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" ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines,... "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Seite 196
von John Keill - 1772 - 399 Seiten
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

Euclid, John Keill - 1723 - 364 Seiten
...Right Angle. Therefore the+jj.^^ other Angles BAD, ABD, are equal to one Right Angle. But the Angle ABF is alfo a Right Angle: Therefore the Angle ABF, is * equal to the Angles* jz. i. BAD, ABD; and if ABD, which is common, be taken away, then the Angle DBF remaining,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 Seiten
...that plane meets it. therefore the angle ABF is a right angle ; but the angle ABC, by the Hypothefis, is alfo a right angle ; therefore the angle ABF is...equal to the angle ABC, and they are both in the fame plane,which is impoffible. therefore the ftraight line BC is not above the plane in' which are BD and...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 464 Seiten
...plans beneath, touches it : Therefore ABF is a right angle. But the angle ABC is alfo fupp.>fed to be a right angle: Therefore the angle ABF is equal to...angle ABC; and they are both .in the fame plane; which [by q. ax.] is impoffible. Therefore the right line EC is not above the plane beneath: Therefore the...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 Seiten
...that plane meets it: Therefore the angle ABF is a right angle ; but the angle ABC, by the hypothefis, is alfo a right angle ; therefore the angle ABF is...angle ABC, and they are both in the fame plane, which is impomble : Therefore the ftraight line BC is not above the' plane in which are BD and BE: Wherefore...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 Seiten
...that plane meets it: Therefore the angle ABF is a right angle ; but the angle ABC, by the hypothefis, is alfo a right angle ; therefore the angle ABF is...angle ABC, and they are both in the fame plane, which is impoflible : Therefore the ftraight line BC rs not above the plane in which are BD and BE : "Wherefore...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1781 - 466 Seiten
...that plane meets it. therefore the angle ABF is a right angle ; but the angle ABC, by the Hypothefis, is alfo a right angle ; therefore the angle ABF is equal to the angle A11C, and they are both in the fame plane, which is impoftible. therefore the ftraight line BC is not...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 400 Seiten
...that plane meets it : therefore the angle ABF is a right angle ; but the angle ABC, by the hypothefis, is alfo a right angle ; therefore the angle ABF is...angle ABC, and they are both in the fame plane, which is impofuble : — therefore the ftraight line BC is not above the plane in which are BD and BE : Wherefore...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 Seiten
...plane, meets it ; therefore the angle ABF is a right angle : but the angle ABC, by the hypothefis, is alfo a right angle ; therefore the angle ABF is...angle ABC, and they are both in the fame plane ; which is impoffible : Therefore the ftraight line BC is not above the plane in which are a 3. n. b 4. it....
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...that plane meets it. therefore the angle ABF is a right angle ; but the angle ABC, by the Hypothefis, is alfo a right ,angle; therefore the angle ABF is...angle ABC, and they are both in the fame plane, which is impoflibfe. therefore the ftraight line BC is not above the plane in which are BD and BE. wherefore...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 Seiten
...in that plane ; therefore the angle ABF is a right angle. But, by the Viypothesis, the angle ABC is a right angle ; therefore the angle ABF is equal to the angle ABC ; and they are both in -the same Suppl. plane, which is impossible. Therefore the straight line BC wv^/ is not above the plane...
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