 | War office - 1861 - 714 pagina’s
...quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. 2. If two straight lines are at right angles to the same plane they shall be parallel to each other. 3. Prove the following formulae : ,,^ ... 3 tan A — tan 3A (1) tan... | |
 | Euclides - 1864 - 448 pagina’s
...them : (xi. 4.) and EFis parallel to AB ; therefore AB is at right angles to the plane HGK. (XI. 8.) For the same reason, CD is likewise at right angles...to the same plane, they are parallel to one another : (xi. 6.) therefore AB is parallel to CD. Wherefore, two straight lines, &c. QED PROPOSITION X. THEOREM.... | |
 | Robert Potts - 1865 - 528 pagina’s
...them : (xi. 4.) and EF is parallel to AB ; therefore AB is at right angles to the plane HGK. (xi. 8.) For the same reason, CD is likewise at right angles...to the same plane, they are parallel to one another : (xi. 6.) therefore AB is parallel to CD. Wherefore, two straight lines, &c. QED PROPOSITION X. THEOREM.... | |
 | Euclides - 1865 - 402 pagina’s
...(xi. 4.) and EF is parallel to AB ; (hyp.) therefore AB is at right angles to the plane HGK ; (XL 8.) for the same reason, CD is likewise at right angles...to the same plane, they are parallel to one another ; (XL 6.) therefore AB is parallel to CD. Wherefore, two straight lines, &c. QED PROP. X. — THEOREM.... | |
 | John Playfair - 1855 - 350 pagina’s
...HGK. For the same reason, CD is likewise at right angles to the plane HGK. Therefore AB, CD jj \ — are each of them at right angles ' ~~ " " to the plane...lines are at right angles to the same plane, they are paral- J^lei (6. 2. Sup ) to one another. Therefore AB is parallel to CD. PROP. IX. THEOR. If two straight... | |
 | Samuel H. Winter - 1867 - 468 pagina’s
...circles of an equilateral triangle coincide, and the diameter of one is double that of the other. 19. If two straight lines are at right angles to the same plane, they shall be parallel to one another. 20. Solve the following equations : (a) x -- ?^- = 15. Find, by the... | |
 | Robert Potts - 1868 - 434 pagina’s
...them : (XI. 4.) and EFis parallel to AB; therefore AB is at right angles to the plane HGK. (XI. 8.) For the same reason, CD is likewise at right angles...to the same plane, they are parallel to one another : (XI. 6.) therefore AB is parallel to CD. Wherefore, two straight lines, &c. QED PROPOSITION X. THEOREM.... | |
 | Euclides - 1874 - 342 pagina’s
...plane HGK (Til. 8). For the same reason, 3. CD is at right angles to the plane HGK. Therefore 4. AB and CD are each of them at right angles to the plane HGK....right angles to the same plane, they are parallel (XI. 6) ; therefore 6. AB is parallel to CD. Wherefore, two straight lines, ifcc. QED PROPOSITION 10.... | |
 | Robert Potts - 1876 - 446 pagina’s
...them : (xi. 4.) and EF is parallel to AB ; therefore AB is at right angles to the plane HGK. (xi. 8.) For the same reason, CD is likewise at right angles...to the same plane, they are parallel to one another : (XI. 6.) therefore AB is parallel to CD. Wherefore, two straight lines, &c. QED PROPOSITION X. THEOREM.... | |
 | Euclid - 1876 - 240 pagina’s
...in the points Q, T, V, X; Y, Z, I, U; and join QT, TV, VX, XQ; YZ, ZI, IU, TJY. Then, because GQ, KT are at right angles to the same plane, they are parallel to one another (£): and MG, EK are parallels ; therefore the planes MQ, ET (of which one passes through MG, GQ, and... | |
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For the same reason, CD is likewise at right angles to the plane HGK. Therefore AB, CD are each of them at right angles to the plane HGK. 
