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" If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let... "
New Elementary Geometry: With Practical Applications; a Shorter Course, Upon ... - Page 117
by Benjamin Greenleaf - 1873 - 176 pages
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Elements of Geometry and Trigonometry: With Notes

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,...
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Elements of Geometry and Trigonometry

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,...
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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
...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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

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...
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Elements of Geometry: With Practical Applications ...

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...
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Elements of Geometry and Conic Sections

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...
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Elements of Geometry: With, Practical Applications

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...
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Elementary Geometry: With Applications in Mensuration

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...
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Elements of Geometry and Trigonometry

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,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

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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