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" Straight lines which are parallel to the same line are parallel to each other. Let the straight lines AB, CD be each parallel to the line EF ; then are they parallel to each other. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 14
by Benjamin Greenleaf - 1861 - 490 pages
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816 - 610 pages
...those two lines will not be parallel, but will meet each other when produced. THEOREM XV. THOSE Lines which are Parallel to the Same Line, are Parallel to each other. I^et the Lines AB, CD, be each of _ them parallel to the line EF ; then shall * y . T> the lines AB,...
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A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volume 1

Charles Hutton - Arithmetic - 1818 - 646 pages
...those two lines will not be parallel, but will meet each other when produced. THEOREM XV. THOSE Lines which are Parallel to the Same Line, are Parallel to each other. Let the Lines AB, CD, be each of them parallel to the line EF ; then shall Ją_ ^ B the lines AB, CD, be parallel...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...straight line, &c. QED PROPOSITION XXX. THEOREM. Straight lines which are parallel to the same straight line are parallel to each other. Let the straight lines AB, CD be each of them parallel to EF . Then shall AB be also parallel to CD. Let the straight line GHK cut AB, EF,...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...angles, then will KL and CD meet, if sufficiently produced. PROPOSITION XXIV. THEOBEM. Straight lines which are parallel to the same line, are parallel...each other. Let the straight lines AB, CD be each of them parallel to the line EF; E then will AB be parallel to CD. PQR, perpendicular to EF. Then,...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...lines will not be parallel, but will meet if sufficiently produced. THEOREM XV. All straight lines which are parallel to the same line, are parallel to each other. Let the lines AB and CD be each par- Q all el to EF: then will they be parallel to each other. Of Triangles....
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...parallel, and consequently will meet each other when produced. PROPOSITION XXI. THEOREM. Those lines which are parallel to the same line, are parallel to each other. parallel to FG; then will the * | B Let the lines AB, CD be each H lines AB, CD be parallel to each...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...to another. XIII. Only one straight line can be drawn joining two given points. XIV. Straight lines which are parallel to the same line are parallel to each other. POSTULATES. I. Let it be granted that a straight line may be drawn from any point to any other point....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...to another. XIII. Only one straight line can be drawn joining two given points. XIV. Straight lines which are parallel to the same line are parallel to each other. POSTULATES. I. Let it be granted that a straight line may be drawn from any point to any other point....
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...interior angles whose sum is less than two right angles. PROPOSITION XXIV. — THEOREM. 90. Straight lines which are parallel to the same line are parallel to...each parallel to the line EF ; then are they parallel to'each other. Draw GHI perpendicular to c EF. Then, since AB is parallel to EF, GI will be perpendicular...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...interior angles whose sum is less than two right angles. PROPOSITION XXIV. — THEOREM. 90. Straight lines which are parallel to the same line are parallel to...line EF ; then are they parallel to each other. Draw GHI perpendicular to ,-, EF. Then, since AB is parallel to EF, GI will be perpendicular A to AB (Prop....
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