| War office - 1861 - 714 pages
...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 pages
...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 pages
...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 pages
...(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 - Geometry - 1855 - 350 pages
...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 pages
...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 pages
...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 pages
...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 - Geometry - 1876 - 446 pages
...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 pages
...through them (b): indEF is parallel to AB ; therefore AB is at right angles to the plane HGK (c) : **for the same reason, CD is likewise at right angles...to the same plane, they are parallel to one another** (d) ; therefore AB is parallel to CD. PROPOSITION X. THEOREM. — If two straight lines (AB, BC) meeting... | |
| |