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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. "
An elementary course of mathematics - Page 13
by Samuel Hunter Christie - 1847
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Examination papers used at the examinations for direct commissions [&c.].

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...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

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....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

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....
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

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....
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

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...
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Mathematical Exercises ...

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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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....
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The Elements of Euclid, containing the first six books, with a selection of ...

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....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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....
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The Elements of Euclid, with Many Additional Propositions and Explanatory ...

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...
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