid's Elements of Geometry, Βιβλία 1-6;Βιβλίο 11

Henry Martyn Taylor - 1895 - 708 σελίδες
...intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3. If two straight lines, each of which is parallel to a third straight line, meet,...

The Essentials of Geometry (plane)

Webster Wells - 1898 - 284 σελίδες
...cannot meet however far they may be produced; as AB and CD. ® D 53. Ax. We assume that but one straight line can be drawn through a given point parallel to a given straight line. PROP. XI. THEOREM. 54. Two perpendiculars to the same straight line are parallel. I...

Plane and Solid Geometry

James Howard Gore - 1898 - 232 σελίδες
...one another, however far they may be produced; as AB and CD. A B D 60. AXIOMS. 1. But one straight line can be drawn through a given point parallel to a given straight line. 2. Since parallel lines cannot approach one another, they are everywhere equally distant...




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