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" 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 the circle, shall be equal to the angles which are in the alternate segments of the... "
The Cambridge Examiner - Page 406
1881
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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 the circle, shall be equal...
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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. • ' N CG 1) c E Let the straight...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...be perpendicular to the line touching the circle. Cor. 2. (Eue. iii. 19.) If a straight line touches 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 shall be in that line. Cor. 3. Tangents...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...— 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...which are in the alternate segments of the circle. Let the straight line EF touch the circle A BCD in B, and from the point B let the straight line BD...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...to the same two ; and when the adjacent angles are equal, they are right angles. PROP. XXX. THEOR. If a straight line touch a circle, and from the point of contact a straight line be draion cutting the circle, the angles made by this line with the line which touches the circle, shall...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...be perpendicular to the line touching the circle. Cor. 2. (Eue. iii. 19.) If a straight line touches 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 shall be in that line. Cor. 3. Tangents...
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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 circle, shall be equal...
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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 the circle, shall be equal...
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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 tangent are equal to...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...perpendicular to DE ; FC is therefore perpendicular to DE. 74 N PROP. XIX. THEOR. If a. straight linf 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. Let the straight line...
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