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" Also, from a point above a plane there can be but one perpendicular to that plane; for, if there could be two, they would be parallel to one another [xi. 6], which is absurd. "
The Thirteen Books of Euclid's Elements - Page 297
by Euclid, Johan Ludvig Heiberg - 1908
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...the smgle CAE is equal to the angle BAE; and they are in one plane, D A which is impoiTible. Alfo, from a point above a plane there can be but one perpendicular to that plane; for if there could be two, l,. 6. ii. they would be parallel b to one another, which is abfurd. Therefore from the fame point,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 466 pages
...wherefore the angle CAE is equal to the angle BAE; and they are in one plane, which is impoftible. Alfo, from a point above a plane there can be but one perpendicular to that plane ; for if there could be two, -.4. ii. they would be parallel b to one another, which is abfurd. Therefore from the fame point, &c....
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pages
...equal to the angle BAE; and ^\"~T~ they are in one plane, which is " -A- •*•* impoffible. Alfo, from a point above a plane, there can be but one perpendicular to that plane 5 for, if there could be two, they would be parallel b to one another, which is abfurd. Therefore,...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 1795 - 400 pages
...Wherefore the angle CAE is equal to the angle BAE; and they are in one plane, which is impoffible. Alfo, from a point above a plane, there can be but one perpendicular to that.plane; for, if there could be two, they P 4 would Brok VK. W ould be parallel b to one another,...
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The elements of Euclid: viz. the first six books, with the eleventh and ...

Trigonometry - 1799 - 351 pages
...THEOR. UIMRE can be but one ftraight line perpendicular to a given plane, drawn from the lame point. For, if there could be two, they would be parallel" to one a 6. n. another ; which is abfurd. PROP. XIV. THEOR. (LANES to which the fame ftraight line is perpendicuiar,...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...angle — — 6.11b. 17. i. BAE; and they are in one plane, J-* .A. JCj which is impoflible. Alfo, from a point above a plane there can be but one perpendicular...for if there could be two, they would be parallel b to one another, which is abfurd. Therefore from the fame point, £c. Q^ED P PROP. XIV. THEOR. LANES...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1804 - 440 pages
...angle CAE is equal to the angle BAE; and they are in D A. J3 one, plane, which is impoffible. , Alfo, from a point above a plane, there can be but one perpendicular to that plane; for, if there could be two, they R would Supplement would be parallel b to one another, which ia abfurd. There. ~ b*6 f° re » horn...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...Wherefore BC the angle CAE is equal to the angle BAE; and they are in one plane, which is impossible. Also, from a point above a plane, there can be but...that plane ; for, if there could be two, they would b6.lt be parallel b to one another, which . is absurd. D \s V DA Therefore, from the same point, &c....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1810 - 518 pages
...Wherefore BC the angle CAE is equal to the angle BAE; and they are in one plane, •which is impossible. Also, from a point above a plane, there can be but one perpendicular to that plane; It 6. 11. would be parallel 1 * to one another, a 3. def. 11. for, if there could be two, they ~ which...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...reason liAE is a right angle. Where- • the angle BAE ; and they are in one plane, which is impossible. Also, from a point above a plane, there can be but...perpendicular to that plane: for, if there could be b 6.1i. two, they would be parallel b to one another, which is absurd. Therefore, from the same point,...
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