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" THEOREM. If two angles, not situated in the same plane, have their sides parallel and lying in the same direction, they will be equal, and the planes in which they are situated will be parallel. "
Elements of Geometry: With Practical Applications ... - Page 184
by George Roberts Perkins - 1847 - 308 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...1.) ; and therefore equal, as has just been shewn. PROPOSITION XIII. THEOREM. If two angles CAE, DBF not situated in the same plane, have their sides parallel and lying in the same direction, those angles will be equal and their planes will be parallel. Make AC=BD, AE=BF; and join CE, DF, AB,...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...parallel planes are equidistant. PROPOSITION XXI. (44) If two angles have their sides respectively parallel and lying in the same direction, they will be equal, and their planes will be parallel. If they be in the same plane, the proposition has been proved in the...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...will be parallel to each other, (336.) ; and therefore equal, as has just been shewn. THEORE M. 344. If two angles not situated in the same plane, have...their sides parallel and lying in the same direction, those angles mil be equal, and their planes will be parallel. Let the angles be CAE, and DBF. Make...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...to the plane MN (Prop. XI.) ; *>-., beih paraUel, •' will be equal, as shown by the Proposition. PROPOSITION XIII. THEOREM. If two angles, not situated...their sides parallel and lying in the same direction, those angles will be equal and their planes will be parallel. Let the angles be CAE and DBF. Make AC=BD,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...thejr will be equal, as shown by the Proposition* u \ 3 p ST \ : H . PROPOSITION XIII. THEOREM. Jf Iwo angles, not situated in the same plane, have their sides parallel and lying in the same direction, those angles will be equal and their planes will be parallel. Let the angles be CAE and DBF. Make AC=BD,...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...1,) and therefore equal, as has just been shown. PROPOSITION XIII. THEOREM. If two angles CAE, DBF, not situated in the same plane, have their sides parallel and lying in tlie same direction, those angles will be equal, and their planes will be parallel. BOOK VI. ABDC is...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...(Prop. XII.) ; and being parallel, they will be equal, as shown by the Proposition. 16 PROPOSITION XIV. THEOREM. If two angles, not situated in the same plane,...their sides parallel and lying in the same direction, those angles will be equal, and their planes will be parallel. Let the angles be CAE and DBF. Make...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...X.); so likewise are EG, FH ; therefore the figure EGHF is a parallelogram; consequently, EG =FH. ME PROPOSITION XIII. THEOREM If two angles, not situated in the same plane, have their si<l<>,s parallel and lying in the same direction, those angles will lie equal and their planes will...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...figure EGHF is a parallelogiam, and EG=FH. Cor. Hence it follows that two parallel planes are everywhere equidistant; for if EG and FH are perpendicular to...in the same direction, and AE parallel to BF, and klso lying in the same direction ; then will these angles be equal, and their planes will be parallel....
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 216 pages
...perpendicular to the plane HGI, they will be parallel to each other. B D GEOMETRY. Of Planes . THEOREM XI. If two angles, not situated in the same plane, have...their sides parallel and lying in the same direction, the angles will be equal. Let the angles ACE and BDF have the sides AC parallel to BD, and CE to DF...
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