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

Robert Potts - 1868 - 434 sider
...which is impossible : therefore BE is not in the same straight line with BC. And in the same manner it may be demonstrated, that no other can be in the...which therefore is in the same straight line with BC. PROPOSITION XV. THEOREM. If two straight lines cut one another, the vertical, or opposite angle*...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 302 sider
...impossible. Hence BE is not in the same straight line with BC ; and in like manner, it may be proved that no other can be in the same straight line with it but BD. Therefore, if at a point, &c PROPOSITION IV. THEOREM. Two straight lines, which have two points common,...
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Appletons' Journal, Volum 7

1879 - 592 sider
...Jeanne picks up her lesson-book, Euclid's " Elements," from the ground. " ' Proposition XV. Theorem : If two straight lines cut one another, the vertical or opposite angles shall be equal.' Then why try to prove it? Why need we go on with these hideous angles and right angles? Why do you...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873 - 580 sider
...greater, which is impossible ; therefore BE is not in the same straight line with BC. And, in like manner, it may be demonstrated that no other can be in the...same straight line with it but BD, which therefore isin the same straight line with CB. XV. — If two straight lines cut one another, the vertical, or...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 sider
...which is impossible ; therefore 4. BE is not in the same straight line with BC. And in the same manner it may be demonstrated, that no other can be in the same straight line with it but BD, therefore 5. BD is in the same straight line with BC. Wherefore, if at a point, &c. QED PROPOSITION...
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Pure mathematics, Volum 1

Edward Atkins - 1874 - 428 sider
...ABE, are equal to the angles ABC, ABD (Ax. 1). Take away the common angle ABC. And, in like manner, it may be demonstrated that no other can be in the same straight line with it but BD. Therefore BD is in the same straight line with BC. Therefore, if at a point, &c. QED Proposition 15....
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 sider
...impossible. Therefore BE is not in the same straight line with CB. And in like manner it may be proved that no other can be in the same straight line with it but BD ; therefore BD is in the same straight line with CB. Therefore, if at a point, &c. QED It is important...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 sider
...which is impossible : therefore BE is not in the same straight line with BC. And in the same manner it may be demonstrated, that no other can be in the...same straight line with it but BD, which therefore id iu the same straight line with BC. Wherefore, if at a point, &c. QED PROPOSITION XV. THEOREM. If...
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Primer of geometry

Francis Cuthbertson (geometer.) - 1876 - 102 sider
...line DE an angle EDK has been made equal to the given angle BAC. QEF VERTICAL ANGLES. PROPOSITION XI. If two straight lines cut one another, the vertical (or opposite) angles shall be equal to one another. Let the two straight lines DEL, FEK cut one another. Then shall L DEF be equal to the...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876 - 784 sider
...to cut oS a part equal to the less. What are the data and what are the qucesita in this problem ? 3. If two straight lines cut one another, the vertical, or opposite, angles shall be equal. State, and work oat, the corollaries. POPIL TEACHBRS AT END OF THIRD AND FOURTH YEARS. — MALES. —...
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