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" If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments. "
Theoretical Geometry: Based on the Various Geometry Books by Godfrey and Siddons - Page xiv
by Arthur Warry Siddons, Reginald Thomas Hughes - 1926 - 173 pages
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The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - Geometry - 1776 - 326 pages
...and from the point of contact a right •*• line be drawn to the circle, the angles that right line makes with the tangent are equal to the angles in the alternate feements of the circle. Let the right line EF touch the circle ABCD in the point B; from any point...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...one angle of a triangle be equal to the other two angles, it is a right angle. PROP. XXXII. THEOR. IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles -made by this line with the line which touches...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 554 pages
...FC is perpendicular to DE. Therefore, if a straight line, &c. QED C GE a 18. 3. ,' PROP. XIX. THEOR. IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching lirie, the centre of the circle shall be in...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 582 pages
...demonstration, that these three perpendiculars BE, GF, and CD intersect each other in the same point AQED 249. If a straight line touch a circle, and from the point of contact two chords be drawn, and if from the extremity of one of them, a straight line be drawn parallel to...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...DE ; FC is therefore perpendicular to DE. Therefore, if a straight line, &c. Q, ED PROP. XIX. THEOR. If a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle, is in that line....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...the same two ; and when the adjacent angles are equal, they are f right angles. PROP. XXXII. THEOR. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...to DE; therefore FC is perp. to DE. Therefore, if a straight line &c. QED PROPOSITION XIX. THEOREM. If a straight line touch a circle, and from the point of contact a straight line be drawn perpendicular to the tangent, the centre of the circle is in that line. •...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...it is equal to the same two ; and when the adjacent angles are equal, they are right angles. XXXI. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line which touches...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...less than a right angle ; wherefore the other ADC is greater than a right angle. PROP. XXIII. THEOR. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...semicircle is acute, and an angle in a segment less than a semicircle is obtuse. PROP. XXXII. THEOR. IF a straight line touch a circle, and from the point of contact a straight line be drawn dividing the circle into two segments ; the angles made by this line with the...
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