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" ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 18
av Robert Simson - 1838 - 416 sider
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Queen's scholarship examination. Amner's eight years' scholarship questions ...

Joseph Wollman - 1879 - 120 sider
...angles fill the same space. All equal angles fill equal spaces, and not the same space. SECTION II. 1. If two straight lines cut one another, the vertical or opposite angles will be equal. Two equal perpendiculars, PA, QB, are drawn to the line AB from points P, Q, on opposite...
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Papers for teachers

1880 - 594 sider
...cut off a part equal to the less. What are the data and what are the quasita in this proposition ? 2. If two straight lines cut one another, the vertical, or opposite angles, shall be equal Why is no construction required in this theorem ? 3. Euc. I. 21. THIRD (OR FOURTH) YEAR. Arithmetic....
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The student's guide to the University of Durham, with information respecting ...

1880 - 160 sider
...line. (ii.) To bisect a given rectilineal angle, that is, to divide it into two equal angles. (iii.) If two straight lines cut one another, the vertical, or opposite, angles shall be equal. (iv.) If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite...
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The pupil teachers' handy mathematical and grammatical question-book, with key

Pupil teachers - 1880 - 1494 sider
...to two right angles; then these two straight lines shall be in one and the same straight line. 15. If two straight lines cut one another, the vertical, or opposite angles shall be equal. Deduce from this, that all the angles made by any number of straight lines meeting in one point are...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 sider
...impossible. Therefore BE is not in the same straight line with CB. And in the same manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same straight line with CB. Wherefore, if at a point &c. QED PROPOSITION 15....
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First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880 - 152 sider
...the third side is called the base. 4. The angles at the base of an isosceles triangle are equal. 5. If two straight lines cut one another, the vertical (or opposite) angles are equal. An axiom is a self-evident truth. That is to say, an assertion so evidently true that it...
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Ten years' Queen's scholarship questions, 1870-9, with answers to arithmetic ...

Education Ministry of - 1880 - 248 sider
...wholes are unequal. All equal angles fill the same space. (These form one question.) SECTION II. 1. If two straight lines cut one another, the vertical or opposite angles will be equal. Two equal perpendiculars, PA, QB, are drawn to the line AB from points P, Q, on opposite...
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The Cambridge Examiner, Volum 3

1883 - 536 sider
...sides of the one shall be equal to the 'angle contained by the two sides equal to them of the other. 2. If two straight lines cut one another, the vertical or opposite angles shall be equal. 3. Given two points, one on each side of a given straight line, find a point in the line such that...
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Moffatt's reprint of pupil teachers' questions, arranged by ed. of 'Papers ...

Moffatt and Paige - 1881 - 176 sider
...opposite sides of it : prove that the line joining their vertices bisects both the vertical angles. 2. If two straight lines cut one another, the vertical or opposite angles shall be equal. OCTOBER, 1880. (Three hours and a half allowed.) ARITHMETIC. Males. 1. A house which cost £3,500 lets...
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The practical surveyor

Thomas Holloway (surveyor.) - 1881 - 132 sider
...of either of the lines CD or E D. In dealing with angles it will be of assistance to remember that " If two straight lines cut one another, the vertical, or opposite angles are equal." * The theodolite being the only instrument with which horizontel bearings can be directly...
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