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" If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD. "
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Page 227
by Euclid, Isaac Todhunter - 1867 - 400 pages
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The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ...

Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...Explain why the properties proved in Book v. by means of lines^ are true of any concrete magnitudes. 2. If two straight lines be at right angles to the same plane, they are parallel. 3. With the four lines which contain a + 6, a + c, a — b, a — c units respectively,...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...to each of them in that point ; these three straight lines are in one and the same plane. PROP. VI. THEOREM. If two straight lines be at right angles...same plane, they shall be parallel to one another. PROP. VII. THEOREM. If two straight lines be parallel, the straight line drawn from any point in the...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...the circumference of the circle in a point F, shew that CD is a third proportional to CE and CF. 7. If two straight lines be at right angles to the same plane, they shall be parallel to one another. 8. If a line be drawn bisecting the angle between the focal distance of any point of a parabola and...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pages
...each of the angles at the base double of the third angle : and deduce the expression for sin 36°. 3. If two straight lines be at right angles to the same plane they are parallel to one another. 4. Chords of a circle pass through the middle point of a fixed chord,...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1855 - 340 pages
...THEOR. Two straigh' lines which are at right angles to the same plane, are parallel to one another, v Let the straight lines AB, CD be at right angles to the same plane BDE ; AB is parallel to CD. Let them meet the plane in the points B, D. Draw DE at right angles to...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...are in the same plane. Therefore, if three straight lines meet all in one point, &c. QED PROP. VI. THEOREM. If two straight lines be at right angles to the same plane, they arc parallel. Let the straight lines AB and С D be at right angles to the same plane. AB is parallel...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...lines cut one another. If two straight lines be drawn from a given point either in or above a plane. If two straight lines be at right angles to the same plane. If two straight lines be parallel. And one of them is at right angles to a plane. CONSEQUENCES. } Another...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 346 pages
...plane. PROP. VI. THEOR. Two straight lines which arc at right angles to the same plane, are parallel (o one another. Let the straight lines AB, CD be at right angles to the same plane BDE ; AB is parallel to CD. Let them meet the plane in the points B, D. Draw DE at right angles to...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...lines be drawn from a given point either in or above a plane. If two straight lines cut one another. If two straight lines be at right angles to the same plane. If two straight lines be parallel. And one of them is at right angles to a plane. CONSEQUENCES. } Another...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...triangles are proportionals ; and those which are opposite to the equal angles are homologous. 12. If two straight lines be at right angles to the same plane, they shall be parallel to each other. J 13. Define the Trigonometrical Functions of an angle, and find their values for an angle...
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