| 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,... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 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... | |
| 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... | |
| 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,... | |
| Adrien Marie Legendre - Geometry - 1838 - 384 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,... | |
| 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... | |
| Nathan Scholfield - 1845 - 896 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... | |
| 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... | |
| 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.... | |
| Charles Davies - Geometry - 1850 - 218 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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