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" The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle... "
Euclid's Elements of geometry, books i. ii. iii. iv - Side 88
av Euclides - 1862
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 sider
...in a circle, &c. QED PROPOSITION XVI. THEOREM. (Extracted from Dr. Simson's Edition.) The right line drawn at right angles to the diameter of a circle from the extremity of' it falls without the circle ; and no right line can be drawn between that right line and the circumference...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...a circle, Scc. QED PROPOSITION XVI. THEOREM. (Extracted from Dr. Simson's Edition.) The right line drawn at right angles to the diameter of a circle from the extremity of it falls without the circle ; and no right line can be drawn between that right line and the circumference...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...at right angles to the diameter of a cirtsDef. 3. cle from the extremity of it, touchesf the circle; and that it touches it only in one point, because, if it did * 2. 3. meet the circle in two, it would fall * within it. " Also it is evident, that there can be...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...angle less than any rectilineal angle." o. ED COR. From this it is manifest, that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it, touches t the circle ; and that it t 2 Def. 3. toncbes it only in one point, because if it did meet the circle...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...angle less than " any rectilineal angle." COR. From this it is manifest, that the straight line whick is drawn at right angles to the diameter of a circle from the extremity of it, touches the circle ; and that it touches it only in one point, because, if it did meet the circle in two, it would e 2....
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...than the more remote; and the greater is nearer to the centre than the less. XVI. The straight line drawn at right angles to the diameter of a circle, from the extremity of it, fulls without the circle ; and no straight line can be drawn between that straight line and the circumference,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 311 sider
...straight line EH less than EK. Wherefore the diameter, &c. QED PROP. XVI. THEOR. iTke straight line drawn at right angles to the diameter of a circle, from the extremity of zY, falls without the circle ; and no straight line can be drawn between that straight line and the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...the straight line AG cuts the circle. COR. 1. From this it is manifest, that the j> [ straight line which is drawn at right angles to the diameter of...circle from the extremity of it, touches the circle ; and that it touches it only in one point ; because, if it did meet the circle in two, it would fall...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...line which is drawn at right angles to the radius of a circle from the extremity of it, is a tangent ; and that it touches it only in one point, because, if it did meet the circle in two, it would fall within it (III. 2). Also, it is evident that there can be but one straight line which...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...that EH" < EK" and .'. EH < EK. PROPOSITION XVI. (Argument ad absurdum). Theorem. The straight line drawn at right angles to the diameter of a circle from the extremity of it, falls without the circle; and no straight line can be drawn between that straight line and the circumference...
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