| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...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,... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...will be equal, as shown by the Proposition. PROPOSITION XIII. THEOREM. If two 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
...FH=EF, which is absurd ; hence the plane ACE is parallel to BDF. Therefore, If two angles, not situated **in the same plane, have their sides parallel and lying in the same direction,** those angles are equal, and their planes are parallel. Cor. If two parallel planes MN, PQ are met by... | |
| Nathan Scholfield - 1845 - 894 pages
...will be equal, as shown by the Proposition. 16 PROPOSITION XIV. THEOREM. If two 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... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...VI, Prop. vn, Cor. 1), and therefore equal: PROPOSITION XIII. 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. Let CAE, DBF be two... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...they will be parallel to each other (Prop. IX.), and, consequently, equal. PROPOSITION XV. THEOREM. **If two angles, not in the same plane, have their sides parallel and** similarly situated, these angles will be equal, and their planes will be parallel. Let the two angles... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...VI, Prop, vn, Cor. 1,) and therefore equal. PROPOSITION XIII. 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. Let CAE, DBF be two... | |
| Charles Davies - Geometry - 1850 - 216 pages
...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... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...they are equal, as shown by the proposition. PROPOSITION XIII. THEOEEM. If two angles, not situated **in the same plane, have their sides parallel and lying...will be equal and their planes will be parallel. Let** the angles CAE and DBF, have the side AC parallel to J2Z?, and lying in the same direction : also,... | |
| Charles Davies - Geometry - 1854 - 436 pages
...equal, as shown by the proposition. 166 GEOMETRY. PROPOSITION XIII. THEOREM. If two angles, not situated **in the same plane, have their sides parallel and lying...will be equal and their planes will be parallel. Let** the angles CAE and DBF, have the side AC parallel to BD, and lying in the same direction : also, AE... | |
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